JPRS ID: 10390 TRANSLATION OCEAN RESEARCH ON HYDROPHYSICAL FIELD VARIABILITY ED. BY R.V. OZMIDOV

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JPRS L/ 103JQ
16 March 1982
1'ranslation
OCEAN RESEARCH ON ~
HYDROPHYSICAL FIELD VRRIAB~LITY
Ed. by
R.V. Ozmidov
Ft~~i~~IGN ~BROADC~?ST INF~R~VIATION SERVICE
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JPRS L/10390
16 March 1982
- OCEAN RESEARCH ON NYDROPHYSICAL
- FI~LD VARIABILITY
Moscow ISSLE�~OVANIYE I2NiENCHIVOSTI GIDROFIZICHESKIKH POLEY ~
V OKEANE in Russian 1974 pp 2-31, 42-65, 83-98, 155-162,
~ 208-211
- [Excerpts from "Ocean Research on Hydrophysical Field
Variability," edited by R. V. Ozmidov, doctor of physica?
and mathematical sci ences, Izdatel'stvo "Nauka", 211 pages,
- n~amber of copies unknown]
Annotation 1
Investigation of Variabi~ity of Hydrophysical ~`ields in
Oceanic Polygon
(R. V. Ozmidov, e t al.)......~ 2
Spectral Chardcteristics of Condu~tivity Fluctuation Field
in Ocean
(V. S. Belyayev, e t al.) 35
Statistical Eval~~ations of Para~ters of Small-Scale Turbulence
(V. D. Po zdynin) 44
Experience in Investigating Microstructure of Oceanic Con-
ductivity Field by Sounding Method
(V. P. Vorob'yev, e t al.) 58
Inertial Interval in Turbulence Spectra iri Stratified Fluid
(Heisenberg-Irbnin Model)
- (A. Yu. Benilov, I. D. Lozovatskiy). 64
Internal Gravitational Waves in Ocean
(Yu. A. Ivanov, e t al.).......... 75
-a- jI - USSR - E FOUO]
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Construction o~ Recoxd~a,i,g Comple~ for znvesti~ating k'~ne .Ocean
Structure ~
(V. P. Vorob'yev, L. G. ~'alevich) 85
Abstracts of Papers in `ISSLEDOVANIYE IZMEN(~IIyQ3TI
GIDROFIZIQiESRTKH POLEY V OKEANE' 95
1
~ - b -
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~ ,
[Text] .
- P.NN~TAT I ON
T'his collection of articles is about the results of experimental and
tl~eoret ical invest igations of the variability of hydrophys ical f ields in
the ocean. Particular attent ion is devoted to the fine structure of fields
and microscale oceanic turbulence, experimental data on which were obtained
on specialized expeditions of the Institute of Oceanology imeni P.P.
Shirshov using newly created t owed and sounding measurement devices. The
articles give the results of large-scale computations oi the statistical
characteristics of velocity and conductivity microfluctuations in sea
water in different regions of the world ocean and also data on the stat-
- isti~al characteristics and parameters of macroscale variability of fields.
A number of arti;e~l~sgive the theoretical and experimental results of inves-
tigations of interna'1 waves and the processes of diffusion of impuritiE~s
in the ocean. Possible types of spectra of fluctuations of velocity, t:emr~- ~
- erature and Reynolds stress in ~he stratified ocean are theoretically a~nal-�
yzed. Also examined are some methoc~ologieal problems involved in the c:oll-
ection and procpssing of data on variability of hydrophysical fields in the
ocean. Information is also gi.vPn on new sensors and measurement systems
f or investigating fine Gtructure in the ocean.
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INVESTIGATION OF VARIABILITY OF HYDROPHYSICAL FIELDS IN OCEANIC POLYGON
Moscow ISSLEDOVANIYE IZMENCHIVOSTI GIDROFIZICFIESKIKH POLEY V OKEANE in Russian 1974
pp 3-31
[Article by R. V. Ozmidov, V. S. Belyayev, M. M. Lyubimtsev and V. T. Paka from mon-
ograph "Ocean Research on Hydrophysical Field V~riability," edited
by R. V. Ozmidov, doctor of physical and ma.thematical. sciences, Izdatel'stvo "Nauka,"
211 pages, number uf copies printed unknown] ~
[Text] Spatial-temporal var~ability is a distinguishing characteristic of hydro-
physical fields in the ocean. The scales of this variability have a wide range.
Due to the turbulent character of movement of ocean waters fluctuations can exist
in it whose minimum dimensions are determined by the effect of molecular forces.
_ The dimensions I,min of such fluctuations in the velocity field can be evaluated
using the formula for locally isotropic turbulence Lmin - ?~E~ Where'V is the
kinematic coeff ic ient of molecular viscosity of sea water, being about 0.01 cm2/
sec; � is the rate of dissipation of turbulent energy in the ocean. The E para-
meter is extremely variable, but with its rea.sonable evaluations in the range
- 10'6-10~ cm2/ssc3 for I,min we obtain values ~.3 mm-1 cm. The minimum time scale
Tmi~ of the turbulent fluctuations of the velocity field can be evaluated using
another formula for locally isotropic turbulence T~in = v/E , which with these
same E evaluations gives the order of magnitude Tmin of 0.1-100 sec. The maximum
spatial scale L~X of variability of hydrophysical fields in Che ocean is evident~-
ly governed by the geometric dimensions of the ocean basins, that is, it can at-
_ tain several thousand kilometers. However, the upper boundary T~X of temporal
variability in general is diff icult to indicate, since together with seasonal
~ variations of the fields there are also year-to-yea.r fluctuations and climatic
variabi].ity. ,
In the experimental investigation of variability of hydrophysical f ields it is
first of all necessary to ~stablish the 1.imits uf the scales of variability which
must be inv~stigated. The fact is that the total duration of the necessary observ-
ations, the position of the observation points and also the characteristics of the
used instruments are related to these limits. In order to determine the statis-
tical character-'-'~ics of field variability the duration of the measurements must be
approximately an order of magnitude greater than the maximum investigated time scale
of variability and the extent of the measurement runs (or the distances between
the extreme points of placement of the instruments) must also exceed by an order
of ma.gnitude the maximimm investigated spatial field inhomogeneities. The~discrete-
ness of the observations in this case shauld be at least less than half the period
(or spatial scale) of the minim~mm investigated field variations and the time con-
stant of the instrument ~and the entire measurement-registry channel) is about
. 2
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1/10 of this period. i~ue to these requirements it follows very clearly that it is
virtually impossible to investigate any significant interval of scales of varia-
bility of this field in tre ocean with instruments of a single t~pe. In actua.lity,
low-inertia instruments (such as thermoanemometers) are usually not capable of op-
erating continuotisly in the ocean for a long time; more approximate instruments
(of the hydrological current meters type) ha.ve large time constants and large meas-
urement discreteness intervals. Accordingly, for this type of investigations it is
necessary to have, in general, an entire "arsenal" of instruments with overlapping
frequency characterisr.ics. It is desirable that the researcher have instruments
capable oF registering the most small-scale field fluctuations. This is important
because without information on such fluctua~ions the data from some instruments
(such as BPV-2 current meters), operating with a great discreteness, can give erron-
eous ideas concerning the spectral structure of the process due to discretization
noise. If there is also information concerning ~microscale fluctuations as well, such
errors can be avoided [1].
If the macroscale limit of the investigated scales of fluctuations is determined, it
is desirable that the subsequent observations be made in the following way. In tl:~
ocean one or mor2 regions (polygons) with typical macroscale cha.racteristics are
selected. Among these characteristics it is necessary to include the mean vertical
profiles of density (temperature and salinity) and current velocity, the character-
istic horizontal current velocities, the direction of the heat flow through the
- ocean surface (heating, cooling), mean reg~.me of wind and waves in the polygon. A
number of such polygons with different sets of typical characteristics to a certain
degree can also ensure investigation of the spatial variability of hydrophysical
fields at the scale of the entire ocean. In actuality, the discreteness of the
points of such observations can attain many tens or even hundreds of kilometers and
therefore in principle it is possible to "cover" the entire ocean with this type of
pulygons. However, for an investigation of the long-period temporal variability of
the fields it is necessary to carry out prolonged observations in a polygon with a
temporal discreteness which is consistent with the investigated processes. For ex-
ample, in an investigation of the statistical characteristics of variability up
to an annual period observations must be carried out in the polygon for about 10
years, but their discreteness can be ~everal days. The greatest attained duration
of continuous observations in such a sort of polygon at the present time is equal to
severai months [2, 3].
The extent of the polygon can be different, but the desire to "overlap" all the spa--
tial scales of variabilj.ty, beginning with Lmin~ leads to a limitation of I.~x to
several tens or a few kilometers. In the ocean area of the polygon there should be
buoy stations with approximate instruments operating for the entire period of ob-
servations in the polygon. However, the duration of operation of law-inertia instru-
ments can be c~nsiderably less, but in this case there should be multiple repetition
of such measu_ements with different values of macroscale factors. In each individual
measurement Zow-inertia instruments cannot operate for a long time, for example,
about 10 minutes, but the number of such mea.surements must be sufficiently great for
a comparison of the characteristics of microscale processes with the meso- and
macroscale factors varying in time and in space.
Investigation of this variability of fields in polygons with the use of low-inertia
instruments was initiated in 1969 [4]. Thereafter several specialized runs were made
by scientific research ships with work in polygons. The tracks ~f these vessels and
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the location of the investigated polygons are ~iven in [5]. In this article as an
_ e~mple we will make a detailed examination of the complex of ineasurements and
give their results in one of the polygons of the seventh voyage of the scientific
research ship "Dmitriy Mendeleyev" (1972).
The polygon was situated in the region o~ the sources of the Somali Current to the
east of Socotra Island (Fig. 1). Work in the polygon was initi:ated from a hydrolog-
ical section whose data were routinely processed on a shipboard electronic computer
by the dynamic method. Sections of the fields of temperature, salinity and geo-
strophic current velocities (Figures 2-4) made it possible to determine the macro-
scale hydrological structure of the w~rk region, define the contours of the branch
of the Somali Current and thereby afforded a po~;ibility fdr validly selecting the
place for setting out a buoy station and carrying out measurements of microscale
variability with low-inertia instruments. A buoy station with BPV-�2 cL!rrent meters
and photothermographs was situated in the current and served as a reference point
for other measurements*.
The macroscale thermal structure of waters in the polygon, according to data for
hydrological stations 488-494 (Fig. 1), is shown in the sections in Fig. 2. These
same data were also used in constructing the section of distribution of water sal-
inity (Fig. 3). It can be seen from the temperature section that in the upper 400-
m layer the depth of the isotherms decreases somewhat in a southeastern direction,
which indicates an upwelling of waters ln this part of the section. The advection
of water masses fr.om adjacent regions of the ocean can be seen from the position-
ing of the isohalines in the section in Fig. 3. The penetration of more saline
and warmer waters of Red Sea origin determines the vertical structure of the upper
layer of water in the northerri part of the section; the existence of a salinity max-
imum at a depth of about 100 m is an indication that the Soma.li Current duri~ig win-
ter carries waters forming in the Red Sea and Arabia.n Sea regions.
Thus, the development and maintenance of the vertical water density gradients in
the polygon region exerts an influence on the horizontal transport of water masses
which acquired their principal physical characteristics prior to arrival in the
region of the Somali Current.
The hydrological structure of the waters in the neighborhood of station 490 was
_ characterized by a relatively poorly expressed temperature jump layer (Fig. 5,
Fig. 6). The mean ~emperature gradient in the upper 100-m layer is 0.02�/m and
increases in the ~ump layer to 0.07�/m, whereas in equatorial polygons, occupied or~
this same voyage in the Indian Ocean, the temperature gradient attained 0.25�/m.
Accordingly, density stratification in the polygon ensured a small vertical stabil-
ity of the wjter mass in the upper layer of the ocean, including the temperature
jump layer., which could facilitate the development of microscale turbulence in the
upper la~rer of the ocean.
Figure 4 ~shows a vertical section of the current field in the polygon, constructed
- on the basis of data from computations by the dynamic method. The figure shows
~
The hydrological work in the polygon was carried out under the direction of V. G.
Neyman.
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that in the region of hydrological stations 490 and 491 there is a clearly defin-
e3 flow with a southwesterly current component whose maximum was situated in the
upper 100-m water layer. To the southeast of station 490 and ta the northwest of
station 491 the current velocity changes sign, attaining values greater than 40
and 50 cm/sec. In the deep layers at the left edge of the section there was again
a flow of southwesterly direction with a current velocity up to 20 cm/sec.
SZ' S.l' SU' SS' S6' 57~~,
~:axom a
~ Soco ra � V9y
v,~J ~p o
~ ~ ~9?
~w9/
V90
_ /!o
I 4B9
4AB
JO'
�OS'
_ � 1 ~ 490
0 2
09
n 4
- ~ S ~a a9s �00'
06 ~
x~ ,
' !0'SS' .
SS'.IS' SS'40' SJ'yS' SS'SO'
Fig. 1. Diagram of polygon for measuring oceanic turbulenee and background condi-
- tions with indication of numbers of hydrological stations. l) hydrological series,
bathythermogram, sounding with AIST instrument and acoustic probe to ascertain cur-
- rent velocity; 2) sounding with AIST instrument and acoustic probe to ascertain
current velocity; 3) multiple sounding with AIST; 4) anchored buoy station with
- curr.ent meters and photothermographs; 5) radio temperature buoy; 6) measurement
with "Sigma" probe; 7) bathythermogram. The solid. line with the arrows indicates
*_he towing of turbulence meters. The rectangle enclosed ir. a dashed line is shown
at a larger scale in the lower part of the figure.
As is well known, computations of currents by the dynamic mPthod give only the
pattern of the current field averaged over a great time interval, dependent at the
same time on the choice of the referen~e (zero) surface. Accordingly, in the re-
gion of microscale measurements a buoy station with BPV current meters was set out;
the current meters were at the horizons 15, 25, 50, 75, 100, 150, 200, 400, 600,
_ 1.,000 and 1,500 m. Figure 7 shows the vertical prof iles of current components aver-
aged for the entire period (63 hours) along the parallel (u) and meridian (v) and
also the distribution of the mean current vectors with depth. The fi~ure shows
that in tl-� layer from the ocean surface to a depth of 1,500 m during the period
of observations there were two almost oppositely directed flowsr which agrees with
dat..a from the dynamic section. The boundary between the flows was approximately at a
J dej:~h of 400 m, bnt the transition zone from one flow to another is already trac-
ed from 20 0 m. In the upper layer the velocity vectors had a northwesterly direc-
tion with a m~~dulus 15-20 cm/sec, whe~eas in the lower layer the current was close
to easterly with velocities N 15 cm/sec (whic]-. deviates from the dynamic section
data with respect to both modulus and directi.an}. It can be seen from the distribu-
tion of the current vectors that in the Iayer 50-I0~ m the vertical current
5
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gradients developed due to a simultaneous change of both current direction and
velocity with depth; in the layer 100-200 m the vertieal curre~.lt gradients developed
primarily exclusively due to a cha.nge in flow direction. Large gradients were ob-
- served in the layer from 200 to 600 m, where there is a marked change in both di-
rection and modulus of current velocity. In the wat~r layer deeper than 600 m the
mean vertical current gradients become insignif icant. The sharpest change in the
meridional velocity component was observed, as indicated in the f igure, in the
uppermost layers of the ocean and the ma.ximum v value was registered at the 200-m
- horizon. The latitudinal velocity component changes relatively smoothly from 18
cm/sec at the upper horizon to 15 cm/sec at the 600-m horizon, after which it re-
mains virtuaI.ly constant to the lowest observation horizon.
Q~~l94 l~9~7 U91 ~9! u90 ~B9 UBB
~00 ' -2s.s
� ~--�----r--- _
~ZO
Z00 ~s -
~/4
~700 13 ~
- y00 ' �
SOO '
10
/000 _
_
lS00 6
' ~ ~
/B00 � ~
M~9y ~9J u91 y9/ U90 ~8.7 4dB
0
16 16
� I / I
~ 1
SO /
I
~ i
~zssl ~ ~ ~
/00 - ~ ~ s
I
~ ~ ~ i
~ I
i
;so ~
10
i
i7 iB /7
ZGO
Fig. 2. Field of isotherms according to hydrological series (a) and bathythermo-
grams (b) in hydrological section. The numbers of the stations are indicated along
the horizontal scales. The temperature values are given in
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_ - . _ . . _ _ .
, ~.9~ v.yJ ~i.~'2 y9! U.9/I U9.9 Ud6
M
~?6?n :
!UU ase; ~
.
Z00 ~s6
. . .
J00 ' ~,~,~F;,~
y00 '.~s 6e � '
. �
. .It6
SCO - ~,rs Eo �
~S 6 �
- _ _ - - .
~ovo J3 ~ -
, isoo - - - v .;.5
0 -1
IBUO '
Fig. 3. Isolines of salinity (in �/oo) based on measurements in hydrological sec-
tion. The numbers of the stations are indicated along the horizontal scale.
M ~9~ ~/99 ~/92 y9J U90 ~ t'99 //BB
0 ,
!00 Io f =~a : , ~
~ � 'v � 10
100
~700 ~~ru
U00 d - - y
,s00
-io?:' ~ 'r: '
JO
-10;� ,f
1000 ' ~ ,a .
a
i JO IO
lSOU ~
Fig. 4. Current velocity field computed by dynamic method (the positive values cor-
respond to the current direction "in the figure").
_ Some idea conc~rning the macroscale variability of the velocity field in the poly-
gon can be obtained from Fig. 8, which showa the curves of the half-sum of spec-
tral densities of fluctuations of the horizontal velocity components on the basis
of data from ctirrent meters at the seven upper horizons at the buoy station. Time
series of the values of velocity components with a discreteness of 5 minutes were
subjected to statistical processing. The spectral functions were scaled into spa-
tial functions using the 1�frozen-in" hypothesis with use of the values of inean
current velocities at each of the observation hori2ons. Due to the short duration
of the series used for the computations the interval of wave numbers of the con-
structed spectral functions E(k) extends approximately only 1 1/2 orders of mag-
nitude, whereas the E(k) values in this interval change approximately by four or-
ders of magnitude. Th~ spectral functions for all seven horizons have virtually
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an identical le~El and in logarithm~c coordinates are close ~to straight lines
with a mean value of the tangent of slope of about 2.7. Such a rapid dropoff of
the E(kl values with an increaQe in k is evidently evidence of a predominance
iri the considered range of wave numbers of well-develope~ two-d.imensional turbu-
lence, for whose spectral deasity the "-3 iaw" can be satisfied [6, 7]. It is also
not precluded that in this k range a~ important role in the velocity field can be
- played by wave movements of different origin.
z1,00 ^0 2J,o0~t,ycn.~d, arbitrary units
.~5,1 ~J S 36, 0 S, % ~
i ~ ~C ~ T ` r
~ O ? IO ~J ~
0 / ~
1 Ut S ~ I
l00 0 _ ~0' 1S'
_ ~ . I
- 100 SO ' I
~
J00 I
y00
i ~so -
600 ,
?00
~ B00 �
r s ~t
l000 ~
l100
,
Fig. 5. Vertical profiles of temperature Fig. 6. Bathythermogram at station 490.
T, salinity S and conventional density
O't according to measurements at station
4 90.
- Due to the great spatial discreteness of observations of current velpcities made us-
ing current meters information on the vertical structure of the flow (including
on its vertical gradients) is quite approximate. A direct comparison of the data
from individual measurements of microscale turbulent fluctuations (with scales
from I~in to 1-2 m) with such macroscale characteristics evidently does not make
it possible to discover any relationships between them [8]. The characteristics
of microscale fluctuations must evidently be directly related to the finer (local)
parameters of the oceanic velocity field. It was possible to obtain this sort of
information on the vertical profiles of current direction and current velocity
modulus in the polygon using a new acoustic sounding instrument developed at the
Pacif ic Ocean Division of the Institute of Oceanology imeni P. P. Shirshov, USSR
Academy of Sciences (now the Pacif ic Ocean Oceanological Institute, Far Eastern
- Center, USSR Academy of Sciences). The instrument registers the Doppler frequency
shift of acoustic oscillations of a signal scattered on density inhomogeneities
moving with the flow. The volume of fluid in which the sc~ttering of ultrasound
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occurs is about 1 cm3 and is quite distant from the instrument housing. The probe
does not require the calibrar_ion ma.ndatory for current meters and thermoanemo-
meters. The error in velocity mea.surements was about 1 cm/sec and ~s determined
far the most part by the error in frequency me3surement. The probe also has a
meter for regi~tering orientation relative to the magnetic meridian based or_ meas-
urement of the signal phase induced in a wire loop during its rotation in the
earth's magnetic field. Current direction is measured with an accuracy to 3�.
Figure 9 shows, e~t,amples of the vertical profiles of current vel~city modulus and
direction obtained using the new instrument. The measureme:~ts were made from a
drifting ship, and as a result, the values for current velocity and direction are
relative, at the same time that their gradients must coincide with the gradients
of true current velocities in the ocean (during the time of sounding the ship's
drift velocity must be considered constant). The curves show how more complex the
vertical structure of the field of currents is in comparison with the pattern ob-
tained using data from current meter observations at buoy stations. Using sound-
ing data it is easy to see the f ine vertical stratification of the current. The
adjacent layers of fl~aid. with a thickness of several meters move at different
velocities differing by 5 and sometimes by 10 cm/sec. The direction of movement
of the fluid in such layers can also differ appreciably. For example, the layers
at depths of 175 and 185 m moved at an angle of 100� to one another. The velocity
gradients, computed on the basis of probe data, are considerably greater than the
values obtained using current meter profiles in Fig. 7. Whereas in this figure the
gradients were found to be no more than 0.1-0.3 cm/sec per meter, according to
sounding data in individual cases they can attain several centimeters per second
per meter. It is clear that such Iocal characteristics of the velocity field must
exert a definite influence on the microscale fluctuations of hydrophysical fields
in the ocean.
Information on the macroscale vari~bility of the temperature field in the polygon
was obtained from phototiiernographs installed at a buoy station at the hori-
zons 100, 150, 200 and ~a00 m. The discreteness of readings of temperature by the
photothermographs was 5 minutes and the duration of observations was 63 hours. The .
resulting series of temperature values were used in computing the spectral density
functions shown in Fig. 10. For the three upper observation horizons the spectral
density functions E(k) for temperature fluctuations were virtually identical, but
at a depth of 400 m the E(k) values were considerably less. The E(k) functions,
computed using data from the photothermographs at the horizons 100, 150 and 200
m, fit well with the sectors of the spectral functions in Fig. 14 situated in the
more high-frequency region (radio buoy data). Comparisons of ~ig. 10 and Fig. 14
also make it possible to explain some decrease in the slope of the spectral curves
in Fig. 10 with an increase in k. It is clearly associated with discretization
noise, since in the interval of wave numbers greater than 10-3 the spectral den-
sity functlon, although it decrea.ses rapidly, is neverttieless different from
zero. The tangent of the angles of slope of the spectral density functions in the
- zone o� wave numbers where the influence of discretization noise is not expressed
is close to ?.5.
More detailed information on the vertical structure of the f ields of temperature,
~ salinity (conductivity) and density in the polygon were obtained using the AIST
= sounding instrument. This instrument makes it possible to determine the vertical
9
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- profiles of temperai:ure and salinity to a depth of 1,000 m and with an accuracy
to 0.02-U.03�C and 0.03-0.04�/0o respectively. Such an accuracy is provided by
a carefully calibrated thertioresistor and induction-t~pe conductometer. The ver-
tical resolution of the instrument for ordinary sounding rates is about 1 m. Ana-
- log signals from the sensors are coded and registered on a punched tape and at
the same time on an automatic recorder. After processing of the punched tape on
an electronic computer the profiles of temperature, conductivity, salinity and
density are fed out and the latter two parameters are determined by computations.
Examples of the vertical profiles of temperature, salinity and density obtained
using the AIST instrument in the polygon are shown in Fig. 11. It can be seen eas-
ily from the figure how much more complex these profiles are with the high resolu-
, tion of the instrinnent in comparison with the "smooth" curves in Fig. 5, construct-
ed using the infrequent points of the bathometric series*. The AIST data reveal
individual layers with an approximately constant temperature which are separated
by interlayers of water with grea.t t gradients. The vertical dimensions of such
"steps" are not constant; the temperature drops from layer to layer are also var-
. iable. It is entirely obvious that such a f ine structure of the oceanological fields
can exert a definite influence on the still f iner field characteristics. For ex-
ample, microscale turbulence (with characteristic dimensions from I,min to 1 m) must
"react" very sensitively to the stepped field structure. In actuality, the density
gradient is one of the most importan't parameters for turbulence; it determines the
expenditure of turbulent energy on work against Archimedes forces (in the case of
a stable stratification) and thereby the form of the spectrum and other statistical
characteristics of turbulence. A confirmation of this will be presented below in an
analysis of the data obtained using low-inertia instruments. However, an attempt
to relate the characteristics of microscale turbulence directly to the mean hydro-
logical conditions in the polygon did not lead to an unambiguous answer [8]. This
example graphically illustrates the thought expressed earlier that it is undesir-
able to have "breaks" in the spatial-temporal scale in an expertmental investiga-
tion of hydrophysical fields in the ocean. In the case of such r~ break it becomes
difficult, and frequently impossible, to establish cause-and-effect relationships
between the studied processes.
The mesoscale vertical struc~ure of the fields registered with the A~ST probe is
extremely variable in both time and in horizontal directions. Such a variat~ility
can be investigated by means of multiple soundings carried out from an anchored or
drifting ship. It is true that it is extremely difficult to determine what causes
the observed variability nonuniformity of the vertical structure of the field
in a horizontal direction or its nonstationary character. In actuality, the drift-
ing ship moves relative to the water mass under the influence of the wind, but in
the case of an anchored vessel the fluid is transported relative to it by the cur-
rent. Accordingly, each subsequent sounding in general brings information concern-
ing the vertical structure of the f ield at different moments and at different
- points in the water mass. In order to investigate the spatial variability of struc-
ture it is necessary ta carry out synchronous soundings at a number of points in
the ocean (for exanple, from several ships at the same time).
* We note that the zigzaging nature of the density profile in Fig. 11 is related
to errors in computing (J't on the basis of ineasurements of the temperature and
conductivity values.
~ 10
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. _ - El~rl~x),cM3c~,r-2
iso 2oa
so~sroo 1,,~ ~C 3
's ~ ~ ~~Z ~ CAt �seC-2
2S v00
s
~ . ~ ' /Ju0 !
O /0 ZOcM/cex o00 ' ~
-ZO -/0 O /O ZO u u cM%ct~r 6 i ~
;
~ cm/sec � ~
. ,
,
, ~
. ~ .
. . y~ .
.
~
SGS � ' ~ '
:
.
I ~
. 1000 .
' ~
~
. ~j , ,
~ ~
_ /S00 1 } I ~
,ti
~ , ~ ~ ~i '
~ ~ ~
.,i ~
Fig. 7. Diagram of current velocity ~
vectors and depth distribution of zonal }~~r' ,
~
u and meridional v components according , i
to data from anchored buo y station. The 1~ ~~~1~'~ 'V ~
numbers alongside the vectors denote ~ +~R 1
i
depths in m. I~
i
J V~ I~' I f'~ ~l
Fig. 8. Spectral densities of fluctua- v ii ~
tions of current velocity according to ~
~ !
data from aikchored buoy station at hor- ~
izons 15 (1), 25 (2), 50 (3), 75 (4), '
100 (5), 150 (6) and 200 m (7). -y . ~.,c,y-i '
Figure 12 shows an example of the processing of six successive soundings (with in-
tervals of about 1 hour) by the AIST instrument in the polygon. The thick curve
represents the averaged temperature profile for all soundings. The profile became
considerably "smoother," but there are individual "steps," interlayers with a vir-
tually constant temperature, zones of increased gradients and a region of tempera-
ture inversions. The extreme curves in the figure show the value of the stRndard
deviations of temperature values at the horizon according to data from individual
soundings from its mean value. These deviations do not exceed fractions of a de-
gree in the upper 85-m layer and then increase to 1.5-1.6�C in layers with large
temperature gradients. Such a temperature variability at this horizon can be caus-
ed by both the spatial-temporal variations of inesostructure of the temperature
field and by c~rtical movements of this entire structure under the influence of
internal waves.
Interesting information on the characteristics and variabi:iity of temperature
field mesostructure in the polygon were obtained using a radio buoy. The instru-
ment temperature sensors were situa.ted in the layer of greatest temperature gradi-
ents at the horizons 103, 115, 126, 138, 150, 170, 212 and 232 m. The discreteness
11
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of interrogatic~z of the sensors was 12 sec, The information received by ship via
the radio channel was registered with digital magnetic record~rs or on punched
tapes9 after which it could be introduced into an electronic computer. The program
for processing on an electronic computer included one-point statistical analysis,
c~nstr.~.iction of the field of isotherms and the field of spectral lensity of tem-
perature fluctuations. Figure 13 shows an example of construction of the field
(section) of isotherms on the basis of data for a 3.5-hour radi~ buoy operating in-
terval. The total number of temperature readings used i~ constructing a section,
as is easily computed, was ap~roximately 8,000. From the macroscale characteris-
tics of the field of isotherms in Fig. 13 it is possible to note a general tenden-
cy to a deepening of the isotherms during the observatio~ period. Such a phenomenon
can be caused, for example, by tidal internal waves of a semidiurnal or diurnal
period. The figure also shows more high-frequency temperature fluctuations with
periods of about 5-10 minutes which can be interpreted as internal gravitational
waves. It is interesting to note that such internal waves did not exist during
_ the entire period of obse.rvations, but only during definite time intervals, disap-
pearing and arising anew. They sometimes occupied virtually the entire considered
layer of the ocean and sometimes were observed only at a few horizons.
a V~CM~CCR'' ~ 1 Ol
- V cro sec-1 y~M zo va iza /60 ~ioo zaa ~ degrees
0
SO
/00 �
- /SO
Z110 - .
. ,
~ ZSO
Fig. 9. Vertical profiles of intensity (a) and direction (b) of current veloci~v
_ according to data from acoustic probe. ,
From the statistical characteristics computed on the basis of radio buoy data
we will cite two families of spectral density curves E(k) for temperature fluctu-
ations at each of the eight observation horizons (Fig. 14). In computing the first
family of curves we used a four-hour record with the number of temperature read-
ings at each horizon equal to 1,200, and for computing the second family a 3.5-
hour record (of 1,032 terms), following the first record approximately after a
1.5-hour interval. The figuYes in the diagrams denote the observation horizons in
the sequence of an increase in depth. The spectral densities were computed by the
Tukey method (_Fourier transform of correlation functions) with a maximum shift
12
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in computing tre corrzlation functions equal to Q.1 the total length of each ser-
- ies and when using a high-frequency cosine f ilter with a parameter equal to 0.2
- the length of the series. On the x-axis in Fig. 14 �we have plotted the values of
the wave numbers k, scaled from the values of the frequencies f of oscillations
using the "frozen-in" hypothesis with a mea.n velocity of the transport current V n
10 cm/sec.
E(,r), Z~adZ.~N degree2 � cm
2
/0 ~ .
~ '
. ~
1'� � .
- . JO ~ ~1�.
1 �
\
~i
1-
~ �
1''
~p 2 ~`i
,
~ .
vi ~ ~ .
~
1~ ~ ~ r,
_ ~
y ~
~
/0 ~ '
~
~ ~
~
~ ?
~ i
~
~
~
. 1
!0 0 ~ ~
~ ~ 1
1 ~ I 1
1~ t~
. ~
I `
u
I
I~
~p-/ i
�I
`
,
_ r~
/O ~
i~ K~ ~K�1
_ Fig. 10. Spectral densities of temperature fluctuations according to data from
photothermographs at }iorizons 1U0~(1), 150 (2), Z00 (3) and 400 m(4).
The principal characteristic of the spectral density curves in Fig. 14 is their
rapid dropoff with k values greater than 10-3 cm 1. The tangent of the slope of
curves in this.region, that is, the exponent in the power-law approximation of the
curves, exceeds -3, grad~~ally decreasing toward the right end of t1.ie graph. The
decrease in the slope of these curves in the most microscale part of the spectrum
13
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can be influenced by discretization noise because the energy of the higher-fre-
quency temperature fluctuations, as we will see below, is quite high. The maxima
on the curves in the region k= 10'3 cm-1 are evidently caused by gravitational
internal waves af the above-mentioned period. However, as can be seen from the spec~
tral density curves, in the polygon during the observation period there were not
_ only these waves, but an entire spectrum of higher-frequency temperature fluctua-
tions. The ener~y gF~ri-i~3eifluctuations does not regularly ~hange wi.th depth; the
curves for different:horizons are intertwined with one another. A comparison
. ' 2~7 S ZU, 0 L' S ZS, 0 1S, S Z6, 0 o't
V
~ ~IS S~S, 7 9S, 9 J61 ~16,J J6, S S, '/oo
~6, 0 1B, 0 10. 0 ZZ 0 1!~ O T' 6
~1 N
SO
. 1 Z ' ~
~ /00
~ /~f0
F00 ~ .
~so
Fig. 11. Vertical profiles of conventional density (1), salinity (2) and tempera-
ture (3) according to AIST data.
/5 IB ' 20 22 2u 1G T� G
- N ' '
~M
SO
/00 -
~ ,
/SO .
I
100 ~
1S0 ,
Fig. 12. Averaged vertical temperature profile (thick curve) according to data from
multiple sounding with AIST instrument. The thin curves represent the mean square
temperature scatter of individual soundings from mean value.
14
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of the families of curves obtained for different parts of the record reveals some
nonstationary nature of the process. In actuality, in Fig. 14,b the spectral curves
on the average lie so~ewhat higher than in Fig. 14,a. Indi~~idual curves also do not
maintain their shape and their relative position: they are somewhat modif ied and
are displaced relative to one another.
- M � .
_ .'00 14
ZJ'
12
rv0 2/
~--'1~.~20
~ !9
iB0 " ~ ~~~-..-lB
' ~ Iv-~ /7 :
,1 p 16
o ~ Z t~ ya~ hours
Fig. 13. Field of isotherms (in �C) using data from radio temperature buoy.
The distribution of the energy of temperature fluctuations by wave numbers and by
depth h is graphically illustrated in Fig. 15. The isolines of spec,tral density
are given in E(f) units; for scaling them into E(k) units it is necessary that the
figures indicated on the isolines be multiplied by V/2 n= 1.59. The figure shows
that in the h, k sections of spectral energy density for temperature fluctuations
there are individual maxima, where it is necessary to anticipate the generation of
energy and from whence it can be propagated into the h, k region with small E(k)
values. In our case the principal zone of energy concentration is the horizon 140
m and a wave number close to 10'3 cm'1. It is interesting to note that at this
same depth there is a density gradient maximum. The position and intensity of the
~ energy density maximum vary very litt'le from one period to the next (Fig. 15),
whereas all the remaining f ield of E(k) isolines experiences appreciable varia-
tions. Thus, during the second period of observations there is a secondary ma.xi-
mum with h, k coordinates (220 m, 10-3 cm-1), and the maximum with the coordinates
110 m, 8�10'4 cm-1 is somewhat displaced and decreased. The configuration of the
isolines in the upper right part of the section also was considerably changed.
The still finer structure of the temperature f3e1d in the polygon was obtained us-
ing a group of thermistors mounted on a special trawl. This special trawl, con-
structed at the Atlantic Division of the Institute of Oceanology, is a towed~ap-
paratus with a system of sensors for the mean and fluctuating values of velocity,
temperature and conductivity of sea water. The optimum rate of towing of this trawl
is 4-6 knots with a deepening up to 200 m. The number and makeup of the sensors on
tlie trawl can vary depending on the situation and the purposes of the experiment.
In measurements in the considered polygon tne traw.L carried a system of ten temper-
~ ature sensors spaced 70 cm apart and two conductivity sensors separated by the
same interval. In addition, there was also a aensor of velocity fluctuations and
the mean velocit.y of movement of tlie trawl relative to the surrounding medium and
a sensor for depth of submergence of the trawl. The conductivity and fluctuations
15
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of velocity sensors were situated in a two-hull container (catamaran) oriented
along the flow. The container also held a depth sensor. Oscillations of the con-
tainer (course angle, banking, fore-to-aft fluctuations) were monitored by angul-
~ ar velocity sensors, which made it possible to avoid signal distortions due to in-
- stability of carrier movement. The measurements were ma.de only in a case when the
velocities of the oscillations did not exceed 1 degree/sec. Such conditions were
ensured virtually constantly due to the system for suspending the container under
a deepener with a great mass preventing the imparting of vibrations from the tow-
ing line to the container with the instrumentation.
~ Thermoresistors with a time constant of about 1.5 sec and a response of 0.05�C
wcre used for measuring temperature. Conductivity was measured by capacitive sensors
designed at the Leningrad Mechanical Institute. The sensing element of this sensor
is a pair of electrodes covered with condenser ceramic, cut into a high-frequency
circuit whose quali.ty varies in dependence on the change in conductivity of sea
water. With respect to operating principle the sensor is inertialess, but it aver-
ages the conductivity spatially with a radius of about 1 cm. The signal contains
both constant and fluctuating components which are separated during the registry
process by means of electric filters. With a constant salinity of about 35�/0o the
sensor reacts to temperature fluctuations with an amplitude of 1C~-4oC with a signal-
to-noise ratio equal to unity.
In measuring velocity fluctuations use was ma.de of a thermoanemometric sensor de-
signed by V. V. Stolypin, whose sensing element is a conductivity sensor with a
microelectrode near which, due to the release of Joule heat,there is a heating of
, the ambient conductive medium. An ordinary thermoanemometric effect arises during
movement of the medium. This is called a hydroresistor thermoanemometer. In con-
trast to the film thermoanemometers used in study of turbulent flows the hydrore-
sistor thermoanemometer has considerably greater mechanical reliability. Its iner-
tial properties are determined for the most part by spatial averaging with a radius
dependent on the dimensions of the electrode. In our case this radius did not ex-
ceed 3.5 mm. The sensor noise level was tenths of a millimeter per second.
The mean rate of towing at the observation horizon was measured by an electric cur-
rent meter. This instrument has a rotor and frame from a standard current meter
and in order to obtain an electric signal near the rotor there is a conductivity
- sensor producing pulses with each revolution of the rotor. The refashioning of the
current meter did not worsen its metrological characteristics and therefore the
error in measuring mean flow velocity did not exceed 3-5 cm/sec.
The depth of submergence was measured using a sensor of the vibrotron type with a
range 0-50 atm and a measurement error of 1.25 m.
The recording devices of this special trawl included four-channel analog magnetic
recorders suitable for the registry of con~tant and variable signals with a fre-
quency up to 1 KHz. These magnetic recorders were used in registering fluctuations
and the mean velocity and conductivity values. At the ;zame time these same signals
were visualized using a low-inertia three-pen automatic recorder and an oscillo-
scope screens.
16
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- F/~'J , zpQa1 �cM . . . - -
a degree2�cm 6
!O 2 ~ Z 3
, ~
. y
~ !
7 .
. . ~ ' p'
10 ~ `y , S . ~ S
~ ~ 6 ~ ~
. ii i ~ I
> .i ;.i B ~
~ I .
f0 ~ ~ ~ I
� B ~t ~
. ~ ;
, ' . ~ . ,
` ~
- i .
~
x ! Y ~
10"~ � ti.~ I
~ 4 ~
g
~ ~ 'M
r Iji .
>O -Z :i~ ~ , , ~
- . a .
I ~ � . (
~ ' f ~
. w~ ( .
,~-3 . ~ I
. ~
10-~ !D'Z ~ IO-3 f0-1 ,r,c,ti-f
Fig. 14. Spectral densities of temperature fluctuations according to data from
- radio temperature buoy at horizons 103 (1), 115 (2), 126 (3),.138 (4), 150 (5),
170 (6), 212 (7) and 232 m(8) for two segments of records with a duration of
4 (a) and 3.5 hours (6).
The temperature signals were registered simultaneously in digital and analog forms
on a digital magnetic recorder and by automatic recorders. The period of interro-
gation of the sensors did not exceed 2-3 sec. The frequency signals of the wave
recorder and the vibrotone were monitored from the dials of electronic frequency
meters and in case of necessity could be registered in dig~tal form an a second
digital magnetic recorder. In addition, the pulsed signal of the wave meter was
registered on an analog magnetic recorder so as to ensure the transformation of
_ the time scales of the investigated fluctuations into space coordinates.
- Figure 16 shows~the vertical spatial sections of the te~nperature field.constructed
using data for ten thermistors during the towing of the special trawl. The first
section was computed on an electronic computer using temperature readings with a
- 1~
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discreteness at each horizon of 3 sec. The isotherms were d~:awn each 0.1�C with
a total length of each of the series of 131 points. In order to construct the
second section (Fig. 16,b) we used data on temperature with a sample of 6 sec with
corresponding smoothing and a length of 227 points in each series. The isotherms
were also drawn each 0.1�C. ~he first section. clearly shows a localizerl layer
- with great vertical temperature gradients in which there are high-frequency tem-
- perature fluctuations against a background of a slower "variation" of isothPrms
with wavelengths of approximatelq 300 and 700 m. In the second section such a lay-
er is absent and due to the smaller scale along the horizontal axis the isotherms
- frequently are very steep. The left part of the section is characterized by a rel-
atively quiet temperature field. Then the field becomes more complex, the isotherms
come closer together, and finally, the field acquires a calmer character. The ver-
tical temperature drops in the zone of clustering of isotherms attain 0.2 and even
0.3�C per meter, whereas in quiet zones the temperature difference of 0.1�C can be
attained at distances of se~veral meters vertically..
The dependence of the characteristics of microscale fluctuations of hydrophysical
fields on local field characteristics ~s illustrated well in Fig. 17, which shows
synchronous records of high- (1) and low-frequency (2) fluctuations of conductiv-
ity, obtained using the special trawl, at tw~o horizons with a vertical spacing of
70 cm. Curves la and 2a correspond to the lower, and curves lb and 2b to the upper
" measurement horizon. In the registry of the high-frequency signals the amplifica-
tion factor for the upper horizon was several times less than for the lower ho�rizon.
Curves 1 and 2(a,b) are somewhat displaced relative to one another in the hori-
zontal direction (approximately by 3 sec) due to design peculiarities of the auto-
matic reco~der. The records of the signals illustrated in Fig. 17 were obtained
during the towing of the sensors at a depth of 94 m(lower.measurement horizon).
The changes in conductivity (curves 2a and 2b) with a period of about 8-10 sec are
related to the influence of rolling of the ship and indicate the existence of a
- local vertical gradient of inean conductivity (temperature) d d/dz. On the basis of
the amplitude of cha.nge in conductivity with the mentioned period it is possible
to judge qualitatively also about the dor/dz vaiue, which with a constant ampl::-
tude of the vertical displacements of the sensor must be directly proportional to
the amplitude of the curves 2a and 2b with a period of 8-10 sec.
In Fig. 17 it is possible to define the following regions arbitrarily: during the
course of the f irst 4 minutes the measurements were made in a layer with a rela-
tively small vertical conductivity gradient, then for a period of 1 minute in
a layer with a large conductivity gradient, in the next 0.5-1 minute again with
a relatively small d~/dz value and then with d~~dz ~ Q. The upper sensor entered
the homogeneous layer (d~Y/dz.:;0) sooner than the lower sensor by approximately
_ 1 minute. The level of high-frequency conductivity fluctuations with relatively
small d~/dz values is appreciably higher than with d0'/dz z 0 and in the layer with
- a greater conductivity gradient. If it is assumed that O'Ndo'/dzw, where and w are
the mean square values of microscale fluctuations of conductivity and the vertical
component of current velocity respectively, then with do~dz ~ 0 with any real w
values the conductivity fluctuations will be small. With identical w values the
0` values must be greatPr in the layer with greater dd/dz values, but with an in-
crease in the vertical conductivity (temperature) gradient it is necessary to an-
ticipate,a considerable decrease in w and as a result this can lead to a decrease
18
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~ 4' . 6 . _B !O'3 - Z-- 9 _ /I 6 B 10-2 ca -i
� Qoo
- ~10 �s
io,o .
J1/0 o.~ac ~
~ \ O~~sS�~o .
16'!.' -
e
/~0 a ~,o

1
Zu~n -
b C 'O ~v h N ~ 0 ~ p p ~
Z2~ 'y y 'y G O O 4 4� 4 p� ~ p~
0
6 ~,2 l0.0
120 56 ~ Q
- ~~(.6~ ~~o~~
~yp '
.
/00
'1f0 .
y N
!BO s, 6 � ~ ~ ~ � ~
?00
J7
S
~ ~ZZO ~o ie ~
~ ~p3~u
h, M .
- Fig. 15. Isolines of spectral density of temperature fluctuations (in degrees2�
sec) according to records of radio temperature buoy with a duration of 4(a) and
3. 5 hours (b) .
in CY . Thus, the change in the level of high-frequency conductivity fluctuations
in actuality is related to variations in the local background conditions (in ac-
_ tuality, variations of the vertical conductivity gradient).
Measurements of microscal2 fluctuations of the fields of current velocity and con-
ductivity were made in a polygon at a number of depths fn the layer from 20 to
213 m. The spectral densities of the high-frequency signals were were computed on
an electronic computer by the fast Fourier transform method by segments of the
record with a duration from 40 to 80 sec with a time discreteness of 1/260 sec.
Fj.gure 18 shows the spectra of fluctuations of current velocity in the range of
scales from approximately~l cm to 1 m. The level of fluctuations of current velo-
city was maximum at a depth of 195 m; its change with depth is nonmonotonic. At
the very same depth the level of current velocity fluctuations can vary consider-
ably (compare curves 13a and 13b in Fig. 18), which should be related to the dif -
ference in local background conditions. In the case of a linear (at a logarithmic
scale) continuation of the high-frequency spectra into the region of lower fre-
quencies their level is higher than the level of the spectra of macroscale
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v ~ .
_ O
~ o,
~ a
. ~ o \ 4 ~ ~ r ~ �
~ `o .
~ ~ ~
~ ~ .
. o ~
~ q .
b
' ,
n~ / M ~
~ N
~o~ 00
~ ~ S".~ ~v a
~ ~
k
~ ~ ~ ^ ~ ~ ~
7 ~
' s~"~ ~
~ ~
~
~ ~
. ~ : ~ ~ ~ . ~
. ~C. 'S N ' w . v
~ ~
. ~ a ~C ~ ' ~
N . ~
, ^ y ~ ~ ` ~
~ w
~ ~ ~ ~ w
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a
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~ ^ ~ a~~~~ '1
^ J ~ ' ~ ,
, ~ ~
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~ ~
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) h
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. a
d
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~ ~ ~ ~ ~ Z
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_ _ .
� . o
m
~ ~ ~7 ~ o
v S ~
r e u~i ~
~ e ^
~ o~
r ~.J w
v
~ b' O o0
O ~ ^ ~ r.
v ~ --~~._s'` ?4 00
^ e ~ cd
d- " q ~ ~ - 1J 00
Q O ~
~-i ~
e ~ ~ r"~
U~
~Q ~ ~P.~
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S M .w
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l ^ ~ O 00
C N w ~
~ h O~ /1
~ cd t0
O ~e h ~ ~
~ ~~~~'b b ~O
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- h_~ w ~ ; .
_
1 ~
o~
~ .
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e ~
, � � ~
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p -O'-_ ~ � . ~ ~ ~
~ ~ � �j w o0
� ~ o ! o'_' G1 ~-1
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J~ ~ ~ aw
h
,o Gl M
a .
< ~ .
< � ~
~ ~ 4-1 N O~
~ _ b ~ O ^ r-i
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~ ~ M ~ c~1
O ~ e o t,l ~
~ -b ~ v r-I O~
q U1 ~-1
.
~ O ~ r-1 ~ ~
.w
~ ~ ~
~1 w N
- ~ e p ~ ~ ~ C~
r-1
_ ~
_ C~~ ~ o q ~
~o ~ y ~
� ,o ~ ~~-----1 ~ ~ ~
� e ~ e e e e= . w o~
~ ~ ~ ~ ~ ~
21
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- ~ h
~ d :
~
b ~ 'O ~ c~
~
~ ~
~
. ~
~
b ~
Ry
C".
~ ~
u
' ~ 4-1
O
N
.
- ~ O
~ ~ N
h ~ ~
~ N
U
~ N
~ N
4-+ a
a
u
~
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a
. v~
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3 a~i
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~
b a~
a 3
c~ o
~
. ~oo ~d
�
w u
0
0
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- s~ w
Q O
1 ~ pp
~ ~
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o a
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0
, .C c,...~d
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0
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^ ~
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a
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fluctuations of current velocity according to data from the anchored buoy sta-
tion (see Fig. 8). This can be caused, in particular, by the infZux of energy into
the region of scales of about 10 m. The distribution of intensity of fluctuations
of current velocity in the spectrum of wave numbers is shown in Fig. 19,a,b. In
the investigated range of scales the contribution to the dispersion of current
velocity fluctuations in general increases regularly with a decrease in wave num-
bers (with an increase in the scales of inhomogeneities), and accordingly, the
microscale range does not determine the total dispersion of fluctuations of cur-.
rent velocity f,n the ocean. Figure 20,a,b gives the k2E1(k) curves characterizing
, the spectral distribution of the dissipation of2turbulent energy. The scatter of
the curves here is considerable, sincs in the k E1(k) spectra there is a clearer
manifestation of different types of interference. However, it can be seen in Fig.
`LO,b that the k~~l(k) curves increase with an increase in k, but do not attain
maxima in the inve�~tigated range of scale's.
If the spectral curves in Fig. 18 are approximated by straight lines with the
slope -5/3, it is found that the empirica.l curves deviate systematically from the
approximating straight lines in the low-frequency region and have a steeper (close
~ to -11/5) slope to the x-axis. This suggests a possible influence of buoyancy
forces on turbulent fluctuations of the current velocity field. Adhering to [9],
it is possible to obtain the universal spectral function fl(x) of longitudinal
fluctuations of current velocity in a stratified mediuin for comparison with the
experimental curves. Matching of the empirical spectra with the universal curve
is accomplished in the following way. The experimental curve at a logarithmic
~ scale is approximated in the high-frequency region by a straight line with the
slope -5/3. A transparent sheet on which the universal spectrum is plotted is
superposed on the empirical graph in such a way that the segment of the universal
curve with the slope -5/3 coincides with the approximating straight line and then
t g the approxima.tino
~_~-'--~-r?o
~ line until the best (visual)
coincidence is attained between the experimental and.theoretical curves. The re-
sult of such an operation with the spectra in Fig. 18 is shown in Fig. 21. The
figure shows that the experimental curves fall well on the model spectrum (in Fig.
21 the longitudinal spectrum of current velocity fluctuations in the model [9] is
shown as a thick curve).
The rate of dissipation of turbulent energy ~ is easily computed from the inertial
segment of the spectrum with the slope -5/3, and the matching of the empirical
curves with the model spectrum makes it possible to determi3~4thi value of the buoy-
ancy scale L,~ (with an accuracy to the constant factor 40[~ r- ~2, where otp is
the ratio of the coefficients of turbulent thermal conductivity and viscosity,
y is a proportionality factor in the He3.senberg hypothesis on the form of the
spectral coeff icient of turbulent viscosity). Using an expression for the buoyancy
scale in a stratif ied fluid [10]
~
- I., _ ~ ,x~~i~ ~
~
where g is the acceleration of free falling, Oc. is the coefficient of thermal ex-
pansion of the medium, it is possible to compute the rates of evening-out of tem-
perature inhomogeneities N. The ~ and N values, according to the data in Fig. 21,
on the average are close to 10-2 cm2/sec-3 and 10'3-10'4 degree2/sec, and the L*
23
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value has the order of the dimensions of "steps" of the fine stiuctu~e of the den-
sity field in the polygon.
The measurements of the high-frequency fluctuations of conductivity in the poly~
gon were carried out synchronously using two sensors which were spaced 70 cm
apart vertically. The spectra of conductivity fluctuations at both measurement
horizons are usually close, but in three cases they are somewhat diff erent from
one another with respect to form and level, which confirms the h;rothesis express-
ed above concerning the dependence of turbulence characteristics on local back-
ground conditions. Figuxe 22 shows the spectral densities of conductivity fluc-
tuations on the basis of ineasurements with one of the sensors. The spectral curve
2a falls considerably below all the other curves, forming a relatively dense group.
We note that the spectrum 2b was obtained by measurements at the same depth of 138
m as in 2a. In the buoyancy interval, according to.the model in [5~, the spectral
density of the conductivity (temperature) fluctuations has a power-law dependence
with the exponent -7/~5. In Fig. 22 ~he spectral density curves in most cases can
actually be approximated in the low-frequency region by straight lines with the
slope -7/5. Thus, the effect of Archimedes forces is man~fested in the flow both
in tne current velocity f ield and in the conductivity field. Figur.e 23 shows the
distribution of the intensity of conductivity fluctuations in the spectrum of
- wave numbers, and Fig. 24 shows the "dissipative" k2E1(k) spectra. In their charac-
ter they are similar to the corresponding curves for current velocity fluctua--
tions.
In the polygon measurements of microscale conductivity fluctuations at great depths
(to 1,200 m) were also made for the first time. The measurements were made using
the "Sigma" turbulence probe, constructed from elements of the special trawl.
The number of sensors on the probe was reduced to the m;nimum adequate for determin-
ing the characteristics of the microstructure of the conductivity field against the
background of the cha.racteristics of field stratif ication. The probe had channels
for the mean and fluctuating conductivity values, mean velocity of movement (cur-
rent meter) and depth of submergence (vibrotron). .The probe was placed at the end
of a three-strand supporting and electrical cable with a fish-shaped deepening
_ weight of 250 kg weight. Measurements with the probe could be made both in a ver-
tical sounding regime and in a towing regime with constant or variable deepening,
which was attained by a change in the rate of the ship's movement and the length
of the supporting and electrical cable.
In the polygon the "Sigma" probe was used in carrying out vertical soundings and
seven horizontal "sections" of the conductivity field were obtained in the range
of depths from 40 to 845 m. The registry of the conductivity signal was simultan-
eous in the two magnetic recorder channels: in one channel the full (unfiltered)
signal was registered, and in the other (with a greater amplification) - the sig-
nal filtered from the low-frequency component. Such reception was caused by limit-
ation on the dynamic range of the recording apparatus, not making it possible with
adequate resolutiori to register the signal in a broad frequency range. The statis-
tical characteristics of variability of the conductivity field were then computed
for two frequency ranges and then "spliced." The computations were made using
records with a duration of about 10 minutes.
24
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~ f~ cM3�ce,r"2 cm3 � sec 2-----
/O ~
J1 J >3a ~
Z'`
\
. 9 ~ ~ . - .
~ ~
' ~a~a ~
'~6ti\ \
>yQ~;~. '
\ ~8~~~~r.
~o , v ~ ~ . .
~ ~ ~ ~ .
; ~ ` ` ~ - .
~ ~ . ~
; .
l~~ ~ . ~
- , ~1 ~ ~
, ~ ~ ~
>o � \ \ , ~
; `''4
~ ~
\ , l.~
~ ~ ~ .;i \
` n~i1 ~ .
~ ~..1 t:r:~ ~
. ` =1 ~ v N ~
` \~.1~
1 ~ 1 .
~
" ~ vl
'0 I
1;n,
. ~
,
.1
t
,i.
` ~
1"~;
~ ~ ~ ~ ~
~o z '~l 6
_ z
i 4a
y6 ~
10'~ ~p O cM'~
Fig. 18. Spectral densities of microscale current velocity fluctuations (according
to hydrotrawl data) at horizons 20 (1), 33 (2), 55 (3), 77 (4a, 4b), 94 (5), 103
(6), 121 (7), 138 (8a, 8b), 141 (9), 157 (10), 160 (11), 168 (12a, 12b), 195 (13a,
13b) and 213 m(14a, 14h).
25
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- .
a _ _
"'Ei(~'l,c,~,z�c~.r-2 cm2�sec-2
.
~z~ ~ ~ .
~ ~ . . ~ ~
~ � ~ ~Jd ~ JyB
~ JZa I. ' ~ I _
~ ~ .
` I ~ `�4 ~ ~ , "~Ei~RI,~N~�~-~'Z cm2�sec-2
? ~
irl. ~~uQ ; ~ I B �1
9~,1` : '1. i ~ . ' io ~
~~'1 ~ ! ; ~ ~ .
~ ~ ~ . 6
Z �6 1 I ~ ~
i i ~ _
~ ~
Ba ~ B6 i~i ~t ~ .
. t. . ~ ~
~
~ ' _ ~ .
1 ~ 1 I ~ . ' . .
1\I 11�\�.1 I , - ' r r
/!Q ~ i~ ; ~ 1
_ \ ~ ~ ~ 1 ~
~ 11~ ; . ~
, � ~ � i. `s~, ~ _ ,
1 ~ ~ ~ ~ ~t/`~�~ 10- !0~ ,r,c~?-~
1 \ ~ � \ ' .
~ ~,\~'.\1 ` \ '
p --~'~~~~`-O - ~ 14 ~ JO ~ 10? .r
Fig. 21. Matching of spectral functions in Fig. 18 with Monin model curve [9].
28
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Ei~~'l,oM-z.~M-~
4 ohni"2 � ~m-1 I
s
~ ~
io-a
ZJ ~ Ba ~ .
6 \ , \
~~/t, .
\ ~ ~ i ~
\ ~:~86 ~ �,n ,
~~J ~ :~9'~, 'v1
L.~ �
, � 1~~..:~ 1-
~
~
10-~I ~ .
~
. 2a I ~ ~ .
I ~ i ~ ,
~
. ~
, ~ .
1~~r1 ~i41 ~
~ ~ ~
~o- ~ j 1~ .
~ ~
1~~N M' 1~~
~ ~ .
r~,
r
~a_~ ~~n K~ cr,-,
Fig. 22. Spectral densities of conductivity fluctuations (according to data from
special trawl) at horizons 94 (1), 138 (2a, 2b), 141 (3), 157 (4), 160 (5), 168
(6), 174 (7), 195 (8a, 8b) and 213 m(9).
As an example, Fig. 25 shows the "spliced" spectral density functions for fluctua-
tions of conductivity for records at depths of 645 and 720 m. The mean vertical
conductivity profile, obtained by means of the probe, is shown in Fig. 26 in
relative units. The depth scale on the profile is nonlinear; the depth marks are
indicated on the profile itself. The figure clearly shows the fine layered struc-
ture of the conductivity field in the entire investigated ocean layer. As indi-
cated in Fig. 25, the levels of the high-frequency conductivity fluctuations at
great depths are comparable in order of magnitud.e with the levels of such .fluctua-
tions in the surface layer of the ocean (Fig. 22). The distribution of intensity
of conductivity fluctuations by wave numbers for these same records is shown in
Fig. 27. In 'the investigated range of wave numbers (scales) the contribuzion to the
dispersion of conductivity fluctuations increases, as we see, almost monotonically
with a decrease in wave numbers, that is, with an increase in the scales of the
inhomo;eneities. The maximum with k= 0.01 cm"1 on curve 2 is not reliable because
29
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it falls in the Iimits of the 95% confidence intervals for evaluation of the kE(k)
values. Thus, the investigated range of scales (from 4 cm to 12 m) does still not
completely determine the dispersion of the fluctuations of conductivity and ac-
cordingly, in the considered case in the conductivity field there were inhomogen-
eities with horizontal dimensions greater than 12 m. The "dissipative" conductivity
spectra k2E(k) (Fig. 28) have maxima in the field of scales from approximately 9
to 16 cm and slowly drop off with an increase and decrease in k.
K E,fK!�IO'r OM-l�~n-I � _ - .
, '
I ohm 2� cm 2 .
4 I
1
. y� ~ .
1
I '
1 j~~`
3 ~ I i
!i
~~i 1 ~
~ i r !i ~i
ea ~�ti! I ~ 1 I I
.
' ` jll
Z ~i ~
~
. ~ .
S ~ ly~ ~~Y 1
\~",wh~/ ~ ~ �
;~Ju
~
,
~ 16\
~ D'0 .~~,f s ~ .
6 `~9
J.` rl ~t� ~ v
~ `y.P ~'~y~ N /
~
1.-
~ � ~ U
2a ~""~,~Z.
''~�~`~,'-'^~~--`:r,.`'....
i
IO /OO N~ CN'J
Fig. 23. Distribution of intensity of conductivity fluctuations in spectrum of wave
numbers according to data from special trawl. The notations are the same as in Fig.
22.
Now we will summarize some of the general results. The illustrations cited above
graphically show how complex and variable are the hydrophysical fields in the
ocean. Against the background of the mean climatic macroscale structures there
are mesoscale processes associated with weather effects and tidal~forces. In turn,
internal gravitational waves are superposed on these and these interact with the
stepped structure of the vertical profiles. Finally, sensitively reacting to local
background conditions, there are microscale fluctuations having a turbulent char-
acter. All these processes interact with one another, frequently in a definite way
determining one another, frequently being related indirectlq or stocliastically.
For example, macroscale density stratification determines the limiting frequency
30
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ii
~n > a~
N 'ri O ~G ~ ~ W
. ~ ,-~i ~ w ~-~i o 3
i ~ ~ � �
~ ~ V ~ ~
' " v~b~ u~ a~
~s ' 0 ~
~ - u�OU~o~~~'
~ W ~d i.? 'J J.~1 rGj
' ~ ~ ~ ,dG ~ v
I ~ p N+~.~ ~-i H~ i.~~
�i a u ,-i
~ ~r~is_ - O Q ~ri 'O d ~ Cl C: �
� ~
~ N t! ~i fa J~ O O~~rl b
N~~' , b~ a ~`o ~
s o ' ~ b0 ~ o " ~
o ~ . 0 g
~ ~ ~ b0 ~1 0Ul
t U ~I i.~ O~ L~. ~
~ ~ ~ ~ a~m~na ma
~ ~ ~ a A c a? o~ o0
_ ~ OO `~O O ~ Q ~ o c~d
. . � ~ O i~+
N ~ 4~i ~ 01 A 'J+
- 1.1 1.~ O V
00 N V i.1 C!
~ri ri cd ~ rl lb ~
w ~v q �o ~ a
. . ~
- a
o .
. ~ ~ .
_ _ ~ . ~ ~ .
1.i C1 N
. .r V ~ f]+ N
,c~.~c,r=;~+ 0~~ ~ w Q r~l
_ _ _ ~s ~ r~ ' ; w r~l
_ e. Gl R)
� . , ~ 1 (A 1.~ 71
~ _ ~ .a ~ cd
� ~ ~
~ c~ O O
. ~ q t Q
~ ~
~
.
C` Lt f r~~ O~~
~
~ ~ � ~ ' ~ 4-1 fA
1,~ ) ~
r' ~ ~ ~ FI W
Ch . ` ~ ~ ~i b ~
~ ~~I I W ~ ~
V ~ ` . ~c N U H
i' N 0 � ~ .~E C1 c0
~ ~ ~ \ c0
ti cd m
,v . ~ ~ `ti ~ ~
� h. ~ ~
~ ~'bV C/~ iJ .
ti
W~ ~ h t~ ~ ~ b Z
I N s ~ N Q �
~ ' ' u 3 ~
~ ~w ~
w o
~ 31 �
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71 ~60 ~
. Zd0 !(~0 .60
10~0 �
~ 6vS ~P0
/100 ' ,
. l000 700 J60 ?ZO 0,00~
i�~~r ~ SO o~-1. Cm-1
Fig. 26. Example of record of inea.n conductivity obtained with "Sigma" probe. The
numbers alongsid~ the curves represent depth in m.
, ,rE(~'J'/0~2,OM"Z~CH-z
ohm'2�cm'2 ~
. ~
y 2 .
. \
~ � 1
~
~ ~
~ ` � .
l
z Jl~t` .
' ' . %j
~i
~11 � ,
/ 1 r~~'~ � �
r ~~n~ - -
! ' L � __1_
. lO-1 . lO~.r,CM'!
Fig. 27. Distribution of intensity of conductivity fluctuations in spectrum of
wave numbers according to data from "Sigma" probe. Notations are the same as in
Fig. 25.
~"f (.rJ . t3~ OM-1 ~N ~J
ohm-2�cm 3
i o ~ ^ --,~i'`~..�,,' ; i~
i
t
~ "i ~r'
~ ~ ~ ~ ~
0, S ~ r v
.
. ~ ; .
~
/O = /0~~ /0~.~.t.~'/
Fig. 28. Spectra of "dissipation" of conductivity fluctuations according to data
from "Sigma" probe. Notations are the same as in Fig. 25.
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of gravitational internal waves, which, overturning, create spots of highly tur-
bulent fluid and "steps" on the vertical profiles of hydrophysical elements. In
turn, microscale turbulence tends to mix the surrounding layers of fluid, leading
them to a more homogeneous state. An intensification of turbulent exchange is
favored by veYoc~ty gradients arising in currents of drift or geostrophic origin,
and also in surface and internal waves. On the other hand, a stable density strat-
ification suppresses turbulence, thereby reducing the intensity of mixing. With
the cooling or salinization of the upper layers of fluid an unstable stratifica-
tion of waters'can arise which gener.stes convective movements, frequently leading
to the appearance of water layers clc~se to homogeneous. Nonlinear interactions of
surface and internal waves with one aiiother and with the mean currents and turbu-
lence can generate movements of diff erent scales and intensities, lead to the
localization of kinetic and potential energy and individual spatial-temporal zones
in the ocean. However, dissipative molecular processes tend to~level out existing
gradients and bring the ocean into a state of thermodynamic equilibrium. But this
process cannot go far due to the constant new receipts of energy in the considered
volume of the ocean through its boundaries. In order to establish qualitative and
quantitative cause-and-effect rel.ationships among all these diverse processes in
the ocean it is necessary to make mea.surements in a broad spatial-temporal range
of scales. An example of such measurements can be the already described complex
of observations in the oceanic polygon. We hope to carry out a more detailed quan-
titative analysis of the relationships among individual processes in the polygon
in the immediate future.
In conclusion we take the opportunity to express appreciation to E. I. Karabasheva
fo~ assistance in carrying out the computations.
BIBLIOGRAPHY
1. Ozmidov, R. V., GORIZONTAL'NAYA TURBULENTNOST' I TURBULENTNYY OBMEN V OKEANE
- (Horizontal Tlirbulence and Turbulent Exchange in the Ocean), Moscow, "Nauka,"
1968.
2. Shtokman, V. B., Koshlyakov, M. N., Ozmidov, R. V., Fomin, L. M. and Yampol'-
- skiy, A. D., "Prolonged Measurements of the Variability of Physical Fields in
Ocean Polygons as a New Stage in Investigation of the Ocean," DOKLADY AN SSSR
(Reports of the USSR Academy of Sciences), 186, No 5, 1969.
3. Brekhovskikh, L. M� Ivanov-Frantskevich, G. I., Koshlyakov, M. N., Fedorov,
K. N., Fomin, L. M. and Yampol'skiy, A. D., "Some Results of a Hydrophysical
Experiment in a Polygon in the Tropical Atlantic," IZV. AN SSSR: FIZIKA ATMO-
- SFERY I OKEANA (News of the USSR Academy of Sciences: Physics of the Atmosphere
and Ocean), 7, No 5, 1971.
4. Ozmidov, R. V., "Second Voyage of the Scientific Research Ship 'Dmitriy Mendel-
eyev'," OKEANOLOGIYA (Oceanology), 11, No 1, 1971.
5, Ozmidov, R. V., "Experimental Investigations of Microscale Ocean Turbulence
at the Inst~tute of Oceanology imeni P. P. Shirst~ov USSR Ac~demy of Sciences,"
ISSLIDOVANIYE OKEANICHF.SKIY TURBULENTNOSTI (Investigation of Ocean Turbulence),
Moscow, "Nauka," 1973.
33
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6. Kraichnan, R. H., "Inertial Ranges in Tw~ Dimensional Turbulence," PHYS.
FLUIDS, 10, No 4, 1967.
7. Batchelor, G. K., "Computation of the Energy Spectrum in Homogeneous Two-
Dimensional Turbulence," PHYS. FLUIDS, Suppl. II, 12, No 12, 1969.
_ 8. Belyayev, V. S., Gezentsvey, A. N., Lyubimtsev, M. M., Ozmidov, R. V., Paka,
V. T. and Pozdynin, V. D., "Some Results of an Experimental Investigation of
Fluctuations of Hydrophysical Fields in the Upper Layer of the Ocean,"
ISSLEDOVANIYE OKEANICHESROY TURBULENTNOSTI, Moscow, "Nauka," 1973.
9. Monin, A. S., "Spectrum of Turbulence in a Temperature-Inhomogeneous Atmo-
sphere," IZV. .AN SSSR: SERIYA GEOFIZ. (News of the USSR Academy of Sciences:
Geophysical Series), No .3, 1962.
10. Obukhov, A. M., "Influence.c,f Archimedes Forces on the Structure of the Tem-
perature Field in a Turbulent Flow," DOKL. AN SSSR, 125, No 6, 1959.
COPYRIGHT: Izdatel'stvo "Nauka.", 1974
5303
CSO: 8144/1839
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SPECTRAI. CHARACTFRISTICS OF CONDUCTIVITY FLUCTUATION FIELD IN OCEAN
Moscow ISSLEDOVANIYE IZMENCHIVOSTI GIDROFIZICHESKIKH POLEY V OKEANE in Russian 1974
pp 42-49
[Article by V. S. Belyayev, A. N. Gezentsvey and R. V. Ozmidov from monoRraph
"Ocean Research on Hydrophysical Field Variability," edited by R. V.
Ozmidov, doctor of physical and mathematical sciences, Izdatel'stvo "Nauka", 211
pages, number of copies printed unknown]
[Text] On the 7th voyage of~ the "Dmitriy Mendeleyev" specialists carried out numer-
ous measurements of high-frequency fluctuations of the conductivity f ield in the
upper 200-m layer in a number of polygons in the Indian Ocean (the location of the
polygons was given in [1]). Data on microf luctuations of conductivity were obtain-
ed using low-inertia hydroresistor sensors with a radius of spatial averaging of
_ ahout 1 mm. The sensors were placed towed line whose descsiption was
given in [2J.
On the voyage use was ma.de of three sets of a towed measurement system which differ
somewhat in design. Using one of the towed lines the measurements were made in
polygons 2, 4, 6 and 8; the second towed line was used in polygons 3 and 5; and the '
third was employed in repeated measurements in polygon 6.
The high-frequency signals were registered on analog magnetic recorders. 1'he signals
were visualized on photopaper and after inspection of the records segments with a
duration of about 1 minute were selected for processing on an electronic computer.
With the input of analog signals into the electronic computer use was made of an
analog-code converter which made the signals discrete in time and quanti~ed them
in amplitude. First the signals were passed through low-frequency filters with dif-
f erent cutoff frequencies for the purpose of decreasing the effect of, discretization
noise. The discretization frequency exceeded the f ilter cutoff frequency by a factor
of approximately 3. In computing the spectral density E(f), where f is frequency,
use was made of a fast Fourier transform program prepared at the Atlantic Division
of the Institute of Oceanology. The program provided for the breakdown of the ini-
tial series into individual "pieces," the Fourier coefficients are computed for
each of them, and the spectral densities are averaged for the entire length of the
series (for nl "pieces") and for a stipulated frequency band (for n2 poin"ts on the
frequency axis). In the~computations the equivalent number of degrees of freedom
'V, evaluated using the formula 2n1n2, was not less than 100. This ensured a
high statistical signif icance of the resulting spectral density evaluations.
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Figures 1-7, at a bilogarithmic scale, represent the one~dimensional spectral
densities of conductivity fluctuations in the 2d-6th and 8th polygons of the 7th
voyage of the scientif ic research ship "Dmitriy Mendeleyev." The spectral curves
in each f igure are numbered in the order of an increase in the depth of ineasure-
ment. The sp~ctra for different nonoverlapping segments of the record at one and
the same measurement horizon are noted by differer- letters. The conversion from
the frequencies f to the wave numbers k was accomplished on the assumption of the
correctness of the hypothesis of "frozen-in turbulence" using the formula k=
2TIf/V, where V is the velocity of motion of the sensor relative to the medium at
the measurement horizon. Accordingly, for scaling the function E(f) into the spec-
tral density El(k) use was made of the fortnula El(k) = V/,n E(f)~.
The range of wave numbers when computing E1(k) extended from 6.3�10-2 to 6.7 cm-1,
which corresponds to the change in scales of inhomogeneities of.the conductivity
f ield from 0.9 cm to 1 m. The f igures show that the spectral density values vary
in a wide range. In the low-frequency region the E1(k) values in each of Figures
1-7 vary in the range from one to more than two orders of magnitude.
Measurements of conductivity fluctuations by means of a towed line of the first
type in polygons 2, 4, 6 and 8 were carried out under different hydrological con-
- ditions and this evidently explains the difference in the levels and diversity
of the shapes of the spectral curves in Figures 1-4. The values of the E1(k)
spectra with k= 10~ cm 1 vary by almost three orders of magnitude (from�y2�10'14
ohm-2�cm'1 to ~ 10-11 ohm-2�cm I). The straight,lines approximating the E1(k)
functions at a bilogarithmic scale have a different slo~e to the x-axis (the tan-
gent of the curve slope varies in the range from -1.4 to -3).
Figure 1 shows the spectral curves (polygon 2) based on measurements in stratif ied
layers with the values of the vertical gradient of current velocity (about 1.5 cm/
sec/mj maximum for this polygon. The lower group of curves is approxin~ated well
by a straight line with the slope -5/3 and the upper curves lb and 2a have a
steeper dropoff with an increase in the wave numbers. It should be noted that the
spectral curves for one and the same measurement horizon can diff er appreciably
from one another with respect to both level and shape, which can be related to a
difference in local background conditions (processes determining the generation
and attenuation of microscale turbulence).
The spectra of conductivity fluctuations in Fig. 2(polygon 4) were obtained from
measurements in a layer with a constant density gradient (curves 1-7) and in the
quasihomogeneous layer (curves 8, 9). The current velocity vector in polygon 4
with an increase in depth (in the investigated layer of the ocean) rotates in a
counterclockwise direction and decreases in value from 45 cm/sec at a depth of
50 cm to 20-30 cm/sec at a depth of 100-125 m. At depths of 50 and 125 m the cur-
rent velocity vectors are directed in the opposite direction. The current velocity
gradient in the polygon is governed for the most part by a change not in the mod-
ulus but the direction of the current velocity with depth. The E1(k) values in
polygon 4 change in the widest limits (in comparison with polygons 2, 6, 8). With
an increase in the level of the El(k) curves the dropoff of the spectral functions
with an increase in k on the average becomes steeper and the slope of the approx-
imating straight lines increases from -5/3 (for curve 9a) to -3 (for curves 2c and
36
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3). The spectral curves 8 and 9a, 9b fall in the lower part of the bundle of
- curves: this is evidently attributable to the fact that measureznents 8 and 9
fall in the quasihomogeneous layer. The bundles of curves in Figures 1 and 2 when
- matched virtually fall on one another.
fi(K),vni-2.ce,r-~ 2�sec'1 _
Ei(~l~ OM'2.CN-J ohm'2. cm-1
y~.
Za. ~ !6 ~
3 x
JO 10-i~ ZB\~ .
. ~
1b~ . ;
10,~ 1~ 7 ~ ~ .
ie ` z6 ~ x
~a~ ~ ~ 96.Z s~ ~ ~ .
.``~\`t t J0_~1 ; ~c 6~\J, ~
' 1~ \ . \ \ L ~ 1i
; ~ ~ ~
-~Z \ :`M,. 9a'�\ 'w~ , `t
~
` ~l ~ ~ ~ ~
' ~
~
~
~ ~ ~p -i~ ~ r~
�`1 1. \~Il ~
i 1
. ~L ~ ti ~ ~
i~ ~ `k~`~ ~
~
~0 -i,~ i.` ~ � , . :1 ` .
~ ~ ~ 1 ~ 1
~
_ . ' k 1'~i
- ~ !0'~y ~'j ~ ' ~i
~ ~ ~
i ;
,~Tr i ~
1
t ~4
t ~
, ~ >0'~ 10~ ,r,C,v-~
!0 . >0 0 n, cn' ~ �
Fig. 1. Spectral densities of conductivity Fig. 2. Spectral densities of conduc-
_ fluctuations in second polygon. Measure- tivity fluctuations in fourth polygon
ment horizons: 77 m(la,b,c,d), 120 m for horizons 49 (1), 60 (2b,2c), 65
(2a, b, c) . (3), 67 (4) ~ 70 (5) ~ 75 (6~ ~ gp
103 (8), 120 m (9a, 9b).
In polygon 6 the measurements were made in the layer with a constant density gra-
dient (curves 2-5) and at the upper (curve 1) and lower (curve 6) boundaries of
this layer situated between the quasihomogeneous layers. The. current velocity
field has a complex vertical structure. The current velocity vector in the upper
75-m layer of the ocean rotates in a counterclockwise direction by the angle 3/4
- and decreases in value from 95 cm/sec at a depth of 13 m to 35-40 cm/sec at a
depth of 50-75 m and in the layer from 75 to I00 m rotates in a clockwise direc-
tion and decreases in value to 15 cm/sec. In the layer from 100 to 125 m there
is a change in current direction to the opposite direction and at a depth of
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. 125 m the velocity was close to 30 cm/sec. At a depth of 200 m the current velo-
city decreases to 10 cm/sec. The spectral curves in Fig. 3 form a dense group
, and fall somewhat above the curves in Figures 1 and 2. The E1(k) curves in Fig.
3(except for 3, 4 and Sa) can be approximated by straight lines with a slope -5/3
and curves 3, 4 and 5a by straight lines with slopes -2 and -7/5. The good ap-
proximation of the curves 4 and 5a by straioht l~ines with a slope --7/S~makes it
possible to postulate a substantial influence of buoyancy forces on microscale
turbulence in the ocean in a number of cases [3, 4].
~j /Kl~ OM'2.CM'/ ohm-2 � cm-1 . - .
~ ~
E/ ~K~. OM'Z.CM-/ OYlIR~2 �Cm 1 .
~
~
~ �
/
~
Z~ \~fa \
\ ~
~
~o-~o . , ~
. .
: . .
~ ~C -9 76 ~
_ ' B 1 ~ , ~Q ~ .
,
se' "y~~~ ,`'~,y ~z � '
b\ ` ~
t . ~ ~ �
~ ~~1 ,
' ~ j \ � '
1i11 N, \
JO-r~ ~ ~ . \ ,
r j ~U-~o ~ �
~`1 \
l~`,~ ~
~ ~
. ~~n ~ ~ ~ ~ ~
i
~ i ~ , ~
j ' ~
~ I~' `y\ .
\
_/2 ~ /0 ' 1/ � 1 1~ ,y~ '
' !0 /O ~ K, cn-~ ~ ~ ~ .
Fig. 3. Spectral densities of fluctua- . \ ~
tions of conductivity in sixth polygon ~
- for horizons 10 (1), 14 (2), 54 (3), ~i,
60 (4), 68 (5a, 5b), 89 m(6). ' I '
io -~z ~~''Jc~
i
-
Fig. 4. Spectral densities of fluctua- ~ L1~~
tions of conductivity in eighth polygon
for horizons 55 (1), 95 (2), 110 (3), ' ~ ' rs
~
141 (4), 145 (5), 161 (6), 170 (7a, 7b), ,s~~''s
175 m (8) . ' ~ '
~O~ n�.:N-i
Figure 4 shows the spectral densities of conductivity fluctuations in polygon 8.
The measurements.were made in layers with different (different from zero) values
of the density gradient (the maximum density gradient is at horizon 3). The meas-
urements 4, 5 were ma.de in the layer with a marked change in curvature
_ 38
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of the density profile. In the layer from 50 to 200 m in polygon 8 the direc-
tion of the flow changes by the angle Nn/4; the current velocity vector below
75 m rotates is a clockwise direction, remaining,unchanged in the layer 50-100 m
(^~55 cm/sec) and decreasing to 25 and 35 cm/sec respectively at depths of 125
and 200 m. The $pectral curves in Fig. 4 form a relatively dense bundle and cari
be approximated at a bilogarithmic scale by straight lines with a slope close to
-2. The bundles of E1(k) curves in Figures 4 and 3 are matched well with one
another, except for curve 4 in Fig. 4.
E~( f~ ~ ON~ZCM-~ ~llut-L/~m ~ .
\
!0-~i E~(~l,aM-z.~M-~ -2 m 1
\ ,S
' 10
� Z6 ~a ~0'~3 6 ' .
~ 9 ~
y~�1 ~ \ Z
~ 1 t7 \
~ ~ E ~
. 1 ~
, ~ ,
~o sa \ ~ 1 .
~ ~
, ~ ~ . ,
, s~ , ~ ~ ; ~
( ~
~
~ j -~.v ~
9 1 1 ' : ~ i~
` ~ ~ ~ 1 4
9 ~ ~6G~ ~ \ \ \ , '
/0'~.1 ~ 1 \ '~\,r'`,\`~ . .
r \ i j 1 , \ ,f
I I ~ ~ ~ 0) the system (20)-(21) does not have
asymptotic solutions (Pr~ 1), since the inequality (37) in this case loses sense;
however, the viscoconvective interval with large but finite Pr numbers, when (37)
is still correct, can exist. Under the condition (38) the functions ~E and ~T
are different from zero only for x values in the interval [x~, xm], where xm
is gi~:en by formula (39) .
It follows from what has been stated above that the turbulence spectra in a strat-
ified fluid can have a different form in dependence on stratification conditions,
Pr number and width of the equilibrium interval, which can be determined by the
- value of the ~ parameter. The inertial interval, as was demonstrated, in a number
of cases can be absent. In the case of a strong stab.Le stratification and a quite
small width of the equilibrium interval (large values of the the turbulence
spectra degenerate, that is, are different from zero in a finite interval of val-
- ues of the wave numbers, which is narrowed wi~th an increase in stability.
III. On the basis of the derived formulas we carried out computations illustrating
the noted characteristics (Figures 1, 2). Figure 1 shows the functions ~E and WT
multiplied by x5~3. These values in the inertial interval, if it exists, become
constant. The computations were made for cases of large (Fig. l,a) and small
(Fig. l,a) and small r~ (Fig. l,b). In the first case the relationships among
the scales are such that the following inequalities are correct:
LT