I ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -- FOREIGN TECHNOLOGY DIVISION MEASURING LOCALLY ISOTROPIC HYDROPHYSICATA FIELDS

Transcription

1 A0 A FOREISN TECHNOLOGY DI WRIGHt PATT ERSON *fl OH F/S a/to MCA5l IRINS LOCALLY ISOTROPIC HYDROPHYSICAL. FIELDS, (U) DEC 78 S DOTSEI*O UNCLASSIFIED FTO ID(RS)T jor ) AD8 ~~~ 5~

2 , I ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ I Ct ~~ FOREIGN TECHNOLOGY DIISION MEASURING LOCALLY ISOTROPIC HYDROPHYSICATA FIELDS S.. Dotsenko DDC Approved for public release; distribution unlimited. s ~~~ ~ ~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~. ~.

3 t Ti it ~~ FTD ID(RS)T EDITED TRANSLATION FTD ID(RS )T December 1978 MICROFICHE NR: 7f ~~ CO/ ~ 71 MEASURING LOCALLY ISOTROPIC HYDROPHYSICAL FIELDS By: S.. Dotsenko English pages : 10 Source : Morskiye Gidrofizicheskiye Issledovaniya No. 3 (53), 1971, pp Country of orogin: USSR Translated by: Sgt. Martin Folan Requester : FTD/SDSY Approved for public release; distribution unlimited. 1 ~ r ~.j GR.) ~ 2?? ~ B L ~~~ r ~ c ccd i By ~~~~~~~~~~~~~ Dist ~ j Jccia1 ~ AH THIS TRANSLATION IS A RENDITION OF THE ORIGI. HAL FOREIGN TEXT WITHOUT ANY ANALYTICAL OR EDITORIAL COMMENT. STATEMENTS OR THEORIES PREPARED BY: ADOCAT EDOR IMPLIEDARE THOSE OF THE SOURCE ANO DO NOT NECESSARILY REFLECT THE POSITION TRANSLATION DIISION OR OPINION OF THE FOREIGN TECHNOLOGY DI. FOREIGN TECHNOLOGY DIISION I SION. WP.AFB. OHIO. :_1 ~ des FTD ID(RS)T l Date 6 Dec 1978!.* kr. ~ ~~ ~~~~~ ~~~

4 ~~~~~~~~~~~~~ ~~~~~~~~~~~ I U. S. BOARD ON GEOGRAPHIC NAMES TRANSLITERATION SYSTEM ~ 1 ~ ck Italic Transliteration Block Italic Transliter ~ t.i A a A, a P p p p R, r Lb 56 B, b Cc C c 5, 5 B i, v IT T m T, t. rr a G,g Yy y y U, u, p D, d F, E e 5 S Ye, ye; E, e* X x x x Kb, kh ~ Zh, Zh Lj u, Ts, ts 3, Z, z Ch, ch ~ 1H H u 1, 1 Ww Sh, sh H ~ i R z ~ Y, y U ~ ii ~ 11$ aq Shch, shch Xx K, k bid I. i n fl a L, 1 bl Y, y i M M M, m b b b o R u N, n 3 ~~,, ~~ E, e Do 0 o 0, o hi ia Yu,yu fln 17 n P,p HR 2. Ya,ya ~~~ initially, after vowels, and after ID, ~ ; e elsewhere. When written as ~ in Russian, transliterate as y ~ or ë. RUSSIAN AND ENGLISH TRIGONOMETRIC FUNCTIONS Russian English Russian English Russian En ~ :iih. sin sin sh slnh arc sh sinn ~~ cos cos ch cosh arc ch cosh tg tan th tanh arc th tanh ctg cot cth coth arc cth c oth _~ sec sec sch sech arc sch sech, cosec csc csch csch arc csch csch Russian rot lg English curl log 1. ~ _ ~ ~~~ ~~~~~~ ~~~~~

5 ~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~ MEA.3URING LOCALLY ISOTROPIC HYDROPHYSICAL FIELDS S.. Dotsenko Abstract We have found a tie between the spectrum of an output signal of an instrument with the spectrum of a locally isotropic field measured by it, the knowledge of which permits correcting the a spectrum s distortion introduced by the instrument. The acquire d r results illustrate, for example, corrections of the spectrum of fluctuations In transmittance of sea water, One of the methods of study ing the physical processes which occur In the ocean is the study of the ~ h ~.rsical fields created b ~ i it such as the flow velocity, temperature, salinity, transmittance, speed o ~ sound, etc. [1]. The methods of measurling these fields can be varied : vertical sounding at a ship s anchorage, measuring the fields with Instruments (on the horizons of buoy stations or on self reacting floating devices), or measuring the ship s path with operatil.f (towed) instruments. The various methods of measurement corre spond to the solution of various oceanographic ~ prob ~~~~~~~ _ ~~~ ~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~ ~~~~~ ; = ~~~~~~ ~~~~~. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

6 ~~~~~~~~ ~~ ~~~ ~~~ ~ lens. WIth vertical sounding, as a rule, we solve the problem of investigating the distribution of determined components of a field with respect to depth. With horizontal movement of the instrument, we usually study the statistical characteristics of the measured field at a given depth, where a change In the determined component of t he f iel d is comparatively small. Let us pause In more detail on measuring the statistical characteristics of the studied scalar field with towing of the measuring instrument. It was recently shown that the physical fields of the ocean are subjected to time and spatial fluctuations with extremely large spectra of frequencies, which change from fractions of a second to a year and more, and from a centimeter to scales of the entire ocean in general. It is apparent that It is not possible to construct a method of measuring these fields, to an equal degree suitable for studying In any ranges of the indicated spectra. The towed instruments are built for studying nonuniformities, the scales of which lie within the limits of centimeters to tens of ~ ieters, and therefore the basic requirement for It Is the best representation of the features which are Inherent to the measured fields within the limits of precisely these scales. S1nc ~ we are speakinr of the statistical characteristics of fields, then the problem of the theor ; of measuring can be formulated here in the following manner: as with respect to t he data of measurements ac riiiired with the aid o the towed measurtng device, to restore tne statistical characteristics of the measured field. Let ur note 2 ~~~~~~~~~. ~~~ ~~~~~ ~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~ ~~~~~~~~~~~~~~~~~~~ ~~~~~~~ ~~~ ~ ~

7 ~~~~~~~~~~~ ~~~~~~~~ that the statistical characteristics of the output signal of the instrument and of the studied field do not coincide, since the instrument possesses properties of spatial averaging and inertia which distort the form of these characteristics. Let us stud i the tie between the statistical characteristics of the output sirnal of the towed Instrument and the statistical characteristics of the studied field In the supposition that the latter Is locally isotropic (this requirement is satisfied L i a wide class of physical fields encountered in the ocean ), and the measurement lasts f or a rather long time. Here, we will consider the condition of frozen turbulence of Taylor for the studied ~ ield as accomplished. The random tridimensiona l field I(1 ~, where 7. radius vector of the field s points, is called locally uniform, if all distributions of probabilities for di ~ ferences of Its values in combination of pairs or points do not change with ~ n:t parallel transfer of all the examined points [2]. The average value of in crements vector ~~~~ of this f ield is linear function of where constant vector, the total second moment of incre rnents o f field (.j,j,. f r ~~ xi ~. ~ j ztj ~ is re lected by the structural function of this f ield with the aid of equation.d(j. ~~ + [ ~~~ )* ) ~ ~ 1 _. ~ 3 _ k L 4~~~~ P ~~~~~~~~~~~~~~~~~~~~~~~~~~~~. ~~~~~~~~~ _ ~~. ~~~ ~ ~~~~~~~~ _ ~ ~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. ~~ ~~~~~~~~~~~~~ ~~~~~~~~~~~~ ~~~~~~~~ ~~~~~

8 . ~~~~.. The structural function is simply determined by its spectral dens ity (tr idimensional spec trum ) 4 ~~~ : J ( ~ ) 25(f co,i ~~ & ~ Z,)d ~~. (2) The locally un iform field, depending only on r ~.I ~~ I, is called locally isotropic. The tridirnenslonal soectrum of this field can be expressed throuph its uniforri spectrum &,( ~ ) with the aid of relat ionsht o ~ ~~~~ 2xv ~ ~~~~~~. if field Y(t) is uniform, then it carries the name of a random process wi th stationary transfers. Its average value is ~ ( ~ 4) where constant, &nd the structural function ~ (i,) fr ~ ~ ~ Y( ~ } (5) is connected with its spectrum in the following manner: (6) The tie between the output signal of the instrument Y($) towed uith resnect to the studied med ium with constant velocity, with the measured f ield L ~ J ~ has the form [3] Y ~ t).j ~ ;f 4~ (t ~ v ~ _yj N ~~~~~~, ~ ere the spread ~ unction of the instrument, char actertzin ~ the rrererties of spatial averaging and inertia which ar ~ j..

9 inherent to it. Thus, in accordance with expression (7), the instrument conducts a transformation of the studied tridlmensional field to an output uniform signal. We show that with towing of the instrument with a constant velocity in the locally Isotropic field its output signal represents a random process with stationary increment s, and we will find the tie of the spectrum of this process with the spectrum of the field. Plac in g ex pression (7) in relationship (14 ), we obtain the average value of output signal ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ which l inearly depend s on ~~, which Is typical for a random process with stationary increments. Let us f ind t he structural function of output s ignal of the instrument. Placing expression (7) in formula (5), we obtain ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~ ) ~ ~~~, (8) in which regard the total second moment of the field which Is lo cated under the integral is determined with the aid of relationship (1) and can be represented through the structura l function of the field in the form f{4~~ t ~~ +ii ~ ~ [ ~ ~~~~~ ~~~~~~ 2 ~[~~~ ~ 9+ ~ J ~.7 ~ } ~ Ith the aid of relationship (2) after uncomplicated transformations, we reduce relationship (8) to form D y (t,)25 eat ~~~~ t,~~.z7 ~ k ~ I ~ i. where ~~~~~ &),!fl (Z; ~~~ I is the energy spectral characteristic of the instrument, in which regard ~~~~ represents a four dimensiona l 5 1 ~~ _... ~~~ ~~~~~~~~~~~~~~~.. ~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ L ~~~~~~~~ ~~ ~~~~~

10 ~. spectrum of the spread function of the instrument ~ (Z, )S ~~ f ~ ~ ) ; Let us take the system of coordinates ~~~~~~ relative to which the instrument moves in such a manner that the velocity vector of towing 9 coincides with the coordinate axis with respect to direction. i ~ ere 2 S[ic ~~~~~~~ ( ~. ~~~~ ~~~~~~~~~~~~~~~~~ ReplacIng in the obtained equation y ~~ 9 ~~ w, we find that the structural function of the outnut signal of the instrument has the form (6) (i.e. the output signal i ~ actually a random process with stationary Increments),in which regard the spectrum of the output signa l 44 ~ Is connected with the spectrum of field by relationship 1(Q ~. ~ ~~~~~~~~~~~~~ For a number of hydrophysical instruments, consisting of non inertia sensor and an inertial measuring nart, condition of seoara ting the energy spectral characteristics Is accomplished With the fulf Illment of this condition and local Isotropy of the field, expression (9) assumes the form ( 10) where the s pectrum at the out put of the non inertia sensor ~~~~~~~ J ~ J/ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (11) ~ e1ationship (10) represents the well known expression of transformation of the energy spectrum of a uniform signal with the passing of it through the linear target. 6. ~~ ~~~... ~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~ ~~ _1_ ~~~... A

11 S ~~~~~~~~~~~~.wfl W... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~. ~~~~~~~~~~~~~ ~~~~~~~~ Let us examine the detailed expression (11). Let us express the signal spectrum at the output of sensor (11) through the un! form spectrum of the field, using relationship (8). After the transformation w e obtain (12 ) where a some typical dimension ofthe sensor, and function will be called the function of transverse averaging. It depends on the degree of averaging of the field by t he sensor In a plane which is perpendicular to the direction of movement, and equal to null, if this averaging is absent. Thu s, this function depends on the cross section of the sensor In a direction nerpendicular to the speed of movement and also means t hat it depend s on the orientation of the sensor. Acc ording to formula (12), generally the spectrum of a signal at the output of the sensor does not lead to the production r ~ f a uniform spectrum of the measured field by an energy spectral characteristic of the sensor, and represents a comp lex transformation of the field s spectrum. This transformation leads to a suppression of the high frequency c omponents of the spectrum. F or finding ~~ ( ~ ) according to the known and 4~~~ ~~~~~~~~~~ It is necessary to solve integrated equation (12). Analytical methods of solving it are complex and, apparently, Inexpedien t, since the spectrum at the output of sensor as a rule, is found in the course of treating the realization ~~~~ of measurement on a computer in a discrete amount of points and is represented in the f orm of ~~~~~~~~~~~~~~~~~~~~~~~ ~~~ ~~~~~~~ ~~~~~~~~~~~~~~~~~~.. ~~~~. ~ ~~.. ~~~~~~~~~~~~. ~~~~~~~~ ~~~~~~~ ~~~~~

12 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ = ~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~ a table of numbers. There fore, the more natural here proves to be numer ical methods, which, for the given instrument, can be inr ~ e diately incorporated in the prorram of computing the field spectrum on a c omputer. One of the simplest and most perspective is the method of simple Iterations [14], consisting of the fact that the ; approximation of the field spectrum is exnressed through & ~~~~~~~~~~~~~~~~~~ the 4 orr i (4.), according to relationship (12), In ~~~~~~ ;,. c ~~~ ) ~~~~ 1 90~ (13 ) In which regard, as the null approximation, it is natura l to take va lue The first approximation doubles the range in which a ~.( s,4 the spectrum obtained In the result o 4 nrocessing, can be computed in coincidence with the field spectrum. Repeating operation (13) many times, we can, in the region where n ~~,,u,j#j, obtain a solution to equation (12) with any previously assigned accuracy. This affords the possibility of obtainin g a field spectrum in a pure form, exc luding the influence of spectral characteristic of the measuring instrument. Let us illustrate what has been proposed above on the example of a signal spectrum at the output of a measurer of optical trans oittance of sea water, wh ich was obtained in the Atlantic Ocean by the scientific research ship t? ~Ikhail Lomonosov on its 21st cruise (curve 1 in the figure) [5]. The base of the instrument has length, speed of movement v,. 45 cm/sec, and tha base of the instrument is oriented perpendicular to the direction of movement. The frequency characteristic of the inertial part of the instrument 8. ~~~~~~~~~~~ ~~~~~~~~~ fl,

13 ~~. ~ ~ ~~~~~~~~~.. has a pass band ~ rhich is wider ~~~~~~ 10 Hz, which gives the ability to consider the instrument In a range of frequencies fro Hz noninertlal. The signa l spectrum at the output of this instrument sharply decreases with frequency. The solution to equation (12) for this case gives a field spectrum reflected by curve 2, the degree of de c) ease of which is substantially smaller than for the signal spectrum. As we can see from a comparison of these spectra, t he transmittance measurer s sensor weakens the high frequencies, whic h can lead to an error Interpretation of the results of measurements. A calculation of the drift and properties of spatial averaging of the instrunent oermits avoiding these errors.. ~~ sharp difference in the spectrum of an output signal and a field s pectrum is caused by t he fact that, In the given case, we are studying the spectrum of spatial nonuniforrnities of the field, the scales oc which are comparable to the dimension of the sensor of the instrument. Here, the sensor represents a spatial filter, separating the higher frequencies ~ If with the measurement we set the purpose of Investigating the spectra of nonuniformities, the scales of which substantially (by 5 or more times) exceed the dimensions of the sensor, then the spectrum of the out put signal practically coincides with the field spectrum, and there is no necessity for these computations.. ~ ~~~~~~~~~. 4. ~~~~ ~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~. ~~~~~~~~~~~~~~~~. ~~~~~~~~~~~~~~~..,..

14 . ~~~~~~~ ~~~ ~~~~... ~~~~~~~ ~!gure. Prectrum of a signal at the output of a transmittance measurer (1) and the spectrum of a field of transmittance (2). PIPLIO GRAPHY 1. KOA CM.zoa Al. A3roMaT.aapOaaaamg. ci ~~ swa ;6 ~ p., tz... p a n ~ ~~ ~~.o6p.6oi ~ i i$opi ~~ aui o uscuz ~~ nax v, oz..wa. B in ~~ AaroMaTa,,aW *my ~~~ x ~~ oi. ~ oa.i ~ $ ~ op.t ~ ogssuo ~ CeBm.roguoJib, ia ~. MflI AN YcCP, 3. MoI ~ tnm A.C, ~~~~~~~ A, M ~ j Wq ~~~ ~ t$. ~ 3. Wec ~ o ~ H.C ~ aw ~~ nu c ~~ * i,o ~~ c ~ rwo ~ U C14y ~~ $q$i ~ ~ QMX, M, C.a. p*n ~ o, , Mrzaai C,1, ~~~~~~~~ XJ 1 flpi ~ ia ~.w k MSTQ. m.rn ~~~~ * m,i ~~~ m. ~ Ix yp.h. ~ Hay ~ a, I ~ 3 ~ Xap ie ~~ o A.C,, N.yø,U ~ r,r. M.z ya. ~~ uc r ~ mo$. wy.z. IM$.* ~ v*.p.. B.. I f ~~ 1 ~ r, MIiI AM YCCP, imir f 10 ~~~~, ~~~~~~~~~~~~~~~~~~~ ~~~~

15 ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ DISTRIBUTION LIST DISTRIBUTION DIRECT TO RECIPIENT ORGANIZATION MICROFICHE ORGANIZATION MICROFICHE A205 DMATC 1 E053 AF/INAKA 1 A210 DMAAC 2 E017 AF/RDXTRW 1 B344 DIA /RDS3C 9 E403 AFSC/INA 1 C043 USAI4IIA 1 E404 AEDC 1 C509 BALLISTIC RES LABS 1 E408 AFWL 1 C510 AIR MOBILITY R&D 1 E410 ADTC 1 LAB/FIO C5].3 PICATINNY ARSENAL 1 FTD C535 AIATION SI S COND 1 CCN 1 C591 FSTC 5 ASD/FTD/NIIS 3 C6 19 MIA REDSTONE 1 NIA/PHS 1 D008 NISC 1 NIIS IJSAICE (USAREUR) 1 P005 DOE 1 P050 CIA/cRB/.ADD/SD 1 NAORDSTA (50L) 1 NASA/KS I 1 AFIT/LD 1 LLL/Code L389 :1 FTD ID (Rs)T ~~~~~~~~~~~~~~~ m ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~