HYDRODYNAMICS

• Document Type: CREST
• Collection: General CIA Records
• Document Number (FOIA) /ESDN (CREST): CIA-RDP80-00809A000600200234-1
• Release Decision: RIPPUB
• Original Classification: R
• Document Page Count: 20
• Document Creation Date: December 22, 2016
• Document Release Date: June 29, 2011
• Sequence Number: 234
• Publication Date: August 17, 1948
• Content Type: REPORT

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s+e '~'
,ENTRAL INTELLIGEpiCE AGENCY REPORT
in~~QRm~T ol~~~r
PUi~
ACQUIRED iI:t3R
0~+
"AT~&3N 19A7
DATE DISTR. 17 eul~xst 3948
N0. OF RAGES 2D
NO. OF ENCLS.
tuareo spow~
SUPPLEMENT TO
REPORT N0.
'1'FIIS 1S UNEVALUATED 9NFORMATION FOR THE RESEARCH
USE C1F TRAINED INTELLIGENCE ANALYSTS
8eaelaa p?~rioAiaal, mY?~~..~?~.r col ZY, No ~,
1967. (~ ~' Abe 1~lvlnelation epeaifioallr reaneotesi. f
t Y FOR TUI''i S 11t3TTDN
OF A S Ct:F:i~SSIt1T.
? D. 'te. Do:idse
AoeA Sat- Qearglao 88R
T~Llie! Matti Iaet, Tbilisi
SnbsitCed 2b Oataber 1948
ere in p3ronthesea refer to the bllalioB~PA9s7
After the roorka of odgvist (]~, 2) I,lohtenetein (3), and Lergv (4):
dsdiisated to 11'~isu: the, theorem cx ttio esdatanoe and vniqusaeas of a
eolutiaa of the taoup=iary probier far tare stiia'jY motion of a vieaous
L'ga;td orith eynal].:teynoids mier, this pratriem asn be coneidos~aE! aom-~
plete],9 developed. Toro ~~acke ai Odgviet (5) and ie~v (6) mey bs cited
ofdoh treat boundary pivbL:.ma for unstoiacly motion.
A eollsticu of firs linear problem ie given ixr Odgviit'~ Bork ew'ttt
saw rathsr ganerat aeaump'~ioree by twc ciffersnt :rathods~dep~ ~ fPan
o~ether a i..r+ite aac 's.Slntts !Ye].d is bail; axeminsd.
a plea3e L a3,eularl/ eoramined in F.erAy'a encteusive work. Le,ey reduaoe
the solution of the.;inear prroblem on a plane to a ayetem of tna sir~n~-
lar Lttetra]. equations. Csiog the method of sucbesaive appro~matian,
yei+gy oleo examines *,ha nonlinear problem nn a pL4ne and share that a
a'ssglo .Kalutiwn of the eo-aallod par~i.a1:4! iinaari?e~ p~biem deer
eoeist.
The present mart: is dsdiaated to the solution of the basis linear
bomadary pvL?1~u fcr t"e u a:to~c~j .^x:ticn =S s rf.a~?: Le ; ~aa~reeaibYe
ltgaid. The probla.. aonaiate of the folloHirgt detercSswt:,or- of regular
i~1+a4Y.eld aolutioias of the linear hydrodynamic equations vdth given,
vsluee of veiocit~ at the beuMary at the iaf,tial .^..~nard. .The field
~, l , ,
CiASSiFICATtOIN RaSTtitCT3i
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17iai1 i'imLd ~ ~iroon here. Tn eontxmet to Odgr3at (6), attar Pa?~'
of the oaa the iars9gaisamese of tho ealutiaa said of the
i~tia7. oroaQitioae to steam, tm est t~s tvntal solutiam by irhioh
th? pi's 2a rsdaased to the solution o2' a syetean og qusei~-ro~u7:ar
luts~csi, od' the seasond lid. ~lhe solution oS this eyetae
is toaad by eaooeeeirA spproriatetion, eissaltaneonsi'' ehoaiatg its neigae-
aueepsrs. '&'he bslutias of the pleas probleQ arieiog oat of tl'i+o geaerai
liaeor ease ie given at the sod at file paper.
ip ooneiderod to be s eir~le oanpenaoAO,y anatteated ,~ ti~ao; 'asid
liaaited tr~- ~a,~n?~a~~itavniy ?xoeea sarfeos -stth a aootsa+_a,~~v?ar~9.s`7hle
' Sew+w ~ .~ ~1~$ti1~17~s Z~ the ~~.~ A~ 'Mw~aW.y
fhe`tia~ ahslogans to the rawy,er6i~e at the
Po'~:~ ed' s. dOUbLu ]syer. They are rsgalar irseido the tia/d, tmt
on erh~ia~ throngl~ the bovndaq enrraos, they esPei3enoe ~ diosanGi--
smilry'dt tke first off, aaoacd3.~ to shish a system as integral
egnatlaas sa d~talnod far dskszmiaatioa 4t the udowsc tcnotiens w a,
w1Nre ri L the l3oitSng ? esit:.on ed the i..,_.,:t n ~dth respect td its.
iieae3ine to the rYnuuiary sur, rasa, ~ (~; arc the gian
~llnes of LRe oao,9aoaotiaoo ~ ,~, ~q of ens
5r'
rar.+ ibnatica.
~i.+ae pa (di se as
bod~diws i~o equtiono (2.13) and (3.12), the a>~reaeions (3.1)
and (3e2) aa'lStr~j- e~s~s (i.d). to sddiW,oa, tt~ re~or6 to aero aL
ffia LdSti~l ~ eiNriiarso~ Ao(o) $ S), apd 3a tha oase of an
a>e~esnal isnl+d ~ aaL~- tda ooaditi,ods Est tba attavaadd;:.on of motico
a4 fnltirAt,. xt ramti:ds to Aatla~r the bawddrr3' owtdit3,ane (1.9).
sFo ebt11 stodgy 01 the bohel~-laor of fi~aotioda (3:1) oith a stredur
lino rt posh: P t0 file staKaee. Fla ram
.g_
ft334R,tCT~
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tT~d~c
9uDstituting t-'f = r~ !4/w'~'; ve: fret
it 3
_ t
.~~.~... e X t r
Therefore the eaoond meNber in the right aide cP foaeemla (3.3)
rwseSna a e~ aoduane than ~Uih~.
Ou the okher head, aacot4irg to Odq~rist+s rssuita, we oan main-
tain that flea intoc~:~al Yar3,es aonticaeous~;y through the ontire range
Srcm !!~(~,, 1t) alor~ the surfaoa ~. From thi.e we ooenolebde that flee
su~taoe Prom tT-s eeaond mea3eer is the right aide of facrmils
(3.3) *~ ~ aoatirwoua when orae~ throuP,h the banndaay aurfaoa.
Caaeequsntl,,,the question is reduced to the study of the first
mee+ber is tFe rSdht side of losmula (3.~)? ~Ys shall Sadiaate it tY
J IIainB the second foxmuYa of (2.8) and expreasiaos (Z.6) for
' ~ iatrodusing the expresaioa
The evooad 3ntagcpl !a Lhe rLght side nt the Iatter formula is
iiedl,aetad ~ J.
~V~
y >z r t
the eoq~s~esslou for J~ can be presented in the fexm
x ~ axK y~~- .~ ~ vt -~ y~ t= - t)
It oac ossify 1>s ahawn test subetitutiog t _T x r i4 v w 2, and
Z~
zl ~ -~ ~cp y r~ dY
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Y3U;.c _ rl
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RESTRIC~E4
'JIK ~a---~- too - ~~dT -7~x~X~ ~'~ ~XP ra
(~.2) ror is tt-e etartaa,igta~a8
the eaaoad a is the ~,~ or $ f3.k~ rd39.
bde 4a~t3rege~o ixs a oYaad. tia]d ~ ~- ~ atth eel ~>?. i~r
9q^$~g tte~ fret t~mbara ~e siotiar t1~et the dlrt~erenao ~i ?.
~~ emtidios the e~tiau
g~il ~'~_ ~ 1lvr t3.~)
~ ~. aren~e to sego at ~e eit~a t moo,
!od AL -!~tlLa1 i~ ie ~+ t? aoeia lme~a thM na1+~.
~. ,r. #' ~ h dts er- ~ ~a tDe sgeLd. ..
tiw ~~ea~ ~ tnoabdm ~ GAP, +y. w~ CRY tM
~ ~3.~) is bhe ~bsn
,.~ "S-,' J ,a~. c~~ y4 t~a~r,Q~Jd~q
D
from this w obt~n
s s
0
. ~f?-il;1dr ~ GAP, C~)dVi~~Br C~,~'1, r - ?!'~cit
(3.6~
0
e~ ~3.5~' t'ajt Hi, it is eaat7~ ehceti b~ iata.
,B; dT = ~? ex ~ d
P
y~o (l.T~
9~
lbr~, ?eoaoMtn~ to i .6), wr caaoapa aW tl~~ ~0?
s
~ K
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ie a omttemaxe i`waotiaaa t tia. awe np tee tha e~a%ao:.
Zhea+etoa~e, J is w~GLmaoaae aa~aout flee eaat4re .~Le].d r .~-!`,
grad bT toe (3.31 ~ Five at the earaa~loea that
~dF ~V;,~dr
F 0
aLD xMae!see m aatinrome rdth the atream-li:te o4 paint P 'taa~d the
sta~taee lr.
~s
L ?
l;+n dP V,?x(J;Mr-r)dx=~df_rV? ~~M,r~?T)d?'
~ ~ r? 0
e L , rL
~df~~Y;dt= fdF (C-1K(M,~')-~(N,r~V;drtw(~;c)'dfJ~~ d~
F o ~ p
~ vilF~ o! t!r eoa~.imdty ofv~ , !se eciromd a e sell as tizw
i3aTSt, fae~ear in the ar3~at side o~ the"lsttevr !'e~ala 3a aa~Sscraotae
t@ae entire arao`e. laaa tide it tol]owe that the ~
amd ]user ]l~dte oY !tM eamdaed inte~raly rdffi the ets+o~,l3~ne of
~t y~ut P to~a+Q tM em~tacw, ass eQu1 to its Yalne at a poSmE
ant errlaee, i.e., to ffis ialregral
~ e0o ~ s aooo~.lt-8 t+o~tdwaalaee (~~7i~aeu! (3?daa )rsaEels~
vI~ lEa`j r+3c arf"d F,'1 ~ ~M~T?~ A(P lH~ ~ -1' ~dT
F o
nbdeb paeeaecte the spatlsl thea'aai. potaatial of a dooDL yt~reor
7dtta a dendt~,r wQ. deoal~frg trs the imam tbtsB]sa tae the
1!altiog velure, iq 7ddoh thr a~rper and l.~a~or liedts aQ tffis
Pam Csea ]gnnte (8)) era
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RESTR~CTER
the limttlog values '~! take the Pura
Oa, the basis of the lattor relations, whist. satisfy the
boundaay amasclitions (l,9), we obtain a ~yetem of throe Integra:
egnstioas for determining the'uaPsnans Punctiaas xi
wfrora #i(N, t) are the ?.vsn limiting values of the comgornmta of
?s$o4ity /t.r ?b 1 in the case of the intexnal problem, anti )~ v ~ l
if the prob]am ie ertaraal.
v'fcrr.?~rnmTnsz.nF mta: ^_rT~t~na
1. ~uation. (3.8) fca~tos a egetem o1 oouapoeite integfal
agn+sttom of the Volterra type. The solution of this ~stmm onn
bo carri~sd out aaslagous7y to the soliatioa of the equatfon ~
tharmel aoadaotivity by using encosasive appro~bions. .7e shalt
eu~aml.ne a epretem Td.th a parcmeter. X
3~tatitutittig is syetam t.';,I)q ws o3tain far the datwr-
ednatian of the membcra,/of the eoriee the recutzwat foraalae
t /t
X;~M;;J = - ~ ~d f ~ (X~,? A f L, ~irnvKi~ dz t4a3}
K
f o
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ey tmmt3.as (3.3), (3.b) ex-d (3.6), tre have
f r lCxrt-~KXxs-~.;Icos y _ra
J o~~J y~, :1T~ ( ~r~ 'ruT J~ t
J e e~?. A
xr^p 'per 4 r 3J ex~a ~r1 ~lct`?'F~~~ dlr
'llstdng into caneideration e~g~reeeion (2.6) for 0,~, it 3~
botmded by' ~aurt+aoe F. eid4 of the ]attar tormiil,a remat~
Yn the tiT as point & t~ a#~s11 e~spsrat4 as iatinite5y
ear~I pert of b' of the eta~aoe T~. and aitall. date ~ polar oo-
sat~ae~tra of H in the plsr~s $a2 bP ro, dten the te~ng
Lltakan inlr~ 6 and the sstb ~ ie dSreoted aaooniiog to the
noetaal. ems, tro trill have vrl.0h aaoia~ou~r o! a traaq !~ die
cos j' _~r~y, dfi ~J~ t~a~'~~t~R~~a . dr- d9
aR, : aX~ ~
whoy rj ~ ~~ arQ) iw tie agw~tiaa of the avr3a~ Fo.
1Ne shad dee~ats bpi dg the iibertnl inte~ra2. ~t tho brut
stem ~t toitatla (t~.~). To obtain an eaalnstion tra preeant it is LM
toa
_ J
-
t1~- - ~F -r-; t - i?,
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RF. C1T;D
In the right aide of this tormula the $rst integral is
limited; teas 4he second integral sve can eraite
Hsn is a ~nAtant related to the surtaoa~ ! y and b ie
the radius-veotax of the cmtottr of the snrtace Fo, ;~betituti~
of
?C v
The right part of the ]after inequsiity io limited for
alt a and t; thsrstore, it can be ccacluded that J.,_ is of t{~tod
Y0.1C11 and +'~
ta.a)
Let ~ be the maximan value among tine piven~ tii~ 3n a4atem
(js.Z). On the beds of the determination oY (1r.8), bg Pommral,s
(4?~) rs a'~tain
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x~sx~zc~
prbexa ci and. s2 st+e positive constanEs ~l..}~ s2 . c.
Tdsa~atore, we ~ vrSte
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Theref~e, the xs~tio of the tiro successive terms of the
ma3ority of aeries (k.2) aril]. be
/'' ~~ ht t 1;!
r~z~hrt r)t1~
which at all finite valuee of t and x tends tcx~rard zezn u~t~an m -~ ~;
oonsequently, with x . 2 eeri?E (4.2) gives a solution a? system
(9.g).
2. Yt ie eaaiay shown that the solution of system (3.8) is
uniquo. actually, the ~ei.stence of tao differont mntinnoua aoa
1uLiona of system (3.8) could iredicata the oxistence of a continue
ous solution other than sero a? the carreaponding homo~rer~oua
~~~
i= o
Pfe shall designate the upper Lfedt of the absolute.valuca
of tfin andnl~.irt:~ of mrn4san ~6_lA) by w _. Av arneafinn (/._1~1 anA: fha
preceding determinations we have - -?- - ~------- ?-- - -
On the brsia of thts