Atmospheric turbulence chamber for optical transmission experiment: characterization by thermal method

Atmospheric turbulence chamber for optical transmissionexperiment: characterization by thermal method

Hideya Gamo and Arun K. Majumdar

A turbulence chamber (0.78 X 0.23 X 2.59 M3) consisting of ten small electric heater/blowers with an alumi-

num foil screen and three screens of 2-mm aluminum wire meshes can generate the nearly homogeneous iso-tropic turbulence within the 0.5 X 0.05 X 2-m3 region at the 0.11-m height of optical measurements. Thetemperature structure constant squared C = 52.9 K2 m-2/3 was obtained from the temperature structurefunction measurements measured by using a differential microthermocouple system. The refractive-indexstructure constant squared C2 at the 632.8-nm wavelength was calculated from C:C = 3.00 X 10-11 m-2/ 3.The average wind velocity and temperature were 0.41 m/sec and 531C, respectively. From the power spec-trum of temperature fluctuations, the inner and outer scales of turbulence are determined: 10 = 5.0 mm andLo = 6.5 cm. The measured temperature structure function and power spectrum of temperature fluctua-tions satisfy the 2/3 and -5/3 power similarity laws in the inertial subrange, respectively.

Introduction

Artificially generated atmospheric turbulences havebeen utilized in a few optical propagation and imagingexperiments. Most of them, however, were performedwithout thoroughly specifying the strength of turbu-lence.1-5 We have designed and built a simple atmo-spheric turbulence chamber with the intention of per-forming optical wave propagation experiments throughthe well defined, homogeneous, and isotropic turbu-lence. Since the refractive-index fluctuations in theatmosphere are mainly dependent on the temperaturefluctuations,6 we utilized the heater/blowers for gen-erating the stronger refractive-index fluctuations andmade the turbulence more homogeneous and isotropicby passing through metallic screens with random foilsand 2-mm screens. In this paper, we shall characterizethe atmospheric turbulence in the chamber by thetemperature structure constant CT which is determinedfrom temperature fluctuation measurements, and thenderive the refractive-index structure constant C, fromCT. The T of the turbulence chamber was found tobe 1000 times stronger than that of the typical atmo-sphere. The characterization by the irradiance fluc-tuation measurements will be described in the secondpaper.

When this work was done both authors were with University ofCalifornia, School of Engineering, Irvine, California 92717; A. K.Majumdar is now with California Institute of Technology, Jet Pro-pulsion Laboratory, Pasadena, California 91103.

Received 29 April 1978.0003-6935/78/1201-3755$0.50/0.© 1978 Optical Society of America.

The histogram, variance, and power spectrum offluctuations of the temperature difference between twomicrothermocouple probes were obtained. The ex-perimental data were processed using a PDP 15/20system. The temperature structure function (the meansquare temperature difference between two probes) wasmeasured as a function of the probe separation. It isshown that the temperature structure function dependson the 2/ power of the probe separation from 2 cm to 6cm in accordance with the Kolmogorov-Obukhov sim-ilarity law.7 The temperature structure constants CTwere obtained from these measurements of temperaturestructure function.8

The power spectrum of temperature fluctuationsmeasured inside the turbulence chamber is dependenton the -5/3 power of the frequency within the fre-quency range from 5 Hz to 80 Hz. This agrees with thewell known f/3 law for the inertial subrange of ho-mogeneous isotropic turbulence. 9 10 By assuming thatturbulence eddies were frozen while flowing at the meanvelocity 0.41 m/sec, we estimated the inner and outerscales of turbulence of the upper and lower frequencylimits mentioned above: lo = 5 mm and Lo = 8.2 cm,respectively.

The refractive-index structure constants C werederived from the temperature structure constants CTby using the temperature dependence of the refractiveindex of the atmosphere. The C2 of our turbulencechamber is 1000 times larger than that of typical tur-bulence atmosphere.

Different methods for generating the homogeneousisotropic turbulence are compared to our method.Possible improvements of our turbulence chamber and

1 December 1978 / Vol. 17, No. 23 / APPLIED OPTICS 3755

Fig. 1. Schematic diagram of the turbulence chamber including themicrothermocouple system.

I

0

cW

1.250 z * O.45m

x2 1.08m10 z 1.50m

.0 z* 2.08m

- AVERAGE FOR 0.45 m

0.75

0.50 ''_ AJ

0.25 …

0.0C10.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

DISTANCE (METER)

Fig. 2. Average wind velocity within the turbulence chamber is

shown as a function of the distance x from the last screen along thedirection of air flow.

some meaningful aerodynamical experiments are dis-cussed.

The measurement of the frequency response functionof microthermocouples is described in Appendix A, andthe rms temperature gradient and characteristic tem-perature of the turbulent temperature field were eval-uated by using experimental results and are describedin Appendix B.

Design of a Turbulence Chamber

The design of the turbulence chamber is schemati-cally illustrated in Fig. 1. The turbulence chamber withinternal dimensions, 2.69 m long, 0.78 m wide, and 0.23m high, was assembled on a shock-mounted opticalbench. The internal surface of sidewalls, top covers,and aluminum plates of the optical bench were coatedby a special black paint (3M 101 CID) in order to min-imize disturbances due to the reflection of the scatteredlight by the chamber walls.

Ten small electric heater/blowers (Sears, 764, H,model 344) were installed on one side of the turbulencechamber. The turbulent flows generated by theheater/blowers are parallel to the optical bench surfaceand perpendicular to the optical transmission direction.The height of the center of the flow was almost equal toour standard height for optical measurements, 0.11 m.

The turbulent flow generated by the heater/blowers washomogenized by passing through a screen of aluminumfoil (commonly used in electronic instruments for ven-tilation filters) and then through three layers of 2-mm2

aluminum meshes, each separated by 1 cm. The tur-bulent flow produced by heater/blowers operated at therate of 750 W was found convenient for the various op-tical transmission experiments because of its largestrength of turbulence.

Average Wind Velocity and Temperature Distribution

The wind velocity and temperature were measuredalong the flow direction (x) by a hot wire anemometer(Alnor Thermo-Anemometer 8500) throughout theturbulence chamber at the standard height 0.11 m. Theresults of wind velocity measurements are shown in Fig.2. The uniformity of the wind velocity in the flow di-rection (x) improved with distance from the last screen.At x = 0.61 m, the wind velocity became fully uniform.The average wind velocity in the 0.30-0.61-m range was0.41 m/sec at the standard height of 0.1103 m.

The temperature profile for the case in which theheater/blower was set to 750 W is shown in Fig. 3. Thetemperature averaged over the chamber was 530C.Comparing the results in Figs. 2 and 3, we notice thatthe temperature distribution became uniform at a muchfaster rate than the wind velocity distribution.

The development of turbulent flow inside thechamber may be explained in the following way.1 Aflow generated by each heater/blower at the inlet of thechamber forms boundary layers on both upper andlower walls, owing to the viscous friction. As flowpropagates along the x direction, the interaction be-tween flow shear and inlet turbulence increases. Thus,the thickness of boundary layers formed on both wallswill increase in the downstream. As a result, the uni-formity of the bulk flow in the y direction will improve.This is exhibited by Fig. 4, where wind velocity profilesalong the y axis (height) for x = 0.013 m, 0.30 m, and0.61 m from the last screen at the distance z = 1.09 mare illustrated. It was concluded that a region in the

e * z'2.08m

80-

sr-1

40

20-

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8DISTANCE (METER)

Fig. 3. Average air temperature within the turbulence chamber is

shown as a function of the distance x from the last screen along the

direction of air flow.

3756 APPLIED OPTICS / Vol. 17, No. 23 / 1 December 1978

_ 1.00 -UI

w 0.75

I

0

0.501-

0.25 -

-0.000 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200DISTANCE (METER) y

Fig. 4. Average wind velocity within the turbulence chamber isshown as a function of the height y with respect to distance x = 60

cm.

chamber of about 0.31 m wide (x), 0.076 m high (y), and2.54 m long (z) has relatively uniform velocity andtemperature.

The Reynolds number Re = ud/v for the region ofuniform flow in the turbulence chamber is Re = 6287,where the average flow velocity u = 0.41 m/sec, distancebetween walls d = 0.23 m, and the kinematic viscosityof air, v = 1.5 X 10-5 m/sec 2 , are used. According tothe standard reference books by Schlichting' 1 andVennard and Street,1 2 the critical Reynolds numbersfor flow between parallel walls are 2740 and 1000, re-spectively. Since the Reynolds number 6287 calculatedfor our turbulence chamber is much greater than thesecritical numbers, the turbulent flow within this regionof the chamber should be locally homogeneous andisotropic.1 3 This is well evidenced by the experimentalresults described in the next section.

Measurements of Temperature Structure FunctionsThe temperature structure function DT(r) is defined6

as the mean square of the temperature difference be-tween two points, r and r2:

DT(r1,r2) = ([T(rs) - T(r2 )]2 ). (1)

When the temperature field is homogeneous and iso-tropic, the structure function depends only on the dis-tance between two points r = r-r2 1:

DT(rlr2) = DT(r). (2)

The experimental setup for the temperature structurefunction measurement is illustrated in Fig. 5. Thedistance r between two microthermocouple probesmounted on an electromechanical translating unit canbe adjusted from 2 mm up to 20 cm by the increment of10 gm. The mechanical translation unit was driven byan electrical stepping motor (SLO-SYN SS50-1009,Superior Electric Co.) with an external controller, whichcan be triggered by the pulse from the PDP 15/20 dataacquisition system through a digital-to-analog con-verter. This electromechanical translation unit wasplaced on the top cover of the turbulence chamber.Only the thermocouple probes supported by the verticalstainless steel tubes were exposed to the turbulent flow(see Fig. 1). The thermocouple probes project hori-zontally upstream by 8.5 cm from the vertical sup-porting tubes. The temperature fluctuations in the

turbulent air flow were measured by using differentialmicrothermocouples of chromel-constantan (type E,Hy-Cal Engineering), of which the diameter is 7.6 Am,and the specified time constant is less than 0.1 m sec.The temperature voltage conversion factor K of themicrothermocouples was calibrated by using two electricovens while keeping the temperature of one junction at530C and varying the temperature of the other oven: K= 0.07184 X 10-3 V/K.

The frequency response of microthermocouples isconstant from dc to 200 Hz and then decreases to 1/2 ofthe dc level at 770 Hz (see Appendix A). Therefore, themicrothermocouple system can accurately measure thetemperature fluctuations of the turbulent atmosphere,of which the predominant frequency component islimited within 200 Hz.

The output voltages of two thermocouples were am-plified by differential amplifiers (Tektronix AM 502),respectively, and two single-ended outputs from theseamplifiers were connected to the differential inputconnectors of the third Tektronix amplifier (AM 502)through two 50-Q coaxial cables of equal length. Thetemperature difference at two points can be derivedfrom the differential voltage o measured by using theformula

T- T2 = [K/(G1G2 G3 )]J0, (3)

where K is the thermocouple constant; G1,G2, and G3are the gains of three amplifiers mentioned above, vo isthe voltage measured by an analog-to-digital converter.By inserting Eq. (3) into Eq. (1), we obtain the tem-perature structure function expressed in terms ofquantities measured and calibrated as follows:

((T 1 - T2)2 ) = K21[(GlG2G3 0 (4)

where the variance (vs) of the output voltage from thethird amplifier was determined from the digitizedoutput voltages by the statistical data acquisition sys-tem illustrated in Fig. 6.

MCRO-| M lTHERMOCOUPLE VOLTMETER

M OC TERTER COMLUTER

Fig. 5. Schematic diagram of measurement system of temperaturestructure function by microthermocouples.

INPUTSIGNAL

D I F F E R E N T I A D C A - I o - D P P - 1 5 / O S t o AU0

AMPLIFIER I AMPLIFIER IICONVERTER COMPUTER CONVERTER RECORDER

S T A N D A R D I C R

Fig. 6. Statistical data acquisition system used for measuring thetemperature structure function, histogram and cumulants, and power

spectrum of temperature fluctuations.


o x. - 0.018.x - 0.30m- x - 0.6m

- _U_.--- A

iI I Ius us us

In the so-called inertial subrange of the homogeneousisotropic turbulence, the temperature structure functionwill depend on the 2/3 power of distance r between twoprobes: 6

DT(r) = CTrII3, (5)

where the distance between probes should be muchlarger than the inner scale of turbulence lo but muchsmaller than the outer scale of turbulence Lo: lo << r <<Lo, and CT is the temperature structure constant. This2/3 power equation is often called the Kolmogorov-Obukhov similarity law.

The temperature structure functions at a location x= 0.38 m, y = 0.12 m, and z = 1.09 m, in the turbulencechamber, measured as a function of the probe separa-tion r, are illustrated in the logarithmic scales in Fig. 7.By inspecting these results, we notice that for the probeseparation r between 2 cm and 6 cm, the 2/3 law holdsreasonably well. The data points for the distance rsmaller than 2 cm deviate from the 2/3 line. However,the experimental results do not agree with the theo-retical temperature structure function for distancewithin the inner scale of turbulence: DT(r) cr2 . Thisdiscrepancy is most likely due to the disturbance pro-duced by stems holding a microthermocouple. Thestructure function measured starts to deviate from the2/3 law at the probe distance r = 6 cm and attains aconstant value for r = 7 cm and higher. This can beexplained by considering that for a large probe separa-tion larger than the outer scale of turbulence, the tem-perature fluctuations at the two probes are uncorre-lated. Since the cross term of temperatures in expan-sion of ((T 1 - T2 )2) vanish, temperature structurefunction DT(r) becomes independent of r. Further-more, the measured DT(r) indicates that the outer scaleof turbulence is of the order of 7 cm, and the tempera-ture field in this turbulence chamber is locally homo-geneous and isotropic within the 6-cm diam at thestandard height.

Using the logDr (r) extrapolated by the 2/3 line at r =

1 in Fig. 7, we obtain the strength of temperature fluc-tuations CT = 52.9 K2 m-2/ 3. From the measured Cwe also derived the rms temperature gradient 1.898K/cm and the characteristic temperature 0.949 K (seeAppendix B).

The uniformity of the strength of turbulence withinthe chamber was evaluated by performing a series ofmeasurements of mean square temperature differenceat a probe separation of 2.89 cm where the 2/3 law ap-proximately holds. From the measured variances oftemperature difference fluctuations, we obtained the

T defined above. The measured CT are shown in Fig.8. It should be noted that CT has a maximum valuedown the turbulent flow from the last screen, while boththe average velocity and temperature distributions willmonotomically decrease. This implies that the meansquare temperature gradient takes the maximum valuesomewhat down the flow around x = 0.46 m [refer toEqs. (B3) and (B4)].

The turbulence strength parameter of temperaturefluctuations CT is small near the inlet of the chamber

2

0.01 0.02 0.05 0.10 0.20 0.50 1.00PROBE SEPARATION r (METER)

Fig. 7. Temperature structure function DT(r) vs microthermocouple

probe separation r, where the slope 2/3 line and CT determined as thevalue at r = 1 m are indicated.

100

60

460

', 40

20

o 2 a 0,45m

x z - 1.08m

A 2 a 1.50m

z 2.08m

)A _'_111

------

0.0 0.1 0.2 0.3 0.4DISTANCE (METER) x

al - - 0 0.6

_ 0.7

_ 0.6

- 0.5

I

0.4 WE

0.3 0

._ 0.2

_ 0.1

Fig. 8. Refractive-index structure constant squared C' and tem-perature structure constant squared CT vs distance x from the last

screen along the direction of air flow.

(i.e., just near the screens adjacent to the heater/blow-ers). This indicates that the temperature fluctuationsof grid-generated turbulence is small. As the heat flowsalong the x direction, the small eddies interact witheddies generated in the shear layer adjacent to constanttemperature walls. As eddies from both sources mix,temperature fluctuations increase. In the region be-tween x = 0.30 m and x = 0.61 m, the interaction be-tween the two sources of eddies become the largest.Further downstream, the effects of wall temperaturebecome dominant, and the net temperature fluctuationsdecrease.

Power Spectrum of Temperature Fluctuations

By calculating the time average of absolute valuesquared of Fourier transform of digitized thermocoupleoutput voltage, we estimated the power spectrum oftemperature fluctuations; 512 digital samples withsampling interval of 1 in sec were processed by the fastFourier transform (FFT) method and were averagedover 20 results. The power spectrum of temperature


I

0.5 0.6

I . .

I

1

I I I

z0I-

Q

1 >

NJ -

0:

U-

! co

CNoa

-

0

W =

L

10.0FREQUENCY (Hz)

Fig. 9. Power spectrum of temperature fluctuation W(f) and f 2 W(f)is shown as a function of frequency (Hz) where slopes of respective

regions are indicated.

fluctuations at the location x = 0.38, y = 0.11 m, z = 1.09m, and the probe distance r = 2.89 cm are illustrated inFig. 9. Over the frequency region f = 10-30 Hz, theestimated power spectrum W(f) is proportional to f-5/ 3.At the frequency higher than 30 Hz, the power spectrumapproximately follows the f7 law, which was obtainedby Heisenberg 9 in the viscous dissipation region. At thefrequency region below 10 Hz, it approaches a constantvalue in a manner similar to the atmospheric turbulencemodel discussed by Strohbehn.14

In order to determine the transition frequency fromthe inertial subrange to the viscous dissipation range,we also calculated f 2 W(f) and showed in Fig. 9. Theupper and lower crossing points of the f- 5/ 3 line for in-ertial subrange with the f 7 and constant lines in Fig.9 are given by fh = 80 Hz and f = 5 Hz, respectively.Since the inner scale of turbulence equal to 10 of theinertial subrange is given by lo = u/fh, by inserting theaverage wind velocity u = 0.406 m/sec and fh = 80 Hz,we obtain 10 = 5 mm. Likewise, by inserting the sameaverage wind velocity and f = 5 Hz into the outer scaleof turbulence Lo = u/f,, we obtain the outer scale ofturbulence Lo = 8 cm. The Reynolds numbers for thesescales of turbulence Re = ulo/v and ReL = uLo/v aregiven by Re = 135 and ReL = 2, 165, respectively.

Statistics of Temperature FluctuationsThe 512-channel histogram of temperature difference

at r = 2 cm was obtained by using the PDP 15/20 dataacquisition system for various locations of the turbu-lence chamber. From these histograms, we derived thecentral moments m and cumulants X up to the eighthorder.151 6 The coefficients of variation yo, skewness

yi, and excess 72 are calculated from measured mo-ments and cumulants, including their error esti-mates:

70 = a;

71 = 31U3;

72 = A4/04 - 3;

(6)

(7)

(8)

where ,t is the mean, ay is the standard deviation, andC)2 is the variance. The smoothed frequency distribu-tion curves of temperature can be obtained by insertingthe above coefficients into the Edgeworth series15:

f (t) = 0S(t) - 3y1y0(3)(t) + !Y2 (4)() + 1y0 ip(6)(Q) +...,N = W 3! 4! 2 6!7

where

0' ' = (2, exp 2)

and ¢(n)(t) is the nth derivative of 0(t);0(n)() = (-)nHnQ)0Q)

= (X -,u)a.

(9)

(10)

(11)

(12)

H,(,) is the Hermite polynomial of degree n:Ho(x) = 1, Hi(x) = x, H 2 (x) =x2- 1, (13)H3(x) = x3 - 3x, H4(x) = X

4 - 6X2 + 3.The smoothed frequency distribution curves for a fewlocations along the air flow are shown in Fig. 10. Thecoefficients of variation, skewness, and excess are shownas a function of x in Fig. 11.

According to these results, the frequency distributionof temperature fluctuations near the screens is veryclose to the Gaussian distribution. Generally, in theGaussian random process, the different frequencyspectral components are statistically independent.However, when the different frequency components arenot independent of each other, statistical distributionsbecome non-Gaussian. In the turbulent flow of inertial

a x 0.3m

a x 0.45m

ax 0.53m

TEMPERATURE ( K)

Fig. 10. Normalized histograms of temperature fluctuations mea-sured for distance x from the last screen along the direction of air

flow.


12

10

I I I I I .4 -

-0.4 -0.3

YC

Yo ~~~~40.26. - _ARD I- ;=;I B2' -

- - - I

- I ~~~~~~I I I I -~~~~~~~~~~~~. .

0.0 0.1 0.2 0.3 0.4DISTANCE (METER)

Fig. 11. Coefficients of variation, skewness, and excess of temper-

ature fluctuations are shown as functions of the distance x from thelast screen along the direction of turbulent air flow.

subrange, lower frequency spectral components willtransfer energy into the higher frequency components.Hence, the histograms of temperature fluctuations inthe turbulent flow are generally non-Gaussian. In the-region of maximum coefficient of variation, x = 0.46 m,the wide range of frequency spectral components rep-resenting various sizes of eddies should be interactingmost actively. According to Fig. 11, the excess coeffi-cients increase along the flow and becomes maximumat x = 0.54 m. However, the coefficients of skewnessincrease monotonically with distance.

Derivation of C, from CT

The refractive-index fluctuations of the homoge-neously turbulent atmosphere at optical wavelength aremainly due to the temperature fluctuations. The re-fractive-index structure function D, (r) = ([n(rl) -

n(r 2 )] 2 ) in the inertial subrange can be expressed in thesame 2/3 law as the temperature structure function:

Dn(r) = C2 r 2/3. (14)

The refractive-index structure constant Cn can beexpressed in terms of the temperature structure con-stant CT by using the equation of refractive index as afunction of temperature and pressure with wavelengthas a parameter. The refractive index of the air at thetemperature T K, the pressure p mb, and the wave-length X gm can be approximated by the followingequations:

n-1 = (77.6P(I + 0253) X 10-6. (15)

Since the refractive-index under the constant pres-sure depends only on the temperature, we obtain' 8

Cn = 77.P(1 + 07 x 10 6CT. (16)7'2 \ /)

For the normal atmospheric pressure p = 1,013.25 mband the wavelength X = 0.6328 /im and the averagetemperature of the turbulent atmosphere T = 326.16K, we obtain Cn = 0.75302 X 10-6CT and C2 = 0.56704X 10- 12C2.

Discussion

1.2 In the above derivation, we assumed only the tem-perature dependence of refractive index of the atmo-

.0 sphere and neglected its pressure dependence. How-ever, we may have to include some effect of pressure

0.8 fluctuations. Since in case of sound waves, pressure

>8 effect is usually treated as an adiabatic process, it would0.6 be reasonable to assume that the pressure fluctuations

induce the temperature fluctuations through the adia-0.4 batic thermodynamical process. Then, assuming the0.2 refractive index n is a function of the temperature T and

pressure P and using a relation for the adiabatic pro-cess,

dP P. (- = cP/cV),dT y-1T

we obtain

C (adiabatic) = 77.6P 1 (1 + 0 00753 10- 6 CT.C~~(adiabatic) =

(17)

(18)

Inserting y = 1.40 of the normal air, we obtain Cn (adi-abatic) = 2.48Cn. Thus, it is essential for establishingthe atmospheric model to compare the Cn directlymeasured by the optical method and the Cn obtainedfrom CT.

When the turbulence of the atmosphere is neither anisothermal nor adiabatic process, we may have to in-clude the pressure structure constant Cp and the pres-sure and temperature cross structure CpT. In case ofthe atmospheric turbulence in the outside field, we mustalso include the effect of the humidity fluctuations andthe density of other gases such as CO2.19

We would like to point out two interesting researchareas pertinent to our turbulence experiment, althoughthey are not directly related to the optical propagation.First, we may be able to clarify the physical meaning ofnon-Gaussian statistics of temperature fluctuationsexemplified in Figs. 10 and 11 by using some of the re-cent research results20 on the temperature fluctuations.Second, by measuring the power spectrum of temper-ature fluctuations within the turbulent boundary layer,we may be able to determine the model of turbulencein the viscous-convective range. This is an interestingsubject, because the bump in the power spectrum oftemperature fluctuation, that is, the deviation from the-5/3 power law, has been observed in the atmosphericsurface layer2 l and is explained by the -1 power law forthe viscous-convective range.2 2 2 3

Two other methods for generating the isotropic andhomogeneous turbulence have been reported: a pro-cupine like array of jet streams used by Betchov andLorenzen24 and the heated grid in a supersonic windtunnel used by Shih-chun Lin and Shao-chi Lin.25 26

Compared to these methods, our turbulence chamberis much simpler to construct and more convenient toapply to the optical transmission measurements.

The performance of our turbulence chamber may beimproved by some modifications: for instance, byadding the array of exhaust fans at the outlet, we shouldbe able to widen the region of uniform strength of tur-bulence. It is also desirable to channel the outlet flows


E

l

I0.5 0.6

FREQUENCY (Hz)

Fig. 12. The output voltage of the thermocouple systems, normalizedby the intensity of modulated laser beams, is shown as a function of

frequency (Hz).

to the air exhaust system in the laboratory, because evena higher temperature setting of heater/blowers may beutilized. By making an array of holes on the walls, wemay enhance temperature mixing and generate thestronger turbulence.

After this paper was prepared, we noticed an inter-esting recent paper by Bissonnette27 on the opticaltransmission in the aqueous turbulence with the spec-ified strength of turbulence. The objective of the lab-oratory simulation described in the paper is very similarto ours. Our atmospheric turbulence chamber, how-ever, has advantages, such as convenience of insertingvarious optical and aerodynamical instruments in thechamber compared to the water chamber used by Bis-sonnette.

Conclusion

The average strength of refractive-index fluctuationsC'of the turbulent flow generated within the chamberwas 103 times larger than that of the typical atmospherein the field. The turbulence was locally homogeneousand isotropic within the region of 6-cm diam. The av-erage strength of turbulence was adequately homoge-neous for the purpose of optical transmission mea-surements within the 0.5 X 0.05 X 2-M3 region at thestandard optical height. Characteristic features of thegenerated turbulence are reproducible within the ex-perimental errors. Various theoretical models of opticalwave propagation in the turbulent atmosphere are beingtested by using the laboratory generated turbulencewith defined C. 28 The determination of C by irra-diance fluctuation measurements will be described ina separate paper.

The authors thank Paul D. Arthur and G. Scott Sa-muelsen (Mechanical Engineering Program, School ofEngineering) for helpful discussions to define the crit-ical Reynolds number of the turbulence chamber andto point out the mixing of two flows, one from theheater/blowers and the other, boundary shear flows atwalls as origin of turbulence generation. This work wassupported by the Air Force Office of Scientific Research(grant 76-3097).

This paper was presented at the OSA Topical Meet-ing on Optical Propagation Through Turbulence, Rain,and Fog, 9-11 August 1977, Boulder, Colorado.

Appendix A: Measurement of Frequency Response ofa Microthermocouple by Using a Modulated LaserBeam

A modulated 50-mW He-Ne 632.8-nm laser beam(single mode, Spectra-Physics 125 A with Fabry-Perotetalon in the cavity extender and Spectra-Physics 320modulator) was focused on microthermocouple junc-tions, while the other junction was covered by a plasticcase. The frequency response of the differential mi-crothermocouple system was measured by taking theratio of the output signal from the thermocouple systemwith those from a photomultiplier tube, which detectsthe modulated laser beam directly. In order to deter-mine the frequency response under the operating con-dition, the measurements were performed with heatedair flow. The measured frequency response is shownin Fig. 12.

Appendix B: Evaluation of Average TemperatureGradient and Characteristic Temperature From

The temperature structure constant CT can be ex-pressed as6

C2T a C,2N14, ?W.3(Bi)

where the parameter a is given by the average energydissipation rate E and the kinematic viscosity v as

a = T/3P. (B2)

A parameter N, which characterizes the intensity of thetemperature fluctuations, is given by the thermal dif-fusivity x and the mean square temperature gradientas

N = x ((VT) 2 ),

X = K/PCp,

(B3)

(B4)

where K is the thermal conductivity, p is the density ofthe atmosphere, and CP is the constant pressure specificheat.2 9

By inserting Eqs. (B2) and (B3) into Eq. (Bi), weobtain

C2 = X6 (AT)2/(9 2 J02 0 /3). (B5)

The average thermal energy dissipation rate T is givenby

(B6)

Since we determined CT = 52.9 K2/m2 /3 and = 0.5cm, inserting x = 0.200 cm2/sec and v = 0.1511 cm2/sec,we obtain the rms temperature gradient

[((VT)2)]1/2 = 1898°/cm. (B7)

The thermal diffusivity x was obtained by inserting K= 2.6 X 10-4 W/(cm C), p = 1.2928/g/liter, and C =0.2398 cal/(g C) into Eq. (B4). By using Eq. (B6)and the thermal diffusivity x-, we obtain the averagethermal energy dissipation rate T:

ET = 0.128 cm2 /sec3. (B8)


T=x3/14q

The characteristic temperature Tc of the turbulenttemperature field is defined by the ms temperaturegradient multiplied by the inner scale of turbulence 10(Ref. 6, p. 64). Using lo = 5 mm, we obtain the char-acteristic temperature of our turbulence chamber Tc =

0.949 K.

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(McGraw-Hill, New York, 1972, pp. 4-144.

John Morrocco of the Amphenol RF Operations at Bunker RamoCorporation


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Atmospheric turbulence chamber for optical transmission experiment: characterization by thermal method