JPRS ID: 8451 TRANSLATIONS ON USSR SCIENCES AND TECHNOLOGY PHYSICAL SCIENCES AND TECHNOLOGY

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i� MAY i9T9 CFOUO 26l?9~ - i OF 2
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Jp~s L/e45~
1.0 May ~9 79
~
TRANSLATIONS ON USSR SCIENCE AND TECHNOLOGY
PNYSICAL SCIENCES AND TECHNOLOGY
(FOUO 2bi79)
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JPR5 L/8451 -
~.a May 19 79 ,
TRANSLATIONS ON USSR SCIENCE AND TE~HNOLOGY
PHYSICAL SCIENCES AND. TECHNOLOGY
(FOUO 26/79)
CONTENTS PAGE
EL~CTRONICS AND ELECTRICAL ENCINEIItING ~
Microwave Rad i~tion Spectra of Forest Fire Foci.
(Yu. P. Stakankin; RADIOTEI~INIKA I F,LEKTRONIKA,
Jan 79) 1
DeCermination o# the Effecti~enass of an Evaluat~on-
Correlation Detector o# Signals With Unknown Delay by
the Method of St~atiatical Simulation
(M. A. Gostyukhina; RADIOTEIQiNIKA I ~LEICTRONIKA,
Jan 79) 7
Optimal Selection of Interference by Duration in a Passive
Infrared Syetem
(N. A. Dol3nin; RADIOTEKHNIKA I ELIICTRONIKA, Jan 79)...... 11
Toward the Evaluarion af the Accuracy of E~holocation Range
Measuremente by Means of Prequency-Modulated S3gnals
(V. I. Aleahchenko, et al.; RADIOTEI~NIKA I
- ELEKTRONIKA, Jan 19} 15
Linear Regenerator Fabricated With EIybrid Integrated
Technology
(A. 2i. Mekkel' , et al, ; ELEK'TROSVYAZ' , J~tn 79)........... . 18
Interference Immunity in Communication Systema
(L. E. Varakin; E7,EKTROSVYAZ', Jan 79) 25
Unified Automated Communications NetWOrk Terms Explai.ned
~ (T. A. Vladiairova, et A1.; ELEYTItOSVXAZ', Jan 79)........ 37
- a- (III - USSR - 23 S& T FOUO]
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- CONTENT3 (Contin~red) Page
GEOPHYSTCS, ASTRONOMY AND SPACE ~
'AIR ~ COSMOS` Reports on `Soyuz-33' Abo'rted Mission
(Pierre Langere~; AI`R & COSMOS, No 162
(21 A~r 79)) 45
StaCistical CharacCeriatice of the Horizontal Structure
of the ~i'ield of 9ma11-Scale Turbulence in the Ocean
(T. D. Lozonatekiy, et a~..; IZVE&TiXA AKADFMII NAUK
SSSR, PIZIKA ATMOSFEAX' ~ OKLANA, No 3, 1979)..�������� 48
Generation of Stationaryr Teanperature Boundary Ial ers by
Surface ~i~ves -
(B. A. Nelep, et al.; ZZVESTIYA AKAAEMII NAUR SSSR,
FIZIKA ATMOSFERY T OKEANA, No 3, 1979) 57
Structure of the Crust and IIppEr Mantle in the Western
~ Ukraine Based on Mater ials From Conprehensive Interpreta-
tion of Seismic and Gravimetric Data -
(A. V. Chekunov, K. A. Bolyubakh; GEOLOGICHESKIY
Z~'URNAL, No 1, 1979) 73
Experience Gained in Combining Seismic Methods in
Studying the Northern Edge of the Caspian Depression ~t
(T. A. Akishev, et al.; GEOLOGIYA NEFTI I GAZA,
No 10, 1978) 90
Study of Rock Denaities in the Caspian Depression Secti~n
Using Gravitational Logging
(V. F. Kononkov, et al.; NEFTEGAZOVAYA GEOLOGIYA I
GEOFIZIKA, No 10, 1978) 97
SCIENTISTS AND SCIENTIFIC 08GANIZATIONS
Meeting of Directors and Leading Workers of Geological
Proagecting Organizations of the USSR Minis~~rp of
Geology
(SOVETSKAYA CEOLOGTXA, No 3, 1979) 104
PUBLICATIONS ~
Successive Linearization Method in Probl~ns o~
Optimization o~ Past
Neutron Rcactors ~
(~lETOD POSLIDOVATEL'NOY LINEARIZAT3I~ Y
ZADACAAI~i OPT7I~IIZATSII REAKTOROV NA BYSTRYKFi
NEYTRONAI~i, 1978) 110
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- CONx~NTS (Cotltiau~d) pgg~
Orbits og Communicat~,ons Satellites
(ORBI',1'Y SPUTNIKOV SVX'AZI, 1978) 114
Simulation of CosomunicAtion Systear ChannelR
(MODELTROVANIYE Kr1NALOV SISTEM S`VY~7I, 1979)......... 116
Computer Programa for Radioelectronic Geai Development
(MASflTNNAXA OPTIMTZATSIYA ELEKIRONNYIQi U2LOV REA,
- 1978)....~a 118 ~
Self Ti~ning Measuring Ampli,#iers Wfth Tes.t Signals
(SAMONASTRAIVAYUSHCHIYESYA IZMERITEL'NYYE
USILIrELI S PROBNYM SIGIdALOM, 1978) 120
Analysie of the Reliability of Eletronic Measuring Equip-
ment in Tts Designing
(ANALIZ NADE2HNOSTI ~LEKTRONNOY IZMERIT~L~NOY
APPARATITRY PRI YEYO ~RAYERTIROVEINII, 1978)........... 122
Simulation and Automation of Electric Power Systems
(MODELIROVANIYE I AVTOMATIZATSIYA ELEKTROENERGET~ `
~ ~ ICHESKII~i SISTEM, 1978) I24
Production of Semiconductors Casings
(PROIZVODSTDO KORPDSOD POLUPROVODNIKOVYKH PRIROROV,
1978) 127
New Book on Application of Microcircuits
(MIKROSKHEMY I IKH PRIMENENIYE, 1978) 130
~
-c-
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ELL'C'rRONICS AND ELECTRICAL CNGINC~RING
UDC 621.37/39.029.64,004:634
MTCROWAV~ RADIATION SPECTRA OF FOR~ST FIRE I'OCI
Moscow RADIOTEKHNIKA I CLEKTRONIKA in Rusaign No 1, JAn 79 pp 177-180
[Article by Yu. P. Stakankin, aubmitted 13 Jan 77]
_ [TexC] 1. The possibiliCy of using microwave radiometry in aCudying foreaC
fires was discueaed in work [1]. It was ehown ChaC the flame apecCrum ia de-
termined by the dimensions and concentraCion of particles in Che flame and
by its heighC. It was also establiahed that, for detecCing and mapping for-
est fire foci when the ~rea is screened by amoke and under the canopy of the
forest, the optimal working wave band is 0.8-1.5 cm, Data of experiments in
determining Che radiation capacity of fire foci cn 0.8 and 3.4 cm waves were
given.
For the purpoaes of further atudies on foreat fire foci by the methode of
microwave radiometry, it became necessary Co examine models of varioua types
of forest fire foci from the viewpoint of the apecial characCeristica of
their spectra of radio-brightness temperaturea, as well as to conducC experi-
mental studies on microwave radiation of the foci in a wide wave range.
2. The main components of a foci which form the spectrum of radio-brightness
temperature are the flame, smoke trail, crown, and underlying aurface.
As a rule, the focua has a complex geometrical ahape, and for calculating
spectra of various foci, it i~ practical to examine a simplified model in
the form of homogeneous isothermal layers of flame, smoke and the crown sit-
uated on an underlying aurface.
It is possible to show that the radio-brightness temperature of the atrati-
fied model described above is determined by the following relation:
T�i~ ( f x(]l) r~~-*,~~?+T=(t -e~ Je-=~l~).~
tT~(f-e-*~~"1)}e-afA).}T~(!-e'~~~~~), ~1~
where yL(~) is the radiation capacity of the underlying surfac~; T1,T2,T3
T~ are thermodynamic temperatures of the underlying surFace, flame, smoke,
and the crawn~ respectively; 'C2, '=3, L 4 are the optical thickneases of
the flame, smoke, and crown, respectively.
1
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The optical rhicknesa in the direcCion of probing is determined by Che rela-
tion
T(1~) d~(~,)G, ~2~
where 'Y(~1.) ia tihe abaorption coefficienC aC a unit of path; L ie Che layer
thicknesa.
If Che volume concentraCion of the particlea of radius a in the layer is equal
to N(a), and o'~ (a) is the value of the effective absorption crosa secCion,
tha~the abeorpCion coefficient
a~~~
'f(7~)� ~ oa(a)N(a)da. ~3)
0
Methods for calculating absorption coefficienta for flame, smoke and Che
crown are given in [1].
3. Varioua foci of forest fires are characterized by different degrees of
heating of the underlying surface, differenC power of the amoke trail, and
different flame parameters. �
Calculations for the spectra of radio-brightneas Cemperature for various foci
were done by the above formulas (1)-(3) with the following ger~eral asaumptions.
The radiation capaciCy of the underlying surfacea was taken to be equal to
_ one for all waves. The height of the flame was 2 m, and the weight concen-
tration of parti~les was 3�10'S g/cm3. The thickness of the smoke layer was
10 m, and the weight concentration of smoke particlea was 3�10"6 g/cm3. Par-
ticles of flame and smoke have the Rayleigh distribution with respect to size
with maximums of 150 and 100 micrometers respectively. The thicknesa of the
crown was taken to be equal to 2 m. The the'cmodynamic temperature of the crown
and smoke was equal to 300 degrees K, and that of flame was 900 degrees K.
The coefficient of absorption i~ the crown at various wsves was selecCed ac-
cording to the data given in work [1]. Cases of changes in these parameters
wi11 be mentiuned specially.
The results of the calculations of the spectr~ of the radio-brightnesa tem-
perature of var.ious foci are shown in Figure 1.
Curves 1 and 2 characterize the spectra of foci covered by Che amok~ trail
and located under the crowns of trees. The temperature of the underlying
surface T1 for case 1 is taken to be equal to 400 degrees K, and for case 2
- it is equal to 300 degrees k.
It can be seen from the curves that temperature changes in the underlying
surface lead to aubstantial changes only in the long^wave part of the apec-
trum.
2
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Curvc 3 churACterizes radineion af ehe hurning secCion ai~uuted in An open `
areri ( n Clie ahAenca nf Cha emako trnil.
In ei~te cuse, in Enxmul~ (1) ~3 0 Attd 24 ~ 0. The temperatutce oF Che
underl,ying suxface was Caken Co be 400 degreea K. -
It can be seen from tt?e above curves rhae in thc: absence of Che screening
effcect of amoke and the crown, a higl~er radio-brigheness Cemperature of the
fnci is observed in the sliortwave part of� the apecCrum thAn in Che case of
foci 1 and 2.
Yt Is oC interest to c~lculute l�he spectrum ot n focua in which there ia no
flame ('~2 ~ 0). By compari.ng it with other spectra, iC is possible to eval-
uate the contribuCion of flume eo Che microwave radiation of the foci. In
- the absence of flnme, Che radio-brightnesa Cemperalure of Che fire focue will
- be deCermined in the region of shortwaves by the radiation of the crown and
the amoke Crail, and in the area of long waves iC will be detexmined by the
radiation of the underlying surface (curve G). Calculation showed that flame
makes the main contribution to the radiaCion of foci in the microwave runge.
T,,,'K
900 ~
800
700 ~ _
600 _
S00 . ?
400 4
300 `
Q8 ~,35 2,25 ,1,~ 10 20 ~,ck
Figure 1. Calculated Spectra of the Radio-BrighCnesa
Temperatures of ~:oreat Fire Foci:
1-- a focus under the canopy of the forest
covered by a amoke trail, temperature of the
underlying surface 400 degrees K; 2-- a foct~s
of type 1, temperature of the underlying sur-
face 300 degrees K; 3-- a focus in an open -
area ~~ithout the smoke rrails; 4-- burnt part
` of a Focu~s withouC flame.
Analysis of curves 1-4 showed that various componenCa of a focus (flame,
emoke, crown, underlying surface) affect substa~itially variouo sections o�
the spectrum of radio-brightness temperaeures,�~hich makes it posaible to
evaluate their parameters.
3
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~
xtiP,E5cr+
I~�'
(1) ypoBeNe
~ u,fny veNU~
- necv
- Ito~ ~
1l~focN
I,o. ~.~o~N ~
Figure 2. Profile of the Radio-Brightnesa Temperature of
a Forest Fire Focua on 2.25, 10, and 30 cm Waves.
Key: 1. Level of forest radiation
.
T~,
a
~ ~oo
- soo
soo
i
400 3 1
J~ Q8 1,35 2,25 9,4 10 YO .t,tM
Figure 3. Experimental Spectra of Radio-Brightnesa
Temperatures of Foreat Fires:
1 and 2-- spectra of burning aections of
the focus; 3-- apectrum of a burnt part of
the focus.
~ 4
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4. Experimental sCudies on tt~e microwave ~radiaCion of foreat �ires were con-
ductad From aboard an airborne laboratory "IL-18" on 0,3, 1.35, 2.25, 3.4,
10, 20, and 30 cm waves.
The main chazacCeriatica ot ttie radiomeeers used for measuring self-radiation
- of foreat firea are given in the table
~
_ Flight No WavPbend, Fluctuation Antenna Pattern
- cm Senaitivity at Width, degreea
''C ~ 1 sec
1 O.g 0.4 3 -
2 1.35 0.3 4
3 2.25 0.2 S ~
4 3.4 0.6 7
5 10 0.5 7
6 20 0 .4 15
7 30 0 .4 26
The flighta were conduceed r~t heighCS of 100-400 m. Radiometric insCrumenrs
were calibrated by the radi~~-brighCness temper~Cure gradient of homogeneoua
sections of the forest and water aurface with known r~diation capaciry. The
exper.imental results were proceased with consideraCion for Che anCennA pat-
terns. Natural fires in Krasnoyarakiy Kray were studied. As a result of ehe
analysis of large volume of experimental material, it was establiahed that
maximums of the radio-brightness temperaturea of fire foci, depending on their
special characteristice, can occur in a rather wide waveband, 0.8-10 cm. In
the long-wave part of the spectrum of 10-30 cm, the radio-brightnesa temper-
ature of fire foci is very low.
The characteristic radio-brightness temperature disCribution in a forest fire
focus on waves of 2.25, 10, and 30 cm is shown in Figure 2. As can be aeen
�rom the figure, the maximum radio-brightness temperature in Che focua zone
is observed on a wave of 2.25 cm. The increment of the radio-brightnesa tem-
perature i.n the focus zone on a 30 cm wave is small.
Figure 3 shows typical apectra of burning edges of foreat fire foci (curves
1 and 2), as well as the spectrum of the burnt parC of the focus (curve 3).
It can be aeen from the curves that the radio-brightnesa temperature of the
~ burning edge reduced to its dimensions is conaiderably higher than the radio-
brightness temperature of the burnt part. This indicates a predominant con-
tribution of flame to the microwave radiation of the foci.
The specinl characteristics of the spectra (1-3) can be explained by the in-
fluence of various components of the focus described above.
Analysis of the obtained theoretical and experimental results makes it pos-
sible to make the followi.;~ conclusions.
S
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1. The specCra of radin-brighCnesa temperaCurea oF �orese fire foci depend
on ~rl~e parametera of Che f lame, on Che power of the smoke Cr.~il And Che crown,
and the degree of heating of Che underlying aurface. _
2. The maximum of the radio-brightnesa temperature o� a forest fire focus
is determined by Che special characCeristica of the focus~ F~~r foreat firea,
_ it lies within the 0.8-10 cm wave range, which ie is most pra~tical Co uge
for detection and mapping of foci.
3. In the 0.8-10 cm wave rc~nge, khe radio-brightness remperat~;re of Che
burning edge is consider~bly higher than Che radio-brightneas cemperature of
the burnt parr of the focus, which con�irma the predominant c,onCribution of _
flame to rhe radiaCion of foci in thia range~ In Che 10-?i! cm region of the
spectrum, the radio-brighCness eemperature of Che focua is determined boCh
by ehe radtation of the flame, and by Che radiation of Che underlying surface.
Bibliography
1. Borodin, L. F.; Ki.rdyashev, K. P.; SCakankin, Yu. P.; and Chukhlantaev,
A. A. RADIOTEKHNIKA I ELEKTRONIKA, 1976, 21, 9, 1945.
COPYRIGHT: Izdatel'stvo "Nauka", "Radiotekhnika i elektronika", 1979
10,233
CSO: 1870
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~~�oit c~rrtr,rnr, u5~: oN~,Y
~ ~EC'ri20NICS AND EL~CTRYCAL ENGIIV~ERYNG
UDC 621.396,96
DCTEEtMINATION THE EFFECTIV~NESS OF AN I:VAT,,JATION-CORRELATION DI:TECTOR OF
- SIGNALS WIT}i UNI~IOWN UELAY BY TN~ MCTHOD G'r' STATISTTCAL SIMULATION
Moscow RADIOTEIti1NI1CA I ELEKTRONIKA in RussiAn No 1, Jan 79 pp 184-185
[Article by M. A. Gosryukhina, submitted 6 May 1977]
[Text] The work [1] gives Che results of u Cheoretical analysis and experi-
_ mental studies of an evaluation-correlation detector of signals with an un-
known delay which uses a follow-up system us a signal delay evaluation unit
with constant parameters and astaticism of Che first order and compAres it
with an ordinary gated detecCor. This article gives the resulrs of Che de-
termination of Che effectiveness of the above-mentioned detectors with posr-
- detecCion processing nf a group o~ radio pulses flucCuating simulCaneously
by the meChod of startstical digital simulation.
Ia Simulating F.he detectors, the following assumptions were made. The obser-
vation time was fixed and was equal to the length of the group of radio pulsea
no. The input signal was a group of radio pulses of the Gaussian shape.
The amplitude distribution law of each pulse was the Rayleigh Law, and the
distribution law of the initial phase was uniform in the interval (0,2`jT).
The correlaCion function of amplitude fluctuations was exponential with the
time of correlution exceeding the duration of the group. The frequency
charACteristic of the UPCh [intermediate �requency amplifier] was coordinated
= with the spectrum of Che input radio pulse. In otder to ensure a wide dynamic
range, the detectors were provided with an ARU [automatic gain control] system.
The detector was a linear inertia-free envelope deter_tor.. The posL-detector
integraCur was a synchronous equilibrium adder.
- In preparing a digital simulation algorithm of the formation of the input pro-
cess and its conversion in the UPCh and the detector, the method described
in work [2] is used. For the formation of discrete components of the signal
and noise, recurring algorithms of the simulation of the realization of ran-
dom processes are used, The envelope method is used in simulating the con- -
version of narrow-band processes by the selective circuiCs of the UPCh. The
UPCh is replaced by an optimal filter with a transmission factor on the res-�
- onance frequency equal to one and an inertia-free amplifier with the gain
factor controlled by means of the ARU which are connected in series. A se-
quence wtth a random pulse shape at the inpuC of the ARU system is replaced
7 -
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with a g~quence of ~ ~funceir,ne with g rgndnm ~nnplitude proporrion~l yd r}1r
- mean vctlue of the envelop~ of ehe ~ignal nnd noise mixture at the UPCh oUt-
- put wiChin the iimies of Che gating pulse~ -
'Che vdleage ae the output of the inCegraeor of ehe evalu~eion-correlneion
detector (~t tihe unie tr~ns~mi~eion coefficienta of eh~ coincidett~e cireuit
and ehe inCegrator) in Che n-Ch period nf r.epetitinn is expreased in Che
Eorm of
vtn~.t~et~f
s(n~.. ~ vln~ mJ'
m~x~*~it~1
wher~ No ie the initi~l poaitton of the reference pulse; mo ie the number of
di~nrete v~luea of the envalope within the limiCa of the duration of tl~e re-
ferenc~ pulse; t~ [n] is rhe time miematct?ing of the signal pulae and the
g~Cing pulae; m~ t/L~t is the integral argument (C i9 the Cime ftom Che mo-
' ment oE Che arrival of the aign�.1 pulg~; Q t ia the quanr,if iceCio~ epacing);
V(n,m] is the envelopc of Che mixture of tt~a aignal wiCh the r.nise at Che
UPCh outpuC [i].
. The time miamatching is equal to [3]
t,(nJ-t.(n-i)-et�(nj,
where ~tM[n] ie the change in the time pnsition of the gating pulse during
the repetition cycle.
The change in the time miamatching ia equnl Co
At~(~~~kr=i~~~~
where kM is the transmission coefficient of the Cime modulator; z R(n1 is
change in cont~�ol voltag+e during the repetition cycle.
The change in t:he contYOl voltage a[ unit transmieaion coeffi~ciente of the
coincidence circuita of the time discriminator ia proportional to the value
Of N~~~~*~~lel r~t~~*~~I~I
1 y~~~ N! V n, m).
~ ~ ~
=~~n~,~ ,
N, ,~~,v~~~t~1
~,~.r~*~~l~l
where N1, N2 are the initial time positiona of "half�atrobea"; mi, m2~~repre-
sent the number of discrete valuea Within the limita of half-atrobes .
The voltage at the output of the integrator of an ordinary detector With a
fixed time poaition of the gating pulse is expressed in the form of
='IRl- ~ VI~, ~l,
_ ~,_r~
8
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~ ~
,i i
~
Q6 a / i ,
.
F 10 _ , dife'n ~ .
Q~ .
/ ~i ~
i
, 0,2 , ~
~ i
i
~ti -z o 2 a 6 ~ g,e~ ~1) LL
UeCecCion ChernaterieCicg; solid curveg nf evalugeion-
correlaeion dercctor at F,o e 0.5; d~shed curves of a
detector with g~ting et Eo ~ 0,5; d~ph-~nd-doe curvea
of a detector with gating at E o� 0; nn ~ 64. -
K~y; 1. dB
where N~ is the tnitiyl Cime poeiCion of the gating pulse; m~ ie ChQ number
of discreee values within Che limiC~ of Che gating pulse.
The charucteriatics of the detector are determined by mettns of the~ method of
the Mnnte-Carlo st~tistiCal teete and the extreme stliCiaCica mer.hod [4]. The
eimulating algorithma were realized on a dtgiCal computer "M-4030". The solv-
ing wns done with the following values of tt~e parAmetera: Q,t � ZH /6 H
length of the aignal pulae), the ratto of the signal cc~rrection time to
the repetirion cycle is equal to 2no, the tranamiasi~n coefficient of the
ARU feedback circuit is equ~l to 1000, the ARU time coneta~it is equal to the
signal correlation tfine. The number oE realiz~tions wae tnken to be aqual
- to 100 in determining the detection character4.stic by the Monte-Carlo method
and equ~l Co 106 in decermining the dependence of the probability of falee
alarm ~ on th;,+ detection threahold.
Detection characteristics ofr the evaluAtton-correlation detector were deter-
mined ae the greatest initial time miematching equal to one-half of the aper- -
ture of the discriminntion characteristic of ehe follow-up aystem. Detection
characeeristics of ehe ordinary detector Were determined bo~h when the aignal
and gating pulses completely coincided in time~ and When there ~?ae the great-
est time miamatching E a expreaeed i~ the duration of the aignal pulse.
1'hr_ fig~~re shows the dependence of the probebility of correct detection D on
the siRnAl-noia~ ratio q Eor the studted detectors ahen the duration of the
signut pulae is equal to the uperture of the discrimination characteriatic
tn tl~e evaluation-correlation detector and to the duration of the gaCing pulse
in tlie ordinary detector. Aa can be seen, the sensitivity of the evaluation-
correlation detector in the presence of the initial time mismatching Q: the
signal and gating pulses is higher then the sensitivity of the ordinary de- -
tector. For example, at � o ~ 0.5, D~ 0.5, F~ 10"~, thc gain ir, senaitivity
is 2.9 dB.
9
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Thus, g~ ~ resulC of ge~ei~eicgl digie~l eimul~tion of po~e-daC~Cror proceo~-
sin~ oE ~ group of r~dio pulses fluceuating eimult~neouely wi~h bn unknown
_ delay, iC is poseible to consider eetabliehed ehae ehe ev~luaCion-correl~-
= Cion proceseing i~ more effecrive ehan the otidinary proce~eing~
' Bibliogr~phy
1. Gostyu~:hina, M. A., and Sosulin, 1'u. G. RAUIOm~KHNIKA I ELEKTRONIKA,
21, 7, 1434~ 1976.
2. Bykov, V. V. "Tsifrovoye modelirovaniye v eCatiseicheskoy radioCekhnike"
[bigiral Simulation in StaCistical Radio Engineering], Ixd SoveCekoye
- radio, 1971.
= 3. Saybel', A. G~ "Oanovy radiolokaCaii" [~'undamen~al8 of Radar~, Izd Sov~t-
~koye radio, 1961.
4. Likharev, V. A. "Taifrovyye meCody i usCroystva v radiolokateii" [Digi-
Methods and bevices in Radar], Izd SoveCakoye radio, 1973.
C~PYRIGHT: Izdatel'atvo "Nauka", "Radiotekhnika i elektronika", 1979
10,233
CSO: 1870
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i:Li:C'CR(7NLC5 ANU 1:LisC'C(tICAL CNGTNI?~itlN(; -
UDC 621.394.326:~521.396.96
�
OP'CIMAL S~IECTION OF INT~itF~RENC~ BY DUEtATION IN A PASSi1?~ INFI2AR~D SYSTEM
Moecow RADIbTEXHIJIKA 2 EL~KTRONYKA Sn Ituseian No 1, Jan 79 pp ~,86-188
~Articl~ by N. A. Dolinin, submiCtQd 23 June 76]
- [Text] UnCil the pre~Ent time, receivers wieh a relatively large Cime con- `
stgnt huve been used in passive radAr ayatems. In Chis cgse, when it is necea-
sary to select targete and idenCify them, iC is very adv~ntage~ua to use a
~ygtem of aelecCion by duration~ because different objecta ,in the f.~frared
range cre~te signats of vgrious lengtha at the input o� the receiver dependitig _
on the ~ngular dimension~ of each object due Co rhe scanning of the opCical
~ syet~m. The functional diagram of thp selecCor (Figure 1) conaiers of n pho-
toelectric converrer (FEP) whoge out uC ie dclivered Co a line~r fi~~er (LF),
and then to a threshold device (UPS ~device for cenversion of aignels]) to
whc,se second input a pulae with the duration Tn is aent from ~ generator of
threshold-duration pulaea (GIP) which ie triggered by the leadtng edge of the
signal from LF~ The deciaion regarding the preeence or abaence of a uaeful
gignal is registered at the output of the UP~ circuit. Let us note Chat FEP
is a receiver performing angle acanning in epace.
4
(2) ~3~ y~C ve~ler~iue
A 4'
fHll -
Figure 1
Kcy: 1. FEP 3. UPS
2. LF 4. Decision
S. CIP
Let us now describe the properties of the uaeful eignal and the complex of
interfering effecta on the aelector. Let us assume that the amplitudea of the
useful signal and the interference are much greater than the fluctuations of -
the internal noise of the FEP, a:~d, conaequently~ it is poaeible to aelect a
sufficiently high value of the threahold C(C ~ 4C~ , where C~ ia the root-
mean-square vaiue of the internal noise of the PEP) at which false crosaing
l~,
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of Che Chreshol~ by noisa or by tluctugrinn~ of th~ inepn~ity of eh~ useful
ai~nal in Che genCly sloping section of Che pulse ie pYgcCically impo~eible~
SignaYs gC Che F~P input from ehe interference and rhe Cargete are coneidered
Co be recCangular pulses wiCh a random ampliCude x dieCri.buCed according eo
rhe normal law wieh different nverage values (A~, A n) and diapersions (6'c,
6' ) for the signal ~nd the interferenc~. We ehall have ehe following sig-
na~ at ehe FEp nnd LF output:
i,(t)~::(t)~
wher~
o, ~ 0.5 cm�sec-~) were henceforth identif-
ied :~s turbulent spots; }~owever, those sectors where su n nf eurbul~ne ~pd~~ ie w~~
- ~umcd thnr the minimum durutinn e~f n gignifi~nnC ~ign~1 nn individuni
pnrCs df eh~ r~nord h~d ed ~xe~ed 1 gE'.C (ehnt i.g, a gCudy wng m~de nf
turbulent inhomogeneities with horizontal ~c~1e~ ttdt 1~~~ ehnn 2 m). ~'igW
ur~ 1 shnws an exampl~ df g~p~ration of the r~cnrd ineo individugl pnrt~.
~ fYi~M'~�~ ~~~H8C~1
1S ts ~ ~ .
4s ? ~
- o ~an tao ,~aa 400 M ,saa
Fig. 1. Cxample of discriminntion nf zonea of bnckground turbulence and
rurbulent spoes on record of signal of inean gqunre vglues of velocity
fluctunCions s~.
Tnble 1
St.lttseicnl Char~cteristics of Uistributiong of Horizontal Dimensione of
Turbulent 5pots and Zones of Background Tnrbulence -
1 x:2 X s~4 4~ a,~.6 L~7 a~~8 ~=9 ~~1 v=~ ~$1 ~_1
~ ~ 7 r. � ~ Y r i ~ ~ ~ ~ u
~ ~u ~ ~o S=S. =9! ~S a' " ~x Kci x:
' u, ad 3.= ~
~ nx r ~L ~~ti x~' L. e~_ S_~ =:i ~~s?
yI~ Y . "7 : ' O G= G~ ~ v ~t-Y t ~ �
~:7 O :tr `n== i~s .;~7 :7ei-i .:y= ..LY U~a Y�8ii G7'^ ~
t f00 l~ tU~ Fi 13~4 f~4 '.'.;8 1!i :.'.2 0.2 4,8 0,5 1M.0
l� 107 4 fi:)fi 32 i8 2.5 6.:i U,2 ~Or'~ O..i 2~94.I1
2 1 W I� 122 6 A~Fi I I:i t~ U t..~i :'.~J 0,'L U,6 0,4 21..i
1� 122 6 rif~ 35 78 2 ~ :~,7 n.e 37,3 ~~.4 3n.'?.cs
20 45 t~ ~2z �:~c t0~ f~~3 ~.n ~~,z io.s o,4 2~~,~?
1� 122 G 320 36 5Ei 1,5 3,0 0,2 ~J,6 O,~i 83,3
K~:Y:
1. No of run 8. Standard deviation, m
2. Towing horizon, m 9. Variation coefficient
7. Parnmecer 10. Asymmetry coefficient
Number of terms ln series 11. St~ndard deviatiun of asymcnetry
5. Minimum value, m 12. Excess coefficient
G. Maximum value, m 13. Standard deviation of excess
7. Mean value, m
On ttie b~sis of tl~e resulting series of horizontal dimensions of turbulent
spc~ts ~Ci* and zones of buckground turbulence Di~ we carried out computa-
ttons of the statistical characteristics and Q~ for ~lch individual
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H'c)li (11~I~ I.GIAL U~L C1NI~Y
run. Aq an example, 'Cc~b].e 1~ive~ C~e ]imit~ ~f change Ln th~ Eir~t ~our
di.grriUueinn momentis for ~nd a~ wel.l ag ehe varLuCion cneffir.i~ne~
V~ d'/~ (where ~ is ~he mean value ~ind 0' iq the ~tand~rd devigtinn of ehe
i~+crl r.y), nennd.~rd drvinei.c~n~ in cdmputrxtions of ngymmerry nA and exce~~
11~; E'r~~m rccor.ci~ di the yt~;?uil s~ c~n ~~11 r.un~.
n a
i i~ i I
6~ ~
~
~i ,
u'
~ b b ,
i~ ,
6~
, ,
, ii i
u'
~ . , ,
Q c
~
u~ I
I , I
, ~ i
D lA9 L, M ?A'!
Hi~;. 2. Cxamples of zones oE "fossil" turbulence (a), microfronts (b) and
density-homoAeneous layers (c) on records of signals u' and' U'.
idc nvte that the number of turbulent spots on the first run (107) Was ~pw
~~rec:[ably less than on Che two subsequent runs (122), despite the fact
eh~~t run No 2 was situated, like run No 1, in the thermocline, and run
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Nd Zc~ in tih~ qungihnning~n~nue layer. The m~~n horizone~l dim~n~ion~
nf Che Curbul.~nC ~pot~ w~re ~pprnxim.~Cely con~eanC in ~pnce gnd equgl
t~ 32-3G m. llowever, eh~r~ w~g an pppreciab].e difference in Cha very dig-
tributinn of the dimensi.ong oF p~~~~ in ehp homogen~du~ l~y~r gnd in tih~ ,
_ th~rmnc:linQ. ror ex~mplE~, th~ va~riability of at a depth of 100 m w~~
con~iderably gr~at~r ChF?n et a depCh o~ 45 m(V~pp d 2.2-2.5, V4S ~ 1.5);
ehe ma.~cimum dimenai~ns m~ in ehe ehermocline (614 gnd 696 m) ~xce~ded
~gx in the uniform lgyer by ~ facenr of mnre thgn 2(uniform layer, 320
m), and the exne~s valueg ~L00 w~r~ 8r~~sCer by a factnr of 4-5 tihnn ~45� '
A11 thi~ is evidence nf th~ congid~rgbly bett~r d~v~lop~d i~tarmitt~nc~ ~
nf the eurbulent gpotg ~n the thermocline in nomparigon wiCh the upp~r
qu~gihc~mogeneous lnyer. [Th~ etntisCical aignificance in th~ differenc~ in
the dispergion~ ~,*2 and mean vnlues at the horizong 100 nnd 45 m waa
check~d uaing rhe Fi~he~.^ nnd SCudent tesCe. The rnCio of th~ digpersion
for *o' i00~ ~452 � 1.~.~4 was greaC~r Chan the tabulated vaJ~ue Pp~gS
(121.121) ~ 1.35, which meana a significant difference betwepn eh~ di~-
persione of rli~ horizontnl dimensiong of Che rurbulent gpnts at the hori-
zon~ 100 und 45 m. A1Ct~ougti the difference of the mean dimensiona ~
n
nnd ~t~5- was not significnnt wiCh this ~ame confidence level, the varin-
tinn coefficients V100 ~nd V45 for chnrncCeriz ing t he var ia b i l ity oi
in the thermocline and rhe homogeneous layer, significnntly differed
from one nnother.J
m (t)
~ I � *
x-~ "
- pg o-2
�-2a
_ ~M
0,7
0,5
r
0,3 , o
0,1 .
.
qs t,o ~,s 2,0 ~s
~ ~o
rig. 3. Empirical distribution functions of dimensions of zones of back-
ground turbulence on runs Nos 1, 2 and 2a. The solid curves repres~nt
the distribuCion functions of the log-normal laW (1), computed for values
of the parameters ~ and ~t , corresponding to the empirical distributions.
The distribution of the dimensions of the zones of background turbulence
~ was characterized by an appreciably greater smoothness than The
variation coefficients for all the runs had values ~--1.4, and the values
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F'nit O~E'IGIAL USI~: ONt,Y
~f tie ~x~~~~ varted in the r~n~e 4.g-1d.6~ Howev~r, eh~ ab~nlut~ ~c~CC~r
~f ~ ~ vulu~e naeurally ~x~~ed~d the ~CntCer df th~ m~ximum dim~n~inn~
df ehe xones of baCkgrdund turbul~nee in Ch~ eh~rmaclin~ and th~ quasihomo-
~~n~ou~ layer were equ~l to ~.344 and 856 m r~~pecriv~ly.
p~~~M`~
0, t
v,as
o ro tn ~o ~o r,u
~ig. 4. l~iatogram of Che digtribution of dimengions of highly turbulent
zones (g 1.1 cm�gee'1) ~n run No 2. The solid curve represEnts the
densir,v ~ietribution of the exponential law (2) for a vnlue of the ~l pgra-
meCer c~~rresponding to an empirical dietribution.
T'able 2
Values of Che Intermittence Coefficient ~ for Three Reading Levels of the
Mean Square Valueg of Velocity Fluctuations su cm~aec'1
x
ra:fca s O,S I iu ~ o,P iu�,�!,t
No
f O.t4 t?,07 0.03
2 (?,23 U,1 f 0.(Ni
:u 1~ ~fS 0,(19 (I,O.'?
A reciprocal analyais of the variability of the signals u' and along
one o� the runs m~de it possible to draW a series of conclueions concern-
Ing the distribution of small-scale turbulence in the thermocline. It was -
found that on the average the number of sectors with intenaive d'' fluctua-
tions exceeds the number of turbulent spots on the u' record and the a?ean
dimensions ~ are greater than u*. This is ~vidence of the exiatence
of both individual zones of "fossil" turbulence [2] and microfronts in
the thermocline. In the latter case the intensification of conductivity
fluctuationa must be attributed primarily to an increase in the mean
- l~orizontal gradient ap~ . Facamples of the posaible manifestation of
Eos~il turbulence and microfronts on the records of the o'' and u' aignals
are shown in Fig. 2,a,b. A rarer phenomenon in the analyzed measurements
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I~Uk t1N'1~'tCtAL USL t~NI~Y
wu~ th~ exigC~nc~ n~ liighl;~ eurbul~ne den~iey-h~mngen~au~ lny~rg, witli-
in ahoge limi.tg ehere wag a high lev~1 of fluctugeiong u' gnd gn ~b~~r?c~ -
~f GondureiviCy flu~eugtiion~. One of ehese ~x~roples i~ ehnwn in ~ig. 2,n.
Th~ edeFficienr of horixont~l intermitC~nc~ of Curbulenee x can be d~r~r-
mined a~ the ratio of the aum of the dimensione of all the turbulent ~potg
(with a given reading 1eve1 e~~) on ~ome run to Che roCal length of tihe
~ntire run. 2'he x v~lu~~, ~~mpueed for the ehree read3ng levele ~u~ ~ 0.5,
0.9, 1.1 cm~~ac'1, at the horizone 100 and 45 m are given in T~ble 2.
'I'he valu~ of Ch~ intermittence coefficient on the firge run ig apprecigbly
leag ehan on the gecond run, where in turn iC remging ~pproximately iden-
tical in ehe rhermoclin~ and 3n the qu~sihomogeneous l,ayer. Thie result,
tnge~her with the appreciable differencea in the excess of the dietribuCion -
o� ~ gnd on mutually perpendicular rune ~n Che Cherenocline,;~an indi-
c~t~ n hnriznntgl anigotrnpy of the coneidered turbulene formatione. The
num~ricul value ~ is essentially dependent on the gelecCed minimum level
~ gu~. Fdr pxampl~, in the quns3homogeneoug layer zon~s oE very ineen-
- yive turbulence, within which eu > 1.1 cm�sec'1, occupied 5X of Che cons~d-
ered space, whereas turbulent apota with mean square values of the velocity
Eluctuutions exceeding 0.5 cm�sec-1 occupied 26X.
'Che dependence of the numerical value k on Che aelected minimum leve], au0
is evidence that the most complete characteristics of the variability of
the horizontal structure of turbulence are not the intermittence coef-
ficiente, but th~ distribution functions both for the dimenaiona of the
turbulent zones and the levels of turbulent energy.
The empirical distributions P( of the dimensions of turbulent apots and
zones of background turbulence wexe computed from the resulCing records
for individual runs. Comparison of the empirical dependences P( Q) with -
the analyCical expressions for the distribution laws P(~,) was carried out
using the test x~[~J, the computed values for which for a log-normal dis-
tribution law are given in Table 1. The comparison of P(,Q.~) and P(,Q,*)
with 12 different distribution laws indicated that on all runs Che dis-
tribution of the horizontal dimenaions oE the zones of background tur-
Uulence with a significance level from 0.05 to 0.15 can be approximated
by a log-normal law (Fig. 3) with a distribution function in the form
.
Q? ~l�, Q) � 1- f e'"n dt when 0,
y~.7[ _r
~1~
ua (lg 1�-�) / o,
where � and O'are the distribution parameters corresponding to the mathe-
matical expectation of the random value z= lg and its standard devia-
tion.
It was demonstrated in (8] that the log-normal distribution asymptotically
corresponds to the particle-size distri:~ution, obtained as a result of a
series of successive independent fragmentations. Such a process of
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~ _
t~nlt tl~'~]:CtAL USL tlNLY
nUCCCl~g.IV~ fr~gm~ntntidn, ~g wtt~ nneed in [9], c~n gerv~ ~g n n~eurnl mnd-
el ~f th~ CggCi~a~ prdc~g~ n~ Enrm~eion of ~ver-gm~ller eurbul~ne formn-
tidng. It cnn eherefore be n~~umed eh~t ehe farmnCidn d� xdn~~ of bnek-
grdund eurbulence (~U < 0.5 cm�gec'1) d~CUrr~d in eh~ oce~n a re~ult of
tti~ Cttgcad~ prn~es~ df fr,ygm~ntatinn oE 1nr~e-gCnl~ turbulent inhomog~n-
eitie~ ~ri~ing du~ e~ in~e~biliCy of tiie nvera~ed moCion.
Hnwpvcr t1� g~ne~ie oE gnoks df int~ngiv~ gm~11-gcal~ turbul~nce (~u > O.S
cm�H~C'i) nE relneively gma11 ~iz~ hnd a differene n~tur~, relnted, prob-
1h1y, Cn Ch~ 1on~1 ingtnbility nf ehe vertiG~1 grgdi~entg nf current vpl-
oci.ty gnd d~struceion n~ shore internal w~ves at i.ndividunl moments in
tim~. tde note thnt thc uppearance df rurbul~ne spoCs was frequenCly noCed
nnt individually, bue in whnl~ groupe. One oE Che ex~mpleg of guch a group
nf ypot~ is ~hnwn in ~ig. 1. Ttie random appe~rnnc~ of turbulent spote in
turn cgn cuu~e a"fr~gmentntien" of the field of bnckground turbulence, -
which i~ ~1so reflected in the 1og-normnl distribution p(~,~).
A comp~rison nf th~ empiri~nl disCributinns of the dimensions of CurbulenC
gpots P( wieh 12 difEerent theoretical p( laws indicuted that in
mogr of tt~.~ considered c~ges the constructed hiseograma cnnnot be
approxim~ted by the besC-known distribuCion lc~ws with few parumetere (as
nn ex~~mple, in Table 1 we give the valueg for ttie X.2 te~t for a log-normal
distribution P(~,*)). However, in individual cnsea, for example, for run
No 2, the distribution of the dimensions of apots wiCh an extremely high
turbulence level (s~ >1.1 cm.sec'1) can be approximated uging Che teaC
x 2 a 12.3 with a significance level 0.35 by an exponenCial curve (Fig. 4),
whose probnbility density is determined uaing the formula
0, z~.0
~P~x, � ~ Ae_"~, x>0' ~2)
where ~.is the sole distribution parameter, known as the density of the
flow of evettts and numerically equal to the inverse value of the mathemat-
ical expectation and standard deviaCion of the considered random value.
The solid curve in Fig. 4 shows the curve for law (2), compuCed for a
value of the arameter 10.8 m 1, corresponding Co the empirical dis-
tribution P( ~em*). W* note that with some assumptions concerning the
distribution Iaw P(~. on the basis of the theory of distribution of the
cxtreme terms in the sample [7] it can be shown that the distribution of
Ctie horizontal dimensions of zones with an extremely high turbulence level -
p~ ~-em~ asymptotically in the case of a large number of turbulent apota
. is described by an exponential distribution (2). 5ince the generation of
turbulent spots in the ehickness of the ocean, having a broad range of change
oE both geometricul dimensions and turbulence levels~ is related primarily
to the mechanisms of local instability, for the P(~, ) density distribu-
tion tt~ere may not actually exist any universal distribution laws.
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~ ~dx n~~ictnL us~ dNLY ~ ~
BIgL~OGttA~'liY
1. 15SLUU~VANIXC I7.MCNCNIVqSTI CIDt~OFIZICH~SKIKN pOL~Y V OKEAN~ (Inve~-
tigution of the Vnriability df Hydruphygical Fieldg in rhe Ocenn), ed-
iCed by R. V. Ozmidnv, "Nauka," 1974.
_ 2. Ng~myth, it. W., "Turbulenc~ nnd Micro~Crucrure in ~h~ Upper Ocean," _
M~M. SOC. KOY. SCI. LICG~, Ser. 6, 4, 47-56, 1973.
- 3. Ldgnvatskiy, I. U., dzm~dnv, it. V., "P~culiaritie~ of th~ Verricgl
Structure of S~n Turbul~nce~" OKEANOLOGIYA (Oceanology), 18, No 1,
19~8.
4. Ozmidov, R. V., "Nineteenth Voy~ge of the Scientific Reaearch Ve~ael
'Dmitriy Mendeleyev'," OK~ANOLOGIYA, 18, No 3, 1978.
5. pnku, V. T., Kuehnikov, V. V., "Carrier of Towed Apparatus for Hydro-
phyeical InvesCigaCions," OKEANOLOGIYA, 18, No 3, 1978. ~
6., Monin, A. 5., Ozmidov, R. V., Lozovatskiy, I. D., "Small-Scale Ocean
Turbulence," GIDROFIZIKA OKEANA (Ocean Hydrophysics), Vol 1, "Nauka,"
t64-183, 1978.
7. Smirnov, N. V., Dunin-Bnrkovskiy, I. V., KURS TEORII VEROYA7'NOSTEY I
MATEMATICHESKOY STATISTIKI (Course in the Theory of Probabilitiea and
Mathematical Statistics), "Nauka," 1965. ~
8. Kolmogorov, A. N., "Log-normal DisCribution of the Sizes of Particlea
During Fragmentation," DOKLADY AN SSSR (Reports of the USSR Academy of
~ Sciences), 31, No 2, 99-101, 1941. ~
9. Obukhov, A. M., "Some Specific Features of Atmospheric Turbulence,"
JGR, 67, No 8, 3011-3014, 1962.
COPYRIGHT: Izdatel'stvo "Nauka," "Izvestiya AN SSSR, Fizika atmosfery i
okeana," 1979 ~
5 303
cso: ta~o
56
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I~OIt C1t~t~'tC1AL USC dNLY
G~OrNYSIC5, AS'TItONOMY ANn SI~AC~
UUC 55]..4G5.41:551.466.3
CCN ~'lthTION 0~ 5TATIONAItY 'TCME'~RATU[t~ ~OUNpARY LAYf:RS BY SUR~ACF: WAVL5
Mo;~c:ow IZN~STIYA AKAU~MII NAUK SSStt~ ~'tZIKA A'I'MOSr'~;ItY I OK~ANA in Ru~si~n
~Inl 15, No 3, 1979 pp ~14--3z5
(Article by I3. A. Nelep, G. S. I?vnry~ninov .~nd A. V. F'rugnv, Marine Ilydrn-
phyyi~nl InstituCe, Ukr:~ini.r~n Ac~demy of Sciences, qubmiCCed for publicg-
tion 24 Februnry 19~8J
[Textj [Abatract] W~thin the fr~mewprk of R viscous quasi-
linear model the aurhors inve~tigute the stntian-
ary temperntur~ bo~ndary layers arising under the
- influence of surface waves. In contras~ Cn studiea
(1-4], cnrried out ~n the basis of potential theory,
it ts sh~wn that surface waves cnuse ~?n avera$ed
- vertlcal convective Cran~port of heuti, the mgximum
of who~e spectrum wieh deepening is shifted into
tt~e direction of the low frequencies. These fluxes _
form stationary temperature boundary layers at the
water-air discontinuity which can be interpreted
~s one of the reasons for existence of a warm sur-
face film. Tt~e conclusion is drawn Chat the great-
est contribution Co its formation must be from
short waves. The joint e�fecr of surfACe and ther- ~
m~~l w~~ves in the averaKed trnnsport of mass is also
s eua lca .
esEeciall~acom lexnbec~iuseYthisasurfaceaitselfrisimog~lenandy ertneable
P Y P P
Eor heat and mass. The most important type of intergction, to a high de-
~;ree determining the thermodynamic state of the ocean-atmoaphere system,
t~ heat exchange. It takes place through the discontinuity and ia depen-
~lent on tl~e parameters determining ti~e properCies of ttie boundary layers.
- flowever, tl~e heat exct~ange problem has bcen poorly studied. For example,
elicrc ~re two import~int phenomena in the thin boundary layer of the sea
which h.1ve been estnblished experimentally.
57
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,
~dtt U~~ICIAL U5~ dNLY
1~ Und~r rh~ influ~na~ oE ~uxfgn~ wavp~ ~n additinnc~l v~reiC~1 h~~t �1nw
nri~~g; Chi~ i~ u Eun~:tion n~ Ch~ pnr~m~t~r~ cht~r~ceerixing wav~~ (5J.
1
2~ Th~ eh3.n boundgry layer ~.n Che fluid ad~ac~nC tc~ th~ di~cont~.nu~,ey i.~
ch~rnct~rized by a~h~rp temperatur~ gradienr ~~hin warm film [6-10~.
'Ph~~~ ~wo �actg have be~n poorly invesei.gaCed experimentally r~nd only pr~-
liminnry nttempt~ have been n~ade Co treg~ them eheoretiically and give a
physi~al int~rpr~CaCion. ~or ~xgmpl~, in (4] ther~ ie an analyeie of rh~
d~p~ndpnc~ of the ~mplitud~ and pha~e of eh~ eempergeurp flucCuaCion~ aC
ehe gurfnce of u fluid in the pre~encp of a progr~sgive w~ve. 7'he angly-
qig wag mgde nn the assumption that the wave is potential and that the -
t~eat flow thrnugh the gurface ie known. A atudy of the averaged f3elds
3en~rated by surfac~ w~ve~ wa~ studi~d in (11); similar effecte, caueed
nnly by C~mper~Cure w~ve~, were examined in (12j. In Chie article we inves-
CigaCe ehe g~neration of atetionary boundary layerg by ~urfnce wave~; we
investignre ~ome of their propertie~ and examinp mateers related to Che
pl~ennmen~ m~nCioned ~bove. At the same Cime, both dynnmic and thermal fac-
rurs arn taken inen c~ccount. (M the bnsis of the ~olutions obtained ehe
- cnnclusion is drewn that surface wnves, as n reeulC of the convection
excited by them, can make nn appreciable contribution to formation of th~
srructure of a warm surf~ce film.
1. ~ormulation of Problem
Experiroental inveatigntions of the upper boundary layer in the ocean ahow
(2, 5~ that when there are wind waves or surge exists ut ite surfnce tl?e
temperature field also oscillates and there is a phase shift between the
rise in the ocean surface and temperaCure variations. Thus, there are
temperature waves as well as surface waves. Together they should induce
averaqed thermohydrodynamic effects within the fluid. We will examine some
- of them.
Assume that a plane layer of fluid of constant density and the depth d is
bounded at the lower surface by n horizontal bottom. We will select a Car-
tesian coordinate system x, z~ with its origin at the bottom; z is di-
rected verticAlly upwr~rd. ~o[ion ie excited by a aurfacc wave. On the basis
of the nbove-mentioned obaervations (2, 5] we will assume that the surface
wave leade to the appearance of a surface temperature wave which ia dis-
placed in phase relative to it. The existence of a phase shift can be ex-
plained by the following physical considerations. The disturbance of the
temperature field in the horizontal direction occurs with the phase velo-
city of propagation of the surface wave. In the vertical direction, how-
ever, the velocity of the dynamic disturbance is much greater than the
velocity of heat diffusion; therefore, a phase shift already appears in
_ the thin molecular layer between them. And since the diffusion of heat
.nnd vorticity in a general case occurs at different rates, a phase shift
arises between the fluctuations of ve~ocity and hpat. Precisely the phase
shift should create a directed vertical heat transfer.
58
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- I~~k (1~'~tCtAL U51: hNLY
Ag~um~ tt~ae n i~ th~ chur~Ct~ristic ~mplitude of tlie ~urt~7ce w~v~, ~p ig
eh~ nmptiCude di thh tc~mperaturh di~eurbnnc~ ~e Ch~ ~luid ~urf~c~, 41 nnd
k tK Ch~ charn~teriqtir. Crc~quc~nr.y nnd w~yv~ numb~r af the di~CurbgnCe, ~
Ly ~rnvil-utinnnl c~cc~lcrnCton, t i~ time, i~ th~ gCr~am futtcCidn fnr -
nur ewn~dimensional mneinn~ We intrnduCe eh~ fnllnwin~ dimenginnl~gg
v~ri~bl~g:
(1.1)
~~kx* :~z+ld, V~~ (~io~d)..,~+~
,
wher~ {u+} ~~}.~,{~~;+/di~, �-t~~~*/t~s~},
(1.2)
u~~nd w are the veldciey cnmp~n~nts hlong x.7nd x respeceively; eh~ ~ros~
denc~t~y dimension~l p~~r~~meCcrs.
We wtll deCermine the temperaCure
?'+~To+( i~-eT), (1.3)
gn ti~nt tiie dettsity, expressed frnm Che equution of stnte, ig _
p~~~o*( ~-}-~*(T~-7'o*) l, (1.4)
where pp+ are equilibrium temperature nnd density; ~_~+TO+
t~ the coefficient of thermal expansion of water).
Then. In dimensionles:~ form the surf~~ce wave, stipulated in the form of
one f~ourier cnmponent, has the form
r~ s a cos(x--t), (1.5)
where t e ak is wave seeepness; a= kd. The equations of diffusion of vor-
ticity r~nd heat nre i
aT
d+ e a+p 8_ ~ a 11 p,~ ~ a p~~+b~. ai ~
{ a~ ~ a~ az az vZ 1 J z (i.b~
Jv a,~ a a~p a lT,~ 2P p~T,
l ac +e~ a: ar`~ ax a~~I ~1.~)
where �~(2 y/a!)1~2d, is the kinematic coefficient of exchange of mo-
mentum; P is the Prandtl number;
~~.~~~~i~~rd: c==~,=iv~,.~a:a=~vx=. ~
The parameters E and ~1 entering into equations (1.6), (1.7) characterize
' the contribution of inertial and viscous forces to the general balance
~nd nre assumed to be small, so that ~Q 1, cY_ Q 1.
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~
~t~[t d~FtCIAL US~ nNLY
'1'h~ b~u~dury condiCinn~ ~t thp gurfn~~ ~r~i cnndieinn d~ ~bg~n~~ nf
~h~~rin~ ~er~gs, which hng'eh~ form [11]
d _ d ~ ~f a~ --d _ ~ c~h~n z~ ~~'~1+ � ~1.8)
Bs' ~x' Jx ex d s
thp kinematic condition ia
~!1 ~ d~1 ~N wh~n s~~~`n~ (1.9)
~~-~-.-..~p
~t dx dx d:
nnd fnr th~ t~mpergeurp w~v~ field exigC~nc~ ~e th~ digcontinuity ~f a
t~mper~eure w~v~ di~plc~c~d in ph~s~ r~lativ~ eo 1~ , thgt is
T~4 cos (x-~t~y) wh~n =`~~~'~1+ (1.10)
whCr~ t~ ~ B~/ E T~+; 'Y ig th~ ph~~e differ~nce between th~ t�mper~Cure and
~urfnCe wnv~g.
On th~ boetom the bnundary condition~ ure the aetnchment conditiong
+p�+~~~�n when z = 0 (1.11)
nnd the absence of wnve disturbances of Lemperature, so that
- T= 0 when z= 0. (1.12)
2. Nonstationnry Fields of Velocity and Temperature
The solution of problem (1.6)-(1.12) will be goughe in the form of series
for the small parameters S and oc with subsequent use of the method of
asymptotically joinable expansions. He ~aill represent ~ and T in the form
.
7'}~' ~ era"{~~~+ Ti^'}+ (2.1)
and the functions ~
~pm, Tp~ as
i A
T ~ [ T }e'~._n+{,~~~; . T~~; }t-~~.-n~~ ~2.2)
�MI �~11 ~ ~M~ �1~1
. ~
where the asterisk denotes complexly conjugate values.
After the aubstitution of (2.1), (2.2) into (1.6), (1.7) and e~uating the
coefficienta with the corresponding powera of o~ relative to t~l~ and g~
we obtain, respectively, first- and second-degree equations which describe
the solutions only in the main region, excluding the viscous boundary
layers at the free surface and bottom. In order to obtain the equations
for :�he boundary layers, we introduce the corresponding boundary layer
variables:
~
at the free aurface ~
!
60 f
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t~'�~i UH~iCIAL U~~ hNLY
a~i~'a$~ +h~x, ~)~~D(x, ~1, ~(r, tl"~(x~ (2.3)
~C e1~~ bateom
s~a~, V'~�T, a~ ~)~~'~f, t), 7'(x? z, t)~C(x, Z~ (2.4)
'Ch~~i, ~ub~eituein~ (2.3), into (1.6), (1.7) ~nr thh gnughC-fur funG-
tinn~ in the upp~r bdund~ry lAypr w~ nbt~in
d ~ ~ ~~p ~ _ D~p ~ 1 ~ + b'a' ~
~ Dt a~ ~g ex ux ~~g~ 1~~g' n~'~
d0 (2.5)
- z r=-I- 2a'd' Jx~t ~ rx'd` -4�a'd~~ vz ,
~ b b
- ~ e a~ ~ v~P a i d`o ~ s~'n c2.6)
j v r_.,...._..- _,...._1 p ~ ~h a 8 ) .
1 dt a` ~7~x dx d g/ ~ "I' \ dg' d,~'
Tlie uryu~tior~~ for th~ bottnm boundary lnyer, in which, in plac~ of
~ we h.~ve c~ , C re~p~ctively, hnve the eamc form. -
ifefnre expregging the Uoundnry cnndiCinng nr Che frce surEc~ce (1.8), (1.9)
in tcrms o� the boundary layer vAriables, they mugt be expanded into a
'1'nylor series relative to th~ undisturbed surfgce z~ 1. Performing Chis
~~rnr~dure nnd representing tt~e deriv~d expresginne in the varinbles ~ and
cp , w[ tt~ an accuracy to o( 6 2) we have
a`E' ~6~a~ d~ ab L~,cos(.r--t)-a'b` as'dgcos(x--t)-
(2.7)
.
~--t,cc'6= ~~t8~sin (z-t) l =0 when 0,
i acp e~ a~~` cos(x--t)- ~~sin(x--t)~ a0 when (2.8)
8 ~in(x-t)-!- ax+ b drd5 ~
Conclitions (1.10)-(1.12) assume the form
6 a~cos(z-t)+O~Ocos(x-t+~) wh~n = 0 (2.9)
m�~:~~ when ~ a 0 (2.10)
C~O WIIeR ~ � O� ~2.11~
in :iddittnn to the canditions (2.3), (2.4), (2.7)-(2.11) the external and
tntcrnal solutions must satisfy the joining conditions (13]
lim T} ~ lim {~p, 0}, lim T} ~ lim {~I~, G}. (2.12)
i..~ t..-~. ~..e
_ For the functions ~f , 5~, e, G we seek a solution in the form (i.l), (2.2).
Substituting the expansions of the sought-for functions into a series for
the small parameters E and ~ into the corresponding equations of motion
61 .
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~OEt 0~'~ICIAL U5L ONi,Y
nnd eti~ bdundary cdndieidnK, r~king inea uccount (2.2) and ~qugCing th~
cn~~ficitnt~ with identiani pnwer~ c~f dC, we have the fnllowing ~quueiong
c~nd bound~ry conditinns in Che gppxnximaCinng (00) gnd (01):
\ B'' ~I-2!) ~~i "'~0, d
J~ (0) ~+0, tpom ~~)'~a�' (1"m), (2.13)
~ b
f -F- 2t1', Oe�,~+0, 00~ (U) ~ (1-m) Oe't, (2.14 )
as w w
a~~ +~~Mm- c 1~-� a~oTne, ro~~o, .
a:~
w w
l o~~ +2t~ a~~~ ~o, ~aL~ (oj ~o, mem(o) ~o, -
~,ar= ~-2r~~ Co~,~o, GoM(0)~0, (2.is)
in which m s 0; 1.
'Phe Einal form of solution of ttie problems (2.13)-(2.15), satisfying the
,joining conditions (2.12), are
ipr�ffi8-', U.~~9e't~~~_~,~p~~
~oo~ (8 sh 8)'' sh bz, ?'eod0, (2.16)
~I?o~~0, do~'~0,
~p�,- (cth 8) 9.,-0,
~ 1-hi ~ .
'~01~2sh'b Shlb(:-i)I? Te~aO,
~ i+i ~
' ~o~" 2shb t~_i~t~.(1-t)~,-1], G~tmO.
It cun Ue seen from expressiona (2.16) that already in these approximations
the vorticiCy of tl~eob3erved velocity ~~a~e fielcl is rlifferent from zero.
liowever, in the future to c`apute the stationary effects induced by the
wuve fields it is necessary to find the solutions for the two following
.tipproximations for oC. The equations and the boundary conditions for them
huve the form
` a ~
~ a~ -t- ?il v~ tp~�=2ib= (tpu-s-f s c{'o~-:-t ~o~-i) .
d~' d~' ag' b (2.17)
~p.~ �0? d ~ 0- (3-n) b,
62 .
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I~UIZ (11~I'I(;lr\I~ U51.; (1NLY
1 ~y, ~~l/~~VOnr=V~~~U11'~11 O\"/~"1
1 u~,=
~ ~ ,
~t/ ~ ~~v~ ii U~ 1 ~~On� i`b~ol1on-l,
v~l
ti -
1'0~ d b=l ron-s~
Zl~ \ az` l _
a� [7=~D ~ ~'~Do~-1 ~o " 1
\ l~ 1 +')t / ~l, ~Ib~ ~~nn-1"~ ~ra - l a r.ron-=1 r
~ Mj
b
~~on
~~on ~r ~Q~ -0+
b
S /
\ f~~= 'f ~ r~ ~ ~ion�b~~on-Z~ ~on
whe re tt= 2, 3.
[n addiC:ion to the bound~ry conditions ent~ring .ineo (2.17), the ~oining
conditians for t}ie external and inCernal solutions are additional. Here
we will cite only the final form of the solutions, omih.tin~; un~oieldy in-
_ tcrmediate computations and the 3oining procedure
p ~1
lb8 L ar~~e CII-tl! ~___.g(1-il~P! 1'+'
1~-~1t,_
~po:=- ?(P-1) P l
a (1-~-i) S i$ ~o$ .
+ ~-I--C2-l---e'T),
2 ~ sh2 8 2 P
2sl~bl\~+ ~p e'i)sh6z+ sl b~sh[S(z-1)~ ] (2.18)
iS ctt? 8
4~�� - [1-(i-i)~-e- l, >
2sh8
(1-1-i)8=f1e~T ~e~~-i~~rt~ T01=G03_~~
~ ~01 41~ '
z
~o~ r ~b= ~t~ a ~ a + St~= a + e ~ ~ + a= s ~ ,
_
(1-i)8 I3 ~_~th~S+~�-e'~)sl~[S(z-1)],
S~~l a l ~ r~
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~0[t d~F'ICIAL U5C dNLY
~
" ~~~E~bir ~-oth'b-i-~�~ e't,-- t--a--(1-~t~h~)~e-c~-nc~.
~0'� t
8\ 3 P 4s1~6 ;
t a Zt
a ~ ~~-cet~~ a + e t ~ .
+=--C'- b!(--1-h1) z ~
l~ sl~ 8 ~ gh
~1~'l~ b~( 3-4- cth' b-4~ ~j e'1) +
~ ~ t,
g~ \ 2 '
bo~'�~'o~~l~oa~0,
_ Thus, wc huve found Eour ~pprnximations of ehe nnnstaCionary parts of Che
stre~m functinn nnd temp~rneure. The inCernnl gnluCions Characterize the
clistribution of the pulsneing velociCy an~ t~mper~ture fieldg in the sur-
fac~ und boundary luyE~rg ~nd the external solutinn in the main layer
of the fluid. Before proceeding eo an examination of the gtationary ef-
fects we will discuss the eoluCions obCained.
7'he ~olutions, obtained on the bnsis of all the deCermined approximatione,
uniformly suitable in the entire region, hnve the following form:
sh bz l-f-i sh[b(z-i) ~_~,-,,,~Q ~
~ r
~'~Z~ bshd +a2shb l shb
= tb ~o~ ,~l sh bz cth b eh[b(z-l) ] r -
+a 2{C~+ P~ / slib + slib shb ~
" ~T Pe,~-~?c,-nia_~c+_n~o~~-n~a~ +
_rZElt'tlle-Il/a_ ~
(P-~~P
+ ctl~ 8 C_~~_n,~Ql -~-a' _~i-i)b' r 3+ cth' b+~~fl e`' I`sht s(h 8 i) J+
shb 1 ~ 4shb ~ _
(i-i)8' r ~oa (pYPe-n_n>~. ~Z.zo~ �
It Eollows from (2.19) that the fluctuations of the heaC field, caused by
~urEace waves, in turn exert an influence on the value and distribution
of tiie velocity wave field. This contribution has the order ~f magnitude
c)(oC) and ia especially important in the boundary layers. It is i.nteresC-
inK to note that the temperature field exerts its main influence on the _
I~orizontal component of the velocity field; on the vertical component
this influence is an order of magnitude less, that is 0(d2). This can
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~oi~ ;~r~~r.r.t~~r. us~ oNi,Y
be ~ttribuCed to the t'~nc:t ~h~~t tl~c~ grndient of ElucCua~ions of t}?e temper-
~ture fic:ld in u horizont~ll direction :ts of Che ar~me ord~r ~f magn;itude
ci:~ L� n vertic~l direcr.ic~n, buC ~lc~nk the verCic~l Che dlf Eugiott nf heuC
~~crur~: .it a le~ycr r,~tn Ci~.+n iey Crc~n~fer al~n~; ei~e hnriznnt~l.
_ , l:xpre~sinns (2.16), (2.18), (2.19) indiCaCe thur in the upper Uoundnry 1~y-
. er Chere is an ~ppre~i7ble ph~se sliift betweett flucCuations of Che temper-
- :iture Lie1d c~nd Ch~ stre.im functidn (ttint is, ttie verticnl velocity compon- _
c~nt). '1'}ii~ phn~e ~hiCt ~tiould give ri:~e Co ,~n averaged wave hege flow in
the vertical direc:tion. In addition, tlie wlve velocity field has a nan-z~ro
varticity. This legd~ ~o a st-nrionary flux o~ momentum ~7nd appearunce of
:~nother secondary efCece yt~etun.nry flow.
3. ~ield of 5tation~ry Velocities
I:qu~~tinns (1.6), (1.7) and ehe boundary conditions (1.8)-(1.12) describe
the t~tal fields of velocity nnd temperature, including both fluctuatiing
nnd secondary station >
~2~ = - ~ (nz cos(=-t)-b' dz=~3zcos(x-t)-4-
.i'~ l when z = 1, (3.3)
-!.4~iT sin (z-'l) 1
~1.r ~7 s
a~' = p when 0. (3.4)
s
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i~nk UE~'S~'tCiAt, t15t~: nNI,Y
It followg from (3.~) thuC rhe e~mp~rntur~ fi~ld ~x~rt~ no direct inf1~-
enc~ an m~an veloeity. Z'h~re ie onLy an implicie dep~nd~nce n~ t/T on T
through the function r~`;r Accordingly, the menn velocity field c~n be com-
puted ind~pendenrly of T.
Taking into nccnune th~C only the r~al pere has physical eense, omiCCing _
ineermediat~ compue~tiong, we i.imn~diatel;~ wriCe a final expregsion for~,
mea?i velociCy, being a solution of the prnblem (3.2)-(3.4), in which j~/ ig
derermined by formula (2.19)
e Y~ a n ~oO91ll~Y~- 4),
u C, _ ,r, ~ ~..~,a sl~ b:, sinr-- -t- -f- s}
a~S yl~' b 1 a ~i ~ Y2l'
-F~~ ~sl~uz e~~_~~~~cos E~i ~~~,flsl~ba r~ cosr YI~z-1 X
~li d a 1)sli 8 L ~ 1 a / (3.5)
I`vlt-1?/o` z~i 1r-11/a C"t/a r a8~1 Vt t
Xe cusC a-~,e ,]+2sli d lt ~ cos--+ `
a
sl?[b(z-1)J z al e-''~�
- s1i b sin a- cl~ dz cos a J~ 4 sh' b+
a a ~09 Y ~
+r-z C4+ p ,z+4sh'd~~
The solution (3.5) shows that the temperature fluctua~ions cauaed by surface
waves make a substantial increment to the field of r.?ean velocities gert~xur~d
by waves.
'Thus, surface waves are propagated in a shear current, the reason for whose -
- .~ppearance was the surface waves themselves. It follows from (3.5) that
with some wave parameters the values and vertical gradients of the mean
velocities can attain considerable values in the surface layer of the sea. -
'fhen it is natural to .7ssume that this can be one of the reasons~for the
appe:~rance of instability and destruction of~surface waves, that is, gen-
eration of turbulence in the surface layer of the sea.
Formula (3.5) expresses the velocity of the mean flow in a Euler represent-
ation. In order to compute the velocity o~ transport of masses by waves
(Lagrangian velocity of motion of fluid particles) it is possible to use
t}ie Longuet-Higgins formula [11J
' (3.6)
V~~u +~s f~ d~ + d-" J iu d~.
'I't~is gives
~ 66
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i~Ult ~11~ l~ f C i ~L U51: ONI,Y
~ ~~U ~in ( ~ (~oi? sl~ ~5~ y ~ z-~ i ~ x
~1 r~ r C. S ~ C (/y \ I ~ /
a 1~I' ~'lE gl~ d a
/p~~_~~lo e-~/a a ?Sh(d~a`�1~~ (3.~)
Xe ~ � [ ~3 ct~ 8z cos sin a/a ] -h ~
l sh 5 ~z sh b
~ 3c-,'r� ~ ch 28z ~ i ~ 8 cth 8r~~~ofl cos ~ z,
~i sti' ~ ~i sl~' 8 h sh' d \ ~ ~
tt tc~llows from (3.1) thnt in the Cran~rorC nf m~s~es ehe fluctu~tting Cem-
perature field pLt~y~ n still gre~Cer roLe, eince Che term 0(~ /oG) ig re-
lated ~pecifiCUlly Co therm~l fluceuaCions nnd disappe~rs when 0. Here,
I~owev~r, it mu~t t+e emph.~sized that Chege conclusions were dr~wn on Che
basis oE ,n qunailinent� npproximation in which the entire analygis ig mnde.
In order Co invesCigc~te these importr~nt effecCS more pr~cisely, the nonlin-
- enr problem must bc sulved.
W t~~ T I~ ~
-0,3 -0,3 -Q1 0 Qf Q? -ZO -f2 -~v c1 4 fP _
* x ~ � ~ ' w
~ w~ r
- ' . a9a : ~ :~,~o,gs
.
.
. ~ * 0,96 ~ 0, 9Z
M ~
. \ " 0,88
~ 0~ 94 .
.
~ ~ ~ ~
; M' 0 9Z ~ O,d+K
' _ y 0, 0 Z _
. 0, 90 M, Z
" 0~ BQ x 't
~ a
o, e s
- t o, ey
Figurc. Depth distributton of stationary heat flows caused by waves (a) and
rie~ln temperature (b), caused by a stationary wave heaC flow: 1) y= 0, 2)
y= n/4, 3) y=?1 /2, 4) 7' = 3.ri /4, 5) y= ~1 ; z was normalized at the
f.luLd c~epth d
4. Averaged Heat Flow and Stutionary Temperature Field
Tt~c ~c~lution~ for thc non~t,~tionary velocity field (2.19) a~~ temperature
('L.'LO) m:ike tt pn:~sihle C~ determine, ati a Function of z, the averaged
I~cat flc~w in vertlcal dlrection caused by waves. Making the correspnnd-
� [n~ computations, we tiave
67
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~ t~OEt (~~~ICYAL U5~ ONLY
.
~T~, ah6z er~~~t-11la8iri`'~Y~= --"f~, .
2d sh 6 a (4.1)
. where, as a eimplificgtion, only the main t,~rm of ehe expansion has been
ret~in~d. ~
It fnllows from (4.1) that in the n~ighborhood z= 1+~(n7t + y)/ ~ the
st~Cionury flow is minimum. rt forlows thnt the nonraonotonicity of gteenua-
tion wiCh depth for the averaged verCical hene f1.ow, cnused by the eurface
waves, is deCermined by the phase ahift beCween the surface and the heat
w~ve, and glso by Che viscngiCy parameter.~ determined by Che phase
ehifC between the aurface and heat wave, and also by the viscosiCy para-
merer OC characterizing Che degree of wave Curbulence. IC also followa
from formula (4.1) that the rate of atte:nuation of the wave heae flow csith
~ clepth is dependent on wave frequency. Tl~e flow caused by the high-frequency
rart of the spectrum attenuatea more rapidly, so that the maximum of Che
specCrum of the averaged wnve heat floa? with depth should be displaced in
the direcCion of the low frequencies. 'Chis conclusion agrees with actual
observationa made in the ocean.
In the figure a represents the depth ilistribution of the averaged wave heat
flow for different values of the phas~e shift between the rise in aea level
and the amplitude of the thermal disturbance in it when ol = 0.1, S~ 1, P
~ 7. Th~ figure does not show the flc~w itaelf, but the value Q s.AnT/~ . It
can be seen that both the value and Lhe depth distribution of Q are essen- `
tially dependent on Y. When r s 0 the maximum of the wave heat flow is ~
situated within the fluid, that is, in this case the main role in heat
transfer through the water-air disc~~ntinuity is played by diffusion. But
~ already at a shallow depth, when a phase shift appears between the wave
velocities and the wave part of tett~perature, the mechanism of vertical
wave heat transport is activated. With other values of the phase shift ~
this process plays a significant role in the upper boundary layer, includ-
ing the diacontinuity itself (all experiments made up to this time show that
under real conditions 7'y~ O;sl). It is of interest to compare the values _
of the heat flows caused by wave transport with flows due to evaporation
and contact heat transfer. It is known that the mean climatic valuea of the
heat flows in the equatorial and tropical regions of the ocean, caused by
the lust two mechanisms, are equal to [14] N 400-500 and 40-50 cal/cm2�
day respectively. However, the r~aave flow Q, computed from (4.1) for waves ~
characterized by the parameters a= 0.5 m, 1 sec'1, e p= 10'3 degree,
Y= 1�, is equal to Q N 38 cal/cm2�day, that is, the effect.of the wave
mechnnism for heat transport c~n be comparable with conCact heat transfer.
Thus, the process of wave heat transfer through the ocean-atmosphere dis-
continuity and in the entire upper boundary layer plays an important role,
which agreea with the conclusions drawn on the basis of observations [5].
ba -
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roK o~~r~cznL usL dNI,Y
Slcirn ~l~~r~ 1H a wave-~raducGd stnCionnry tiettt �1.aw in ii verCic~l direcrion,
iC n~Cur~lly forms "its" ~ecnndury gtutinn~ry temperatiure field. The w~ve
flow i~ ~~igni~icanr funr.rion d� depCh. Accnrdingl.y, the sC~Cion~ry Cem-
per~~Cure field form~d by it nlso changes wi.th depeh, th.~e ie, there is a
vertic~l gradiene of rhe ~tneionary remper~eure field, r~nd ns a result,
~ diffusion arntinn~ry henC fldw in tlie verrical direCCion Qg =-~a'r/a z
nlsn arises. Much as thc~ equation for sC~tiion~ry velociey wae derived, by
~verr~ging (1.7) we obtain th~ following equr~tion describing Che stgCionnry
temperaCure field
~ a~ a:~ y e a~~~,~ (4. 2)
21' 8z' ~ ~(x,z) ~
Since in rhe constdered ca~e the stationary heaC exchange between the aCmo-
sphere and ocean is accomplished only due to twn mechanisms wnve trans-
~~ort and stationary diffusion, in the sCeady case, which is investigated
here, rl~e total heat Elow caused by them must be equal to zero; otherwise
tliere wi11 be heating or cooling of t1~e fluid. In dimensionless form this _
condition has the form
- a3 a~ + w?'~0. (4.3)
2Pe ~ 8 z
In ~~ddi~ion, according to (4.1), the wave heat flow aCtenuates exponential- -
ly witli depth. Accordingly, the stationary field formed by it also should
~ittenuate exponentially with increasing distance from the water-air dis-
continuity. Therefore, we require that
T= 0 when z= 0. (4.4)
The solution of the problem (4.2)-(4.4) is
fi~z~ = e f} yP sh ba e~p