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Full text of "Altitude dependence of CT2 over the ocean"

NPS-61Fr77101 



UBRAflT 

TECHNICAL RFPCRT SECT1 
NAVAL PC 'ATE S 

MONTEREY. CALIFORNIA 



NAVAL POSTGRADUATE SCHOOL 

Monterey, California 




ALTITUDE 


DEPENDENCE 


OF C T 2 OVER 


THE OCEAN 






C. W. 


Fairall 










and 






Ralph 


Markson 


and 


Jan Sedlacek 






1 October 


1977 





Approved for public release; distribution unlimited 

spared for: Naval Air Systems Command 
FEDDOCS Washington, D.C. 20360 

D 208.14/2:NPS-61Fr77101 



NAVAL POSTGRADUATE SCHOOL 
Monterey, California 

Rear Admiral I. W. Linder J. R. Borsting 

Superintendent Provost 

The work reported herein was supported in part by the Naval Air Systems 
Command, Washington, D.C. 

Reproduction of all or part of this report is authorized. 

This report was prepared by: 



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BEFORE COMPLETING FORM 



1. REPORT NUMBER 

NPS-61Fr77101 



2. GOVT ACCESSION NO 



3. RECIPIENT'S CATALOG NUMBER 



4. TITLE (and Subtitle) 



Altitude Dependence of C- Over The Ocean 



5. TYPE OF REPORT & PERIOD COVERED 



Sep 1976 - Jun 1977 



6. PERFORMING ORG. REPORT NUMBER 



7. AUTHORS 

C. W. Fairall, Ralph Markson and Jan Sedlacek 



8. CONTRACT OR GRANT NUMBERfa; 

NAVAIR N00019-76-C-0588 
and NAVSEA PMS 405 



9. PERFORMING ORGANIZATION NAME AND ADDRESS 

Department of Physics § Chemistry- 
Naval Postgraduate School 
Monterey, CA 93940 



10. PROGRAM ELEMENT, PROJECT. TASK 
AREA 4 WORK UNIT NUMBERS 



II. CONTROLLING OFFICE NAME AND ADDRESS 

Naval Air Systems Command 
Washington, D.C. 20360 



12. REPORT DATE 

1 October 1977 



13. NUMBER OF PAGES 
50 



14. MONITORING AGENCY NAME 4 AODRESSf// dlllerent from Controlling Office) 



15. SECURITY CLASS, (of thla report) 

UNCLASSIFIED 



I5«. OECLASSIFI CATION/ DOWNGRADING 
SCHEDULE 



16. DISTRIBUTION STATEMENT (of thla Report) 

Approved for public release; distribution unlimited 



17. DISTRIBUTION STATEMENT (of the abatract entered in Block 20, It different from Report) 



18. SUPPLEMENTARY NOTES 



19. KEY WORDS (Continue on reverae aide it neceaaary and identify by block number) 



20. ABSTRACT (Continue on reverae aide It neceaaary and Identity by block number) 

The height dependence of the temperature structure parameter, C T , has been 
measured with microthermal sensors mounted on a light aircraft. This work 
was done in conjunction with optical propagation and turbulent transport 
research in the marine boundary layer. These measurements indicate that, 
in the absence of a strong inversion, the constant stress layer can be 
surprisingly thin. The measurements also substantiate the strong role played 

by temperature and water vapor discontinuities in turbulence above the boundary 

la ver 



W 1 JAN 73 



1473 



EDITION OF 1 NOV 85 IS OBSOLETE 
S/N 0102-014- 5601 | 



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SECURITY CLASSIFICATION OF THIS PAGE (When Data Bnierod) 



ALTITUDE DEPENDENCE OF C^ OVER THE OCEAN 



C. W. Fairall 

Environmental Physics Group 

Naval Postgraduate School 

Monterey, CA 93940 



and 



Ralph Markson and Jan Sedlacek 
Airborne Research Associates 
46 Kendal Common Road 
Weston, MA 02193 



ABSTRACT 



2 



The height dependence of the temperature structure parameter, C ' 
has been measured with microthermal sensors mounted on a light air- 
craft. This work was done in conjunction with optical propagation 
and turbulent transport research in the marine boundary layer. 
These measurements indicate that, in the absence of a strong inver- 
sion, the constant stress layer can be surprisingly thin. The measure- 
ments also substantiate the strong role played by temperature and water 
vapor discontinuities in turbulence above the boundary layer. 



ALTITUDE DEPENDENCE OF ATMOSPHERIC TURBULENCE OVER THE OCEAN 

I . INTRODUCTION 

A. General Comments 

1. Optical propagation 

2 . Transport 

B. Other Work 

C. Operational Games 

II. INSTRUMENTATION AND TECHNIQUES 

A. Platform 

1. Airplane 

2 . Other measurements 

B. C T 2 

1 . Two wire definition 

2. Probes 

3. Noise 

III. THEORY 

A. Boundary Layer 

1. Define U*, T , R. , L 

2. Expressions for C~ 

3. Expected height dependence 

B. Above Boundary Layer 

1. Length scale 

2 

2. C^ 

IV. RESULTS 

A. Ship Results 

B. Airplane 

1. CEWCOM 76 

2. NJ 

3. HAYES 77 



V. CONCLUSIONS 11 

A. Boundary Layer 

B. Above Boundary Layer 

REFERENCES 13 

FIGURE CAPTIONS 15 



li 



I . INTRODUCTION 

2 
We have made measurements of temperature structure parameter, CL , from 

a light aircraft using microthermal sensors as part of a study of turbulence 

2 
in the marine boundary layer. C T is important for optical propagation 

studies due to its relation to the index of refraction structure parameter, 

C N 2 , [Friehe (1977)] 

C N 2 = (79 x 10" 6 P/T 2 ) 2 (C T 2 + .11 CL + 3.2 x 10" 3 C 2 ) (1) 

2 
where: C is the water vapor structure parameter, 

C T is the cospectrum structure parameter, 

p is the pressure in mb, and 

T is the absolute temperature. 

The water vapor fluctuations are usually relatively small so we can write 

C^ 2 = (79 x 10" 6 P/T 2 ) 2 C T 2 (2) 

2 2 
This relationship is shown in Fig. 1 with C^ /CL, as a function of altitude 

for the U.S. Standard Atmosphere. Turbulence is also of interest because of 
the role of eddy diffusion in the transport of heat, water vapor, and pol- 
lutants. These factors are important in the formation of marine fog and air 
pollution modeling. 

2 
Only a few measurements of the altitude dependence of CL, have been made 

2 
to date. Korpov and Tsvang (1966) have made measurements of CL with an 

acoustic anemometer on an airplane and have related their results to the 

vertical temperature gradient. Microthermal sensors have been used to measure 

2 
CL with balloon borne equipment by Bufton (1973) and airplane borne equipment 



by Lawrence (1970) and Collins (1977) . Recently, Hanson (1976) has combined 

airplane microthermal measurements and remote scintillometer determinations 

2 
of C, and compared his results with an impirical model developed by Yura. 

Based on this body of data, Hall (1977) has compiled a conglomerate curve 

2 
of C_ as a function of altitude (Fig. 2) for daytime overland data. Only 

Ochs (1973) has reported measurements over the ocean. 

The data we are reporting on were taken as part of three separate 
research operations . The first was the "Cooperative Experiment for West 
Coast Oceanography and Meteorology - 1976" (designated CEWCOM 76) , a marine 
fog research project off San Diego. CEWCOM 76 was organized by the Naval 
Postgraduate School and the Naval Electronics Laboratory Center. The second 
was a marine fog and aerosol project in the Gulf of Mexico off Panama City, 
Florida (designated FLORIDA 77) . The third was in conjunction with a turbu- 
lence and aerosol research cruise on the USNS Hayes in the Atlantic (desig- 
nated HAYES 77) organized by the Naval Research Laboratory. 



II. INSTRUMENTATION AND TECHNIQUES 

The platform for our measurements is a single engine turbocharged 
Bellanca operated by Airborne Research Associates (Fig. 3) . This aircraft 
has been flown as low as 3 meters and as high as 10,000 meters and makes an 
excellent tool for the low altitude flights required for boundary layer 
research. The aircraft is well instrumented, allowing simultaneous measure- 
ments of air temperature, altitude, dew point, electric field, visibility, 
infrared surface temperature, and microwave refractive index. The data is 
normally recorded with an eight channel strip chart recorder. 

The temperature structure parameter is measured using the paired sensor 
method. Given two temperature sensors, 1 and 2, a distance d apart, then 
[Lumley (1964)] 

C T 2 = < (T 2 - T : ) 2 > d' 2/3 (3) 

This quantity is related to the Kolmogorov power spectral density of tempera- 
ture fluctuations, <j> T (k), 

* T Ck) = .25 C T 2 k~ 5/3 (4) 



where k is the wave number. Equation 4 applies in the inertial subrange part 

of the spectrum where the turbulence is nearly isotropic, allowing a one- 

2 
dimensional representation of <J> T (k) . C™ is independent of d in the inertial 

subrange . 

2 
The device we have used to measure CL, is a DC Wheatstone bridge (Thermo 

Systems Model 1044) that senses the relative resistance fluctuations of a 



pair of 2.5 micron diameter platinum wires separated by about one meter. 
The sensors were originally mounted on tne leading edge of the wing (CEW- 
COM 76 and FLORIDA 77) but the noise level was very high so the sensors 
were moved to the present wing tip location (Fig. 4) . The output of the 
bridge (proportional to AT = T 2 - T,) is processed by an RMS module with 
a 5 sec time constant and recorded on the strip chart recorder as AT RMC . . 
The sensitivity is limited by the broad band noise of the system due to 

inherent amplifier noise and pickup from the aircraft ignition system. 

2 -4 
For CEWCOM 76 and FLORIDA 77 the noise level corresponds to L ~ 4 x 10 

2 2/3 2 -4 2 2/3 

k /m , for HAYES 77 the noise level is lower (CL — ' 10 k /m ) since 

we were using the wing tip probe configuration. It is possible to improve 

the accuracy by correcting for the noise. If we assume an RMS noise level 

of N, then the noise correction appears as 

c t 2 = c < A W 2 - n2 i d " 2/3 & 

Since 2.5 micron wires are fragile, breakage is a continual problem. 
Except for one bad batch of wires, we have found a typical lifetime of one 
or two flights for a given wire. We presently have two pairs of sensors 
mounted and can switch to a good pair if one wire breaks . 



III. THEORY 

The boundary layer is that part of the atmosphere where friction 
with and heating by the surface play an important part in the generation 
of turbulence. Near the surface the shear stress and scalar fluxes are 
essentially constant. In this region the fluxes can be represented by 
scaling parameters (such as U # and T*) that are independent of height. 
We shall refer to this layer of nearly constant stress and flux as the 
surface layer. In the surface layer, the height above the surface, Z, 
is the appropriate turbulence length parameter. For a complete treatment 
of the surface layer equations we suggest Lumely (1964) , Businger (1971) 
or Kraus (1972) . The normalized momentum flux, F , and the normalized 
heat flux, F, , for turbulent transport are 

F = - < u'w 1 > = LL 2 (6) 

m * 



F h = - < T'w' > = U*T* (7) 



where u' is the horizontal velocity fluctuations, 

w" is the vertical velocity fluctuations, 

T' is the temperature fluctuations, 

U* is the friction velocity, and 

T* is the scaling temperature. 

The atmospheric stability is represented by either the Monin-Obukov length, 

L, or the Richardson number, R. , 

l 



2 
T U* 

L ■ wz (8) 



g(3T/3Z) 

R. V —j (9) 

T(3U/3Z) 



where T is the virtual potential temperature, 

g is the acceleration of gravity, 

U is the mean horizontal velocity, and 

K = .35 is the Von Karmon constant. 

The mean and fluctuating temperature dependences on height are given by 
[Wyngaard (1971)] 

T 

I = kz f i w (10) 



C T 2 = T* 2 Z _2/3 f 2 (Z/L) (11) 



Under near-neutral conditions f, and f ? are equal to unity, resulting in a 

2 -2/3 

logarithmic mean temperature profile and CL proportional to Z ' . Under 

2 -4/3 

unstable conditions (- Z/L » 1/7) C T is proportional to Z . These 

relationships are based on measurements made on a flat Kansas plain with 
averaging times of about one hour. Due to the shorter average time invol- 
ved in aircraft profiles, one expects scatter about the curve of Eq. 11 
even in the surface layer. 

Wyngaard points out that although these results are based on surface 

measurements (Z < 22 m) they are valid to somewhat greater heights. In 

2 
the case of the well developed unstable boundary layer, the predicted CL, 

profile is valid well beyond the surface layer. Although Davidson (1977) 

has found evidence of wave influence restrictions on the lower limit of 



the oceanic surface layer equations, the primary interest of optics and 
transport users is in establishing the upper limits of validity. 

The upper limit is often assumed to be at least half the distance 
to the first inversion. This distinction becomes even more tenuous if 
there is no low inversion. Above the surface layer, equations 10 and 11 
become meaningless when defined in terms of the absolute height above the 
surface, Z. Since the vertical gradients are still meaningful, Richardson 
number remains a useful representation of stability. The appropriate 
length parameter is the integral scale (or outer scale), A, which is a 
measure of the largest size (or minimum wave number) for which the 
Kolmogorov spectrum of equation 4 is valid [Hinze (1959)]. In the surface 
layer A is proportional to Z . In this representation we have 

I = Fa t f i (V ™ 

C T 2 = T* 2 (A T )~ 2/3 ff» (R.) (13) 



where f,' and f ' are analogous to f. and £~ 



IV . RESULTS 

2 
Shipboard and platform measurements of C_ have shown fairly good 

agreement with the predicted height dependence in the near surface layer 
(Z < 25 meters). Fig. 5 shows a profile taken at the Naval Coastal Systems 
Laboratory's Stage I in the Gulf of Mexico during FLORIDA 77. We have 
found the marine surface layer to be predominately near -neutral with a 
tendency to be slightly unstable. Based on numerous shipboard measure- 
ments we have found typical values of L: • 100 meters and T* r - .08 °C. 

2 
Using these values we have indicated typical surface based C T profile 

(from equation 11) as the dashed line in Fig. 2. Under these conditions 

we would expect C„ ** Z to be a good approximation for Z > 20 meters. 

However, during HAYES 77 we found the Atlantic Coast from Cape Code to 

Newfoundland to have a stable surface layer. It has been our experience 

from various shipboard operations that stable conditions are most likely 

2 
to produce anomalous C T profiles in the near surface layer. 

The surface layer is usually well defined off the Pacific Coast of 
the United States due to the persistence of a strong marine inversion. 

Consequently, we can expect C T to be well described by the Z or Z 

2 
equation. In Fig. 6 we have two aircraft measurements of C T before and 

after a radiosonde balloon launch during near neutral conditions. The 

C T profile is very well fit by the Z~ law until the inversion is 

2 
reached, where C T increases rapidly with the temperature gradient. In 

this case the surface layer dominates the entire boundary layer. The strong 

2 
peak in C T at the inversion (Z ~ 200 m) is in agreement with the ship's 

acoustic sounder. 



The Atlantic Coast data taken during HAYES 77 is considerably less 
encouraging. In Fig. 7 we can see a well developed surface layer similar 



to the Pacific Coast profile of Fig. 6. The marine inversion occurs at 
Z = 200 meters. There is also a strong layer of turbulence which occurs 
above a sharp temperature discontinuity at Z - 1700 meters. In Fig. 8 

the well defined surface layer extends only as high as Z - 30 meters. 

2 
Note the strong peaks in CL which occur at the dew point discontinuities , 

indicating the importance of water vapor in atmospheric stability. In 

Fig. 9 we find very low levels of temperature turbulence above the inversion, 

2 
but below the inversion the values of C T are very large considering that 

2 
these are stable conditions. Figs. 10 and 11 show low values of CL, near 

2 
the surface with CL, increasing with height as we approach maximum tempera- 
ture at Z =^ 400 meters. In this case, the normal surface layer equations 
are a very poor representation. It is also interesting to note that a 
nearby profile (Fig. 12, taken about 100 km south of those shown in Figs. 
10 and 11) is completely different. 



10 



V. CONCLUSIONS 

In the presence of a raised marine inversion, such as off the Pacific 

Coast, a well mixed turbulent boundary layer is usually found. The height 

2 
dependence of C™ in this layer will be well described by the standard 

surface layer expressions up to the inversion. In the absence of a strong 

raised inversion, such as is often the case off the Atlantic Coast, there 

may be no well mixed turbulent boundary layer. This is particularly true 

2 
under stable conditions where the magnitude of C T found at the surface 

may in fact be dominated by a low level temperature discontinuity. Under 

these conditions, the standard surface layer equations may be invalid above 

heights on the order of 10 meters. 

Above the boundary layer, air mass boundaries and other sources of 

temperature, velocity, and water vapor discontinuities play a critical role 

2 
in the magnitude of C T . This is even more significant for optical propa- 

2 
gation because C,. is also affected by water vapor fluctuations (eq. 1). 

A profile taken during FLORIDA 77 (Fig. 13) shows that these layers can 

produce large effects as high as 5,000 meters. 



ACKNOWLEDGEMENTS 

The authors wish to recognize the contributions of Dr. K. L. Davidson of 
NPS. Work supported by NAVAIR contract N00019-76-C-0588 and NAVSEA PMS 405 



11 



REFERENCES 

1. Bufton, J.L., Comparison of Vertical profile turbulence structure with 

stellar observations, Appl . Opt. 12, 1785-1793 (1973). 

2. Businger, J. A., J.C. Wyngaard, Y. Izumi and E.F. Bradley, Flux profile 

relationships in the atmospheric surface layer, J. Atmos . Sci. 28 , 
181-189 (1971). 

3. Collins, S.A., Y.J. Liu and L.E. Pape, Altitude dependence of C^ eval- 

uation of airborne refractive index fluctuations, Proc. of Optical 
Propagation through Turbulence, Rain and Fog, Boulder, CO (1977). 

4. Davidson, K.L., T.M. Houlihan, G. Schacher and C.W. Fairall, An exami- 

nation of scaling laws for Cj^ in the layer adjacent to ocean waves, 
Proc. of Optical Propagation through Turbulence, Rain and Fog, 
Boulder, CO (1977) . 

5. Friehe, Carl A., Estimation of refractive-index temperature structure 

parameter over the ocean, Appl. Opt. 16 , 334-340 (1977). 

6. Hall, Freeman F., Index of refraction structure parameter in the real 

atmosphere - an overview, Proc. of Optical Propagation through 
Turbuelnce, Rain and Fog, Boulder, CO (1977). 

7. Hanson, Donald W. , Atmospheric turbulence measurements at AMOS, Proc. 

of Optical-Submillimeter Atmospheric Propagation Conf . , Colorado 
Springs, CO, 245-254 (1976). 

8. Hinze, J.D., Turbulence , McGraw-Hill, New York, p 184-204 (1959). 

9. Korpov, V.N. and L.R. Tsvang, Characteristics of very small-scale tur- 

bulence in a stratified boundary layer, Atmos. and Oceanic Phys . 
22_, 1142-1150 (1966). 

10. Kraus, E.B., Atmosphere - Oceanic Interaction , Clarendon Press, Oxford, 

Ch. 5 (1972). 

11. Lawrence, R.S., G.R. Ochs and S.F. Clifford, Measurements of atmospheric 

turbulence relevant to optical propagation, J. Opt. Soc. Am. 60 , 
826-830 (1970). 

12. Lumley, J.L. and H.A. Panofsky, The Structure of Atmospheric Turbulence , 

Interscience, New York (1964). 

13. Ochs, G.R. and R.S. Lawrence, Temperature and C^ profiles measurements 

overland and ocean to 3 km above the surface, NOAA Technical Report 
ERL 251-WPL 22 (1972) . 

14. Wyngaard, J.C, Y. Izumi and S.A. Collins, Behavior of the refractive- 

index-structure parameter near the ground, J. Opt. Soc. Am. 61 , 
1646-1650 (1971) . 

15. Yura, H., Interim Report for ARPA order 2843, SAMOS TR, unpublished. 



13 



FIGURE CAPTIONS 

2 2 

1. Height dependence of C^ /CL, based on eq. 2 for the U.S. Standard 

Atmosphere. 

2 

2. Height dependence of C T . The solid line is the ground average com- 
piled by Hall (1977) for daytime overland profiles. The dashed line 
is an extrapolation using eq. 11 from typical shipboard oceanic sur- 
face layer measurements. 

3. Airborne Research Associates, Inc., Bellanca research aircraft during 
operations off Nova Scotia with the USNS Hayes in May of 1977. 

2 

4. Wingtip probe configuration for measurement of C T . 

2 

5. Height dependence of CL, measured from the Naval Coastal Systems 

Laboratory Stage I off Panama City, Florida during FLORIDA 77. 

2 

6. Height dependence of C„ for two profiles during CEWCOM 76 with a 

simultaneous ship launched radiosonde. 

2 

7. Temperature and C T profiles off the New Jersey Coast, 22 Feb. 1977. 

The top of the haze layer was 1700 meters. 

2 

8. Temper ature,dewpoint and C T profile (HAYES 77) near the Nantucket 

Light Ship on 16 May 1977 at 1325 ADST. 

2 

9. Temperature, dewpoint and C„ profile (HAYES 77) near Cape Sable, N.S 

2 
on 17 May 1977 at 1525 ADST. The x's denote C T values and the arrow 

denotes the ocean temperature measured from the USNS Hayes . 

2 
10. Temperature, dewpoint and C„ profile (HAYES 77) about 20 km east of 

Cape Canso, N.S. on 18 May 1977 at 1625 ADST. The x's denote Cp 2 

values and the arrow denotes the ocean temperature measured from the 

USNS Hayes. 

15 



2 

11. Temperature, dewpoint and (L, profile (HAYES 77) about 20 km east 

of Cape Canso, N.S. on 18 May 1977 at 1715 ADST. The x»s denote 

2 
C T values and the arrow denotes the ocean temperature measured from 

the USNS Hayes. 

2 

12. Temperature, dewpoint and Cp profile (HAYES 77) about 100 km southeast 

of Halifax, N.S. on 18 May 1977 at 1750 ADST. 

2 

13. Temperature, dewpoint and CL, profile (FLORIDA 77) south of Panama City, 

Florida on 19 February 1977 at 1300 CDT. The values of T > T are not 
real but represent a calibration shift of the dewpoint instrument. 






16 



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19 




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FIGURE 4 




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23 



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FIGURE 5 



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FIGURE 6 



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27 



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37 



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41 



INITIAL DISTRIBUTION LIST 

No. of Copies 

1. Defense Documentation Center 2 
Cameron Station 

Alexandria, Virginia 22314 

2. Library, Code 0212 2 
Naval Postgraduate School 

Monterey, California 93940 

3. Dean of Research, Code 023 1 
Naval Postgraduate School 

Monterey, California 93940 

4. Asst. Professor C. W. Fairall, Code 61Fr 5 
Naval Postgraduate School 

Monterey, California 93940 

5. Professor K. E. Woehler, Code 61Wh 1 
Naval Postgraduate School 

Monterey, California 93940 

6. Dr. Ralph Markson 5 
Airborne Research Associates 

46 Kendal Common Road 
Weston, Massachusetts 02193 

7. Assoc. Professor K. L. Davidson, Code 63Ds 1 
Naval Postgraduate School 

Monterey, California 93940 

8. Assoc. Professor T. Houlihan, Code 69Hm 1 
Naval Postgraduate School 

Monterey, California 93940 

9. Assoc. Professor G. Schacher, Code 61Sq 1 
Naval Postgraduate School 

Monterey, California 93940 

10. Mr. Murray Schefer 1 
Code Air-3706 

Naval Air Systems Command 
Washington, D.C. 20360 

11. LT M. Hughes 1 
PM-22/PMS 405 

Naval Sea Systems Command 
Washington, D.C. 20362 



43 



12. Dr. Stuart Gatham 
Code 8326 

Naval Research Laboratory 
Washington, D.C. 20375 



44 



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'''"£iKir RARY ■ research rep ° rts 

5 6853 01069629 7 



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