SCIENTIFIC ABSTRACT GERSHUNI, G. - GERSHUNI, G.

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• Collection: Scientific Abstracts
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• Sequence Number: 12
• Publication Date: December 31, 1967
• Content Type: SCIENTIFIC ABSTRACT

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11-31:1

82727
Regulation of a Neural Pulse Stream in the S/046/60,/006/003/003/012
Auditory System B006/BO63
area of the cortex attains amplitudes of up to 70 Av, and the dependence
of the amplitudes on the sound intensity decreasen rapidly (Curve 3). Next,
the author discusses special electric reaction diagrains which were taken
under different conditions, and studies the effects of disturbances
(e.g., anesthesia, partial destruction of the auditory area of tho cortex),
The results discussed here were, for the major part, published ty
Ya. A. AlItman, They illustrate the importance of the various ways of im-
pulse regulation in the organism. 1) The current of impulsearesulting
from an acoustic stimulation in a nerve is limited, The secondary current
caused by this current are also limited. 2) The current of impulses result-
ing from the action of a special system of (reverse) connictions radiating
from the center is limited. 3) The current of inpulses in the higher
ranges of the auditory system changes under the action of sections of the
central nervous system outside the auditory system. The author discusses
two mechanisms of the regulation of information transnitted by currents
of nervous impulses which may occur in the auditory syetem under the action
of 3ounC The first mechanism consists in a change of 'the participating
elements# and the second one in a change of the level of the characteristic
noise in the system. Mention is made of Ilikolay flikolayevich Andreyev and
Card 2/3 ~K

82727
1 Regulation of a Neural Pulse Stream in the 3/1046/60/006/003/003/012
Auditory System BOO6)/Bo63
A. M. Marueeva. There are 5 figures and 24 referencen. 13 Soviet and
3 US,
ASSOCIATION: Institut fiziologii im. I. P~ Favlova LeninFrad
(Institute of Pbysiology imeni I. P. Pavlov, Leningrad)
SUBKITTED: May 18, 1960
t/
Card 3/3

GEPZHUNI, G.V.
Evaluation of the functional significance of electrical responses
of the atiditory system. Responses to short sounds (clicks) and the
determination of the initial moment of the, stimuliui action. Fiziol.
zhur. 48 tio.3:241-250 Mr 162. (MIFLA 15:10
1. From the Laboratory of Auditory Analyser Physiology' I.P.Pavlov
Institute of Physiologyp Leningrad.
(HEARING) (BUXTROPUTSIOLOGY)

KUZINI A.M., glav. red.; GELIFAND, I.M., red.; LIVANOV, M.N., red.;
GERSHUNI G V , doktor mad. nauk, redej OURGIN, Ya.Lt doktor
rl-K~m-aiem. nauki red.; KOCHEREUKIN, VA, kand. biol. nauk,
rod.; GURFINKELI, V.S., red. Izd-va; MWOVA, T.P., tekhn.red.
(Biological aspects of aybematics]Biologichaskie aspekty kiber-
notiki; sbornik rabot. Moskva, Izd-vo Akad. nauk SSSR, 1962.
237 p. (MIRA 16:1)
1. Akademiya nauk SSSR. Nauchnyy sovot po kompleksnoy problems
"kibernetika." 2. Chlon-korrespondent Akademii nauk SSSR (for
Kuzin, Gollfand, Livanov), (CYBEFOISTICS)

GERSHUNI, G.V.
Ev*k,~d potentiala and utAchanisms of dia,~rimlnat:lan of an ex-
ternal signal. Zhur. v-ys. nar7. deiat. 13 no,5tP82490
S-0'63 (MIRA 16t1l)
1. Laborutory of A.ccustic Analy-aer RqBlalogy, Favlov Insti-
-P Physiologyv U.S.S.R. Academy of ScIen-t-9, Leningrad.

GF I G.V . ' ~)ii
6pr~:. :C p r
In r r,3 I n h
Of th~ ~T-vil

IMUKOV, Yo.S., kitrid. trikhn, nauk (Cholyabinok); GEMMUNI, G.V., prof.
-11- 11 .
Is our ear a radio loudspeaker? Pr1rodn '3 ri(--).9:124-125 164.
.:., (MIRA 17:10)
1. Inatitut fiziologii im. 1.P. Pavlova (I*or Gershuni).

GERST?i : , Il'l. V.
Grgan -,Zft*, i ~,r, (A' a f 11 ;.,4 :11.!, , - : -, "': :. ~ : ~ " -
yo. r,!:.- v - 4,~ i -a' ~ - ~,:
s'-,nals of varlous d-aratLcti. -,
I ~ ~ I
26)-273 It- - "~ r:, ' C' 5 . I - ~ I, , ,
.L, Institu' fiziolog"t Ime-i'l !,N ~l'.',!!.,-

GERSHUNI, G. Z.
USSR/Physics - Heat Transfer
I Oct 52
"Free Thermal Convection in Space Between Vertical Coaxial Cylinders,"
G. Z. Gershuni, Molotov State Univ imeni Gor'k:Ly
DAN, voi 86, No 4, pp 697-8
Investigates thermal convection in a liquid between ccaxial cylinders
at dif2erent temperatures. Finds that heat ti-ansfer from hot to cool
cylinder depends on molecular thermal conductivity of liquid. It holds
true as ling as Gr. Pr 13 (Prandl-Grasshof number). Crvee this limit
solution is unstable and tnrbulence occurs. Presented by Acad M. A.
Leontovich 3 Jul 52.
252T96

Gi~RJU:lll G.
"S..,unu
t
url-tv I , '~Q 1, ~pp
Ano,i:i,lou,sly soun,i nbeortiticil ir. r! 1*t!T1'0!Jtf-:lv~Lc r tb~ %rlo
point, to enerar dissii)atloll of the "rund W~ ve , If! Ivl,'Lyzc~:~ 1'c r -
'l,ula of 1 ini%~r rl)~,-x-tion Is tierived.

GERSHUNI, G. Z.
2797. NEKOTORYS SOPPOSY USTOYCHIROSTI STATSIONARNYKH KONVrKTIVIAYRII DEIZHEPIIY. MOLOTOV, 1g':4,
9c 2L CH. (M-VO VY35H. OSRAZOVANIYA SSSR. WtcTovsxiy Cos. vN-T im. A. M. Go*txoao)
100 EKZ. B. T3. - (54-56626)
50; KNIZHANAYA LETOPIS, VOL. 2, 1955

Gi,,RSIUIII, G. Z., and Uerntsimova, S. 11.
-ai- -c of' Convecticn
ert -n Cris
C
P-Mcient to Tpmnera'
C, Wre
Uch. ZaD Molotovsk. uri-ta, 9, ~:Ifo 3, 1.954, ~7-90
~,,qw,ttiolit; 0.~., 'Iri! "'wIlle(I tni'l-l" ::~r,!,-,,~~Iult
ir. the case of rin infi-ito vertical ril.it wLt',) 111a:,e p,ir::t!
to different 'emnernture~-. .`mact stntionary solutlo,:~i ar,! Cuin~! ir -,.,c
caf-,es Ln wb.L~,!) the rrLiLcj of viscosity to tomper,11,111,-, t;;
BUC-IIHS~-,tY'0 '1011111111~. T11 I Q urf~ fl ~ 0~ C. L(,)!. I !I
this cai,,.~ is a!id the licat transCer fi-cri hol: to Lol J ,:!L1 I
mined by 'lie molecul*.r lh-~at conductivity of th-2 IiqizU.
1.955)
SO: : Sum-710 737, 12 Jan 56

MRSHUN19 G. Z.
nCertain Problems of the Stability of Stationary Convective Navements."
Cand Phys-Math Sci, Molotov State U, Min Higher Education 'USSR, Holotov, 195h.
(KL No 2. Jan 55)
Survey of Scientific and Technical Dissertations Defended at USSR Higher
Educational Institutions (12)
SO: Sm. No. 556, 24 Jun 55

USSR/Physics Convective movement stability FD_3051
Card 1/2 Pub. 153 - 20/23
Author Gershuni, G. Z.
Title Problem of the stability of planar convective movement of a liquid
Periodical Zhur. tekh. fiz., 25, February 1955, 351-3Y(
Abstract Earlier the author investigated (ibid., 23, 1838, 1953) the sta-
bility of stationary convective movement of a liquid between ver-
tical parallel planes heated to different temperatures or between
planes arbitrarily oriented relative to the gravitational field,
the investigation showing that for varioiis angles of inclination
the crisis of stationary movement occurs for different causes;
further, this problem is of interest for its own self since it re-
lates to the practical important problem of hent transfer through
liquid or gas layers. In the present work the author considers
the convective movement of a liquid in the portion of a planar
slot remote from the ends which is formed by two planes berween
which is maintained a constant temperature difference T. He drives

Card 2/2
Abstract : the related equations and solves.
threshold of convection is a
turbulence, as noted by V. S.
197, 1954). He thanks V. S.
erences: e.g. V. S. Sorokin,
Institution : -
FD-3051
He clarifies that the so called
special case of the occurrence of
Sorokin (Pri.kl. mat. i mekh., 18,
Sorokin for discussionz. Seven ref-
Prikl- mat. i mekli., 17, 39~ 1953.
Submitted : June 25, 1954

SOV/139-58-4 --- 6/30
AUT11ORS: Gershuni, G. Z. and Zhukhovitskiy, Ye.
TITLE: Two Types of Unstable Convective Flow Between Parallel
Vertical Planes (0 dvukh tipakh noustolychivosti
konvektivno6o dvizheniya mezhdu par~tllellnyini
vertikallilymi ploskostyami)
F~RIODICAL: Izvestiya Vysshikh Uchebnykh Vavedeniy, Kizil-~,
1958, Nr 4, pp 11.3-47 (USSR)
ABSTRACT: The stability of stationary convoctive flow betvie~,~n
parallel vertical planes held at different t.-Fiperatures
has already been investigated by the first author, 'asint-'-
Galerkin's method (Ref,l). In the prescnt Da;)er the
authors have used a more complicated form fo:- th-,.
approximating functions (see Eqs.5), and have so fi~~ind a
more accurate apDroximate solutiot--. This has ellowed a
more accurate calculation of the earli,:~r rt~sults ?~id has
in addition uncovered a seconcl type of J.nzi-vabilit~r, not
6iven in the earlier work at all, a -,yp,~ i,.,ith null rhase
velocity which the authors- c~:tll a "standiaL.; disti:~,,- b&nce"
as opposed to a "travellinj, di,stu-T,brince" Taki nL,, t. he
planes to be x = � 1, the diiaensionles!~ equaticns for
Cardl/4 stationary oonvective flow are t!,iven by The

SOY/ 13c, - c- 8 --4.,6/ 3 0
V j:: 4 C
Two Types of Unstable Convective Flow Betweeri Pirallel il
Planes,
streaiii and temperature functions (p litid 0 of r; lane
I, ~
harmonic disturbances are ~;iven by- Eqs.(:?) and Z~I V,ith
boundary conditions as in ~,q.(4). G -tind P tire tilc Grasshof
'lie ,iava LiluiIber kw-~ ! ~:o;ii-,)Iex
and Prandtl numbers, k aLid w ti
frequency of the dist-,u,bance. These V:-~Ie deriVed
by the first author (Ref 1), The qu-~,stiuo. a'k-, --* 1 i ty
has thus been reduced to that of firidiiw
, 6h~~
of equations (2) to (4). 'I"he aurliors fin,.1 ;~.-n ~--7,)roximate
r an(!
solution to this problem b-, a -um n~; forms f
of the type given in Eq.M., S62helr the~-n malKe
guesses at Els,(C-) and,
(P1 I
boundar-
y conditions are now sauisfieel b,), 'he ~-mate
solution, This solution differs froia Lhe crud,~11
ination the first author used previous! 'ef i) ir, that the
y
stream function T is now 'the sura of two 1"unctions, with
two variable coefficients, th*,t uli~! additional
boundary condition on G, Eiq.(?), is taken intc ,;~ccotult.
Usin~~ Galerkin's method, the auth(;irs *btrain iv-4 12 .) f D
real eigen values of w, and Eq,(Il) foi: the C Crile Epoli'~ I li~
Card2/4 relation between G and k. Eliminat;:i-rit, (,) bet't~C(1111

SOV/139-58 -4-S/30
Two Tjpes of Unstable Convective Flow Bet'.-,*e,':!n Fa-ralle-1
Planes
and Eq.(12), z~ curve is oIA.,Aned in Lho
,:ihich the -authors call a 'neutral curve-I - i.e. ozic-
correspondiab to r(,al v_~ilues of (o. From Ole nof~fr-t
U;ie :~'-ini:iiwd On this curve th,~ crit,;1c,11. valuos of r-':
Gresshof number G and thL- wave n=t-.,e:r- k C:~'Ii I, fc111--o'.
W = 0 6ives a colueion of ~&q.(12), and thu,
curve of G a&-ainst lo~, P is- -hown in, Fi-; , 1, In. tte
r1ange shown k was practically constalit,
from 1.C to 0. This is the insm-bilitu.-; th:A nat
revealed in the earlier (Ref 1). Excludizn:'::~- 0,
for P -1 LI
> 1.8 the authors obtain the tyi,,o
tli~-- "travellin6" type, F:),,, ',,hiz G
-Ls plotted aglainst 1o6 P in FiL,'-.2 (z'ijll E-.(111) is
as,yrimptotically true and -a .,-ood for !?>~:'O'
For this type k m increases from, 0 VI-c at F>~),
For this type of disturbance -i"'nere
t.ho author's earlier ~-,-ork (Re.f 1), "hus eq.(14)
Faso obtained, thou~,h with, 224 instead of 214 in -3he
U
r-.u.ierator, and the as-,piptote wi,,! re;-I---!'~e'd 0.", P -- 0.96,
Card3/4 .'~Iie xi~;ia results can be swaimr-J'sea thuo,:

6OV/139- 58 -.4-6/30
T-.~.,o Types of Unsbable CoLvective Flo-.-i Betl4e;~i, Ver'uical
PlL. no E,
For convective flow between two pax-llel planes iield at
different temperatures, instobilities a')K)eu-r if ttlere is a
large temperature difference bet,vuen tbe i~lanez, 119-L"andIng"
disturbances correspond to P< 1_3, types are
pusi,ible for P '~ 1.8, thou6li for P tile " Ljl O-Iellin~
disturbances are the more d,'in~,,ero'js as Lhey corr-,-,rcj-,d tto
a quialler Grasshof number.
There are 2 fiGures and 1 Soviet referen,-,e,
'OCIATIONS: Permskiy gosuniversitet S-~L,te iniverzity' -and
Aoo
Pmiiskiy edap---icheskiy in-~j.Lut;
Institut
SUE`.IIT-2..0: January 8, 1958
Card 4/4

SOV/'126-6-2-22/34
AUTEORS: GeU~4.~L,_ G.. Z. and Zhukhovitskiy, Ye. R.
- -1
TITLE: Forced Vibrations in an Elasto-Plastic System
(Vynuz,1idewiy,ye kolebwAya v uprugo-plas~ticlieskoy sisteffle)
PERIODICAL: Fizika Metallov i Metallovedeniye, 1958, Vol 6, Nr 2,
PP 339-346 (USSR)
ABSTRACT: Forced vibrations in an elasto-plikstic system beyond
the elastic limit are considered. Friction and hysteresis
are taken into account, The resonance properties of such
a system are discussed and compared with the experimental
data given in Refs. 1 and 2. The equation of motion of a
point under the action of an elasta-plastic force F(x)
and an external forcErG sin (wt + 9) is of the followinE
form
43
my + Xx + F(x) = G sin (wt + ~p) (2)
where X is the coefficient of friction and F(x) is given
by-
FI= k3. x? FI, = Fm + k2(x - T~idl (3)
Card JILL FIII = klox. -A), FIV = -Fm + k2 (-Y~ + x. _A).j

307,/126-6-2-22/~,'4
Forced Vibrations in an Elasto-Plastic System
where the various constants have the maesnin6 indicated
in Fi~,.1. The above equation is then re-written in the
dimensionless foria
x + OZ 4 g Oill (Pt -1 41)
where
p W/Wo, g G/Fm, X/mw,, f + F/Fm
f X, f 11 1 + a (x - 1),
fIII ~ x 5) fIV ~ 1 + a (x + 1. 6),
6=ja- and cc= 2
xM k1
The problem consists of finding periodic solutiona of' the
above equation which have a period 2rr/p, i.e. equal to the
period of the forcer. The appropriate system of bouiidary
conditions is Eiven by Eq.(6). The equi~tions, ar,:! solvA by
Card 2/4 an approximation method suEE;ested 'by B. G. Galerkin,

Forced Vibrati.,ns in an Elasto-Plastic System WV126-6-2-22/31/4
In the case P = 0 the resonance curves are as shown In
Figs. 2 and 3 (a = k /k cf Fig.1). The for-a of the
2
curves indicates the prhenc; of considerable absorption,
due to hysteresis. The as,~yimnetry of the curveo
becomes aiore pronounced as ot decreases. The low,
frequency side of the resonance curve Is steeper than
the high frequency side. When the coefficient of
friction is not zero the resonance frequi.,rcy beyoInd the
elastic limit increases as friction incri.,aseE. In
Seneral, the resonance frequency deci-cas,~!.- -t lar6er
amplitudes of vibration and the relation bet%ieen the
amplitude of vibration and the owl'Aitude of the forcl-I.,
function is non-linear. The problem sui~t~ested by
Professor INI. Ko.--afelld. There are 7 fiEures omd
4 references, 3 of %,:hich are Soviet, 1 EnElish.
Card 31L~

Forced iri an ~,lasto-Plavjtic Systam ;ll'.JV1l~r,_r.
ASSOCLITION3: P--.v~iiskiy gosudarrtvennyy universitet
(Per:, ' O"tate University) and
1,ori.isldy pedaGo~ichesl:iy instLtUl;
(Perm' FedaL;o:7ical Institute)
SUBMITTJO. June ',', 1c,'456-
Card 4/4 1. Vibration-Theory 2. Mathemat-ics-Applications

r
AUTHORS: Gersh zhilkbovitskiy, Y-_.. sovl 56-34 -,,-2c
TITLE: The itationary Convective Motion of an _;`loctrically Conducting
Liquid Between Parallel jurfaces in a 11.1agietic Field Stp.Loion-
arnoye konvektivnoye dvizheniye elektroprovodyashcht~.y zhid-
'.osti riezhdu parallellilymi ploskostyani v m~iq~:nitnom pole)
PERIODICAL: Zhurnal Ekoperimentallnoy i 'Poore ti clie okoy Tiziki, I-)5a,
Vol. 34, Nr 3, 1,P. 670-674 (U~jil)
ABSTRACT: The t~ao planes referrred to i,, th~! title iirt~~ be ~ieated to
various t enperat tires. First, the eijU_'Lti011S of t,ie mr--ticn ;f the
medium (these are the equations of convection in the case in-
vestigated here) and the Maxwell equations for the field in the
medium are written do-in. In the equation for the curl o-. -the
raa,--netic field, the displacement cu,.--ent is neglected and in
the equation of heat conduction - the tou~-,h dissiration and
Joule dissipation. The electric field stren,--th and the current
density are eliminated first from Maxwell's e:,uation. The
above-mentioned equations are subs-~quently converted into di-
mensionless variableo. 4 dimensionless parwiieters occur in
Card 1/3 these equations. The authors i rive!; ti,qa to h(.'Ve the steadj

The Stationary Convective Motion of an Llectrically
Liquid Between Parallel Surfaces in a 'magnetic Field
Card 2/3
ffV/56-34-3-20/55
Condue ing
convection in the space between vertical parallel surfaces
in the case of the prejence of an exterior in-,te.,,tietic field
which is vertical to the surfaces. If the linear dimensions
of the surfaces ar~? sufficiently vreat compared with the
distance between them, then an accurate 3o-lution of tl-~e above-
-mentioned dimensionless e(iuations can be determined which
describes the steady solution in t"he part dio-tanced from the
ends of the Eap formed by the surfaces. 'Zhis motion has the
following pecularities: 1) The velocity v is always parallel
to the ---axis. 2) The temperature T Jepends only on x. 3) The
field-vector 7 is situated everywhere in the surface (xz),
viz. it holds H = 0; 4) All values do not dcLend on y
y j
(plane problem) and e:ccept pressure, neither on z. In this
case the z-8-xis is parallel to the 3%irface!Li and the :c-axis is
vertical to them. The authors determine here the distributicii
of teraperaturep velocity and field strength an the c-2oss
section. First, T = -x is found. -Ilso the terms for the
velocity distribution and the m~-,gnL~t;c fiold 3tron-th are
given explicitelyi all these formula; to, 'etfter repr~e3ent the
solution of the problem discussed here. A dia.!-ram lemorl'strates
the velocity-distributions for the Gartrr-ian numbers '.: -

SOV/56-34-3-20/55
The Stationary Convei~tive 1.1otion of an Electric.,-,Ily Ccnducting
Liquid Between Parallel Surfaces in a 114'agnatic Field
The velocitydistribution v - Gx(x2 - 1)/6 is obtained with
lacking field. The notion decreaser, raEidly with incrapsin(,-
field strength. Moreover, a peculiar boundary layer uccuro in
the flow: A thin layer with an i ~portmnt --radient of vel,~Citz(
is formed in the vicinity of the -ffallt~. Alca t'-e distri'jutior,
of t1he induced ma~~netic field on cros3 i3 dalonstrat-
ed Ivy a diagram. Co-ic1.id1-'n[:, a furimil.,!. for the vei,tical Co.,.-
vective thernic flow is Jven. The *olution fcuad '-,ere de-
scribes the motion in a vertical E;ap in th,~ j--esence of a
transverial external field. It may, however, be readilf
generalized for cases with inclined ~.-tp and with an external
field oriented at random. There ur- 2 fiEures and 3 refe.-~uces,
1 of which is Soviet.
ASSOCIATION: Permskliy gu3udarstvennyy univer:iitet (Perm state university),
PerM3kiy pedagogicheskiy institut (Perm Pc:dajorical Institute,
SUBMITTED: Septei,,iber 19, 19557
Card 3/3

7~ -2 ~ /r 7'
A UTIIC R.";; Y,!. S07/ 56- 34
TITY': On the Stability of Stently Convective I.lo',Iion of :in
"Ipctric;~Ily Clonductim LiquN !-r..Ilel
:Irmor, in :i 'I!,,rnotir Field l0b 0
ko.--v ivnn-o .1v i i,~ a r~p.,rovo'y-l
1.1 1 1 ny,~i v ~rt. ikal
nolo 'I
P..IRIC-DTCtT,.- 7hii-t-mil i - .0 1,
nn.. 'U3 ;R)
ABSTRACT: First the authors r-~'tar to t 'I,;
s ame witt j e c t mctri- th,~ one vi !J i i ie I bly 4: h v e I,io s (I.-, f', I
'Ph e n f? r - I i 7 P. o ri i c., h r. c r~ :i o C) !-o:1 c, I
11 (.j.'; L 01 0 1'0 Ll f'; '~'l 1. , t h't -I i - I t 11 9 U!, 1~ I I t t~ aly
pro-)Ie:;i rr: o Otit in the same Vey as G.Z. Gersh=i
in his studY o ~j 11 f. ~ o: 1:1 1* 0 r t II t?
nerturb.9 t i r u d o,.-i n t h e ai~ t 1) o r r nv Yi
L
t,vto-dimens lon%~.l p;.,rturbP tion.~: I ~,o A. curri;n t func tio -I -T:
C,?r,l 1/ 4 a v,:~ c t o r )o t e n t i.,~ I n r- ; n t roduc T! i n f t1h i. i n n

On thin Stnbility of 33tenly Cori,-(-~iv,-- 1.0ti-)-i of 'In SOV/56-34-3-21/55
callyConductLn,g LiquI.1 ~etwr.,rin Vertimil 1~% xr! - !i.,t ic
Field
part of the fr:2,!uenryul 0w beh,%viour of s-Ir'll
perturbations. The mithorli then ieritior, t+~,
equations for thF~ nmplitiHos t!i-~ perfuri)F-tioni,-, of velo-
city Pnd tern w,rfi tii ro :molk in f1ti. pilr,:-Ilol
V) i -- r Y
plr.nr~s bounlin 'rr the liqiii,l; '1w ouri
con-UlAwi,. Pre :,ill lown. '.1if, 1) ()r *,,!Jj~
fi-Ad no,!-I, ir. ,-,-n,~ral, r;
I- nol, Ii is Imimdury con
dition~j for tho field ni(!rvo the w;-0 -c-0; I iriv~ on Qvt
2eparating surfacev of th-~ !vAi'-.' farthermore' trto poorjiblo,
ori-~.,itationa of the ronst.tint, fi-~dd it-1,. inv-,.-:;ti,-rtterI:
1 . -Thp C0!13 f i Vi t h-)iion-otious extert~!-~I fi--Id iS 3ituat~-i at
th il
rizrlit
V:! CGVI 1:1 lot"Ofli of t1lo liql.,il.
of th,
2.-The externr!`%. fi(Ad hP7 th, :3"~,i
city. 'Ath !,~,Ili fl.-v! the
P
,,Iplitiltie of t~i voctor T)ot~~!itiai rl' th~,
th", field C:-.11 b 'h
thon r,Auk!1) ; to Ahp f ()f t1w of the CI.I-rimit
functioa nn,l of lv~):.j t1r, .' -,-jur oLI the
C--ri 2/ 4 ~ro))Iem an-I the I cf),iIitII:I!I to Lt.

Oil the Stn.1" of sleal,; con,,!--Ctiv~! "'.otior. 0, an SOV/%-34 -','-21,/5,=
1.11., Liquid 3ptw,~eri P rallf~l V,~-rtic!il in -i
Tlii~- pro~l~-mi will. h)*,r,-~ a solutio.,; o-ill, for cort.,dn vql~i~,-,
c~ tl,,e co,ipIc2x numbor W . In tho .jocorill chtipter of thii
,,-orl,z t!,. ~ probl~ri for i-iI is accorli-w,
1 1, C) 'I
,o `i- nothotl bit ',.-iler'.in, tho of ,ti
b,-,inl--~ lollow;A st -p by 3tpp. "he r~,3sults obtali ned are
,iopar-itoly for th.. case of ti lori,,itu,11mil ~rld
n t ntlaxil? ril ~ C t:-., Id .Fri f,~W 1, V;1,,1.1Vtirio Oio (~ri t ical,
wave numb!~r k iecreasi~,--; monotonougl.-T ith iq.(,~reasinf-, It
fic-11. 3tr:)a-t?r th 'it , ,
i.!?. %vith the ing, -j f, e
lenc~tli of tho at.?ady perturblAions, Residios,
the inve'sti-a"A s'l,),il,! L a i ".1i
I . . iol,-ion :-j ilso L
r,~gard to rionsteady perturbationn, when a tra-i3v2rse
iii or23ent. Such a 1nstk1R1)t1i.t1-,v ap:-.,~nrs at sufficiently
great fiold 3tr ,-,ngth:;;. A -lia,-ra~i showi the flepondence of
the critical. ~vlvo iumbur on tho fiold strea.,,:th. T-i tho
case of a longitiijinal field thu -~tnlrl.lLty con ~.3
couipensated on1j, by st~--P-rly perturbations withu)= 0 . A
Card 3,14 Ion,~itul'n:il f Lelc! incroasoi th~ 1,~01h' 1' ty -.)f -,ot,*(,n

Gfl the StabilLti of Stea~ly ConvQeVvu, ~,otLon of -m SOV/ 56-34 -3-2 1,11,'z
Slectrim,illy Conluctinj~ Liquid Betwoon P!~rall,-~-l Plr~-.fln in a
.1agnatic Fleld
much le.,jo than n ti-vitivorno f-I
fiold tho criticnI vvlr~ auril),.!r innoto,'.0uoly
~"' 1 th ;ncr- ~ n!- ' ! ~ 11 3 t V~117, t h. Tho IV, 1 1 7--- r~~ ~jn I-,"
obtained can be made more precise by their
lull, 10'4 Wlr!d. ~ r'-' :' I t'
ond 9 r,~f ~r,arwoa, 4 of .-Ii i.nh ii r!-~ Lo t.
AS~30 C I A T I C,;: Per-a3k.iy -oottrip-rot,,runny u-i iv,~ri t~~ t tat:~ -'niv,~ ~i 1 ty
Pe r';-L) Per is kiy !7oz;lt pe :.,,i -or i "I n3 t i t1i t
"~Per:,.i I-tritu Pedalr0l,"L.- InsT i tu ~, o
SUB,',-IITT,"D:
Card 4/!l

rt /6 V-2
--IA twrr.-d
11-tr%
PI-14 p -~W qI rrwU -IA
&r&
--d-A aq,
ri-Id zr--~ftx
-..q 2v ..TITTXM
;c .1-M J. -4*w
-7- 1---" 'ME T-2-2
J. 21.,
(-rs -arl) r~_ J.
.-Cm ~j -1 1-.. J~ -j.--TTdd. Am
-.."d Inv. -.9 -TI- cc J. Penn_ .%Ma
A%rrpqw
_2':W M-14 - -9 --, J-
R% V_ .. i 1
..r-Cp..VCqmwq_ S".
"e6. -d
I- rm---n -1 --nR-L-d Vt. Vp S-C Z_= .0
V-.7-TV .1 V-q --I -oj V~lpu~p " = -0- , i
Aq --d-6 -.d.4 . . . . . . .J~ "S
*RM -n V"q -%
q% v% At-r%9- Vj.% q m -
.-.j- -TpTV -.dd j;~ pm ,m -pa
%-&A-9 -4~ J. ft~d I.-III.TV -~j -d C.7t
V.rrdA. al -n-1A vI S. qk ftU-n.9
%.-.JJTP .1 q~__ sm- ., . .,
.R. -.q %~-. IN--- V.7t.. V= T..n-
-O-R% -t "-I I-q r. q% ja "MT
'qZ ". V" 1".Ldd -3 --tq-d - 'OM -W
.3 _aUK-nu 'MMKNM
V-
J. Inns -n v%-T.Tb4d AOS Vp~.T " X.K M IXMU=g
9_16
'-rA V-
"VVTP-2 'TMTA *V'A 1"T"-WS-K
'-x,A v- -,T-em a- aow-a
W -M-4 'It-P-10A 'X-1
t-4 ATX"__M_T_A1 -ea rp~ft Tnftlm
-P"V 19--ow
-Tdov oootl ~p*3.xpftn CM wwwLxg
Am"T.".1 " -pn --u
I-O.-t4 _,w 99 _j%am)
A...qd 1PET-m I prv-.rp..Vo A-=. A--"A
-WIC '.*I& *.qT-.Tp-Vo A~l d
N====M 3m x now
---- ------

24(8)
AUTHORS: ~e~.shuniG. Z. , ~/hukhovitskiy, Ye. Mi. SOV/2G-l 24-2-15/71
TITLE- A Closed Convective '-Poundary Layer
(Zamknutyy konvektivnyy pogranichnyy aloy)
PERIODICAL: Doklady Akademij. nauk SSSTI, 1959, Vol 124, Jr 2, pp 296-300
(USSR)
ABSTRACT: The present paper solves the problem of the closed convective
boundary layer in a horizontal circular cylinder. The surface
of the cylinder with a radius R is kept at the temperature
To = Osin x, where x denotes the coordinatealong the circle and
@a time-constant amplitude. The temperature assumed to be
homogeneous in the core is considered to be the temperature of
refdrence. The core is assumed to rotate as a solid at the rate
vf = W r, where the angular velocity W is required. The
boundary layer equations (in disregard of the curvature of the
layer and with introduction of dimensionless variables) are;
~vx vx 2v x 10
v
Card 1/3 x 'Dx , 'Y Dy ~Y2 + G sin x T

A Closed Convective Boundary Layer
v DT =v -DT 1 2T
X ~)X Y by - Pr ~Y2
Card 2/3
SOV/20-124-2-15/71.
~vX ~v
+ Y - 0
X "a Y
Here G = g p 0 R3/V 2 denotes the Grasskhof number and
Pr = VIX the Prandt! number, The velocity layer and the
temperature layer are assumed to have the same thickness
6(6