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PARAMETRIC ARRAYS IN AIR WITH

APPLICATIONS TO ATMOSPHERIC SOUNDING

T. Muir, M. Vestrheim

To cite this version:

T. Muir, M. Vestrheim. PARAMETRIC ARRAYS IN AIR WITH APPLICATIONS TO AT- MOSPHERIC SOUNDING. Journal de Physique Colloques, 1979, 40 (C8), pp.C8-89-C8-94.

�10.1051/jphyscol:1979816�. �jpa-00219521�

(2)

PARAMETRIC ARRAYS IN AIR WITH APPLICATIONS TO ATMOSPHERIC SOUNDING T.G. Muir and M. Vestrheim

Applied Research Laboratories, The University of Texas at Austin, P.O. Box 8029 Austin, Texas 78712 USA

Résumé.- On étudie les propriétés et les possibilités d'application d'antennes paramétriques à faisceau étroit se propageant dans V a i r . En ce qui concerne la description du champ sonore â faible intensité (variation du niveau de pression et de la réponse azimuthale en fonction de la distance) «on généralise les résultats précédemment obtenus en tenant compte de la self-démodulation du régime transitoire et des effets provenant de la saturation des primaires à haute intensité. On étudie également les effets propres aux expériences réalisées dans l'atmosphère : variation diurne de température, d'humidité et par conséquent d'absorption. Enfin les possibilités d'application des antennes paramétriques à la détection sonore dans l'atmosphère sont examinées. On trouve que les variations diurnes ne causent pas de grandes difficultés. Par contre un problème non trivial se pose dans le cas d'applications requérant une source à haute intensité. Des solutions de ce problème sont suggérées.

Abstract.- Theoretical and experimental results are presented to demonstrate the character and utility of narrow beam parametric arrays operating in air. Beginning with the delineation of the field at low intensities (variation of pressure level and azimuthal response with increasing range) we expand pre- vious work to include the self-demodulation of transients and high-intensity effects associated with acoustic saturation of the primary radiations. Effects peculiar to experiments in the atmosphere are also presented, such as the diurnal variation of temperature, humidity, and consequently absorption.

Practical applications associated with the use of parametric arrays in atmospheric sounding are exami- ned from the feasibility standpoint. It is concluted that normal diurnal variations pose no great difficulties, while the low parametric efficiency poses a nontrivial problem for applications requiring high source levels. Solutions to this problem are suggested.

1. Introduction.- Since its discovery in 1960 (1), the parametric array has been researched and deve- loped predominantly in underwater acoustics. Only a few papers dealing with experiments in air have appeared in the archival literature (2-5). The not application of parametric arrays to air acoustics problems has been received with skepticism (6).

The purpose of the present paper is to expand the present knowledge of parametric experiments in air with a view toward assesing the potential of possible practical applications.

The parametric array generates a narrow, low- frequency sound beam with no side lobes through the nonlinear interaction of intense high-frequency radiations emitted from a small primary sound source. Three general types of parametric arrays have been identified and discussed in some detail (7). Each has its own characteristics and special theoretical models. Their distinction is based on the relative size and shape of the interaction region.

I.' Experimental illustration of a parametric acoustic field.- As in any acoustic experiment, the transducer is usually of primary importance. Non- linear acoustics requires intense radiation, which normally leads to a peak pulse power demand at the

expense of a low duty cycle. Applications in air are further influenced by practical emphasis on 1) reasonable efficiency, 2) wide bandwidth, 3) good impedance coupling, and 4) low internal distortion.

The transducer used has a 5.7 cm diameter face consisting of 7 clamped plate resonators whose center frequency is displaced from that of the mass-loaded ceramic driver. The primary radiations are launched at the two resonances. Figure 1 illus- trates the 0.56 m f/2 parabolic reflector mounted on a two axis rotator column, as well as a micro- phone and its supporting 6 m tower. (The face of the transducer is turned away from the reflector in this figure). The tower rides on a car rolling on a 250 m railway. A double FM radio link relays received signals for analysis as a function of range r from the source.

This equipement was used in a purely explora- tory approach to air acoustics applications, with no particular detection or sensing requirements imposed. The resulting data of Figs. 2 and 3 demons- trate the acoustic field of primary and secondary radiations acquired in the course of some measure- ments in a dead calm atmosphere at 25°C and 111 relative humidity. The primaries were transmitted with an acoustic power on the order of 1 Watt. It

Article published online by EDP Sciences and available at

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979816

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C8- 90 JOURNAL DE PHYSIQUE

RANGE - ^m

( 0 )

(b)

F i g . 2 : The a c o u s t i c f i e l d o f primary r a d i a t i o n s a) propagation curve, b ) half-power spot s i z e o f t h e beam.

2-

F i g . 1 : The experimental arrangement f o r propagation measurements.

E l -

I

can be seen t h a t t h e transducer beam i s somewhat l a r g e r than p r e d i c t e d , g i v i n g t h e r e f l e c t o r an e f f e c t i v e diameter o f 0.34 m.

The f a r - f i e l d parametric pressure i s modeled by the Westervelt formula (1). Good agreement between theory and experiment i s shown i n F i g . 3 f o r t h e sound pressure l e v e l o f t h e 1 kHz d i f f e - rence frequency r a d i a t i o n . I t can be seen t h a t t h e experimental spot s i z e i s somewhat s m a l l e r t h a n t h e p r e d i c t e d value. I t i s a l s o about 6 times s m a l l e r than t h a t which c o u l d be r a d i a t e d l i n e a r - l y from t h e same e f f e c t i v e a p e r t u r e a t t h e same 1 kHz frequency.

0 MEASURED DATA

-

3. Atmospheric sounding. Remarkable advances i n t h e use o f acoustics t o probe the atmosphere have been made s i n c e 1968 (6). Amongst t h e p r a c t i c a l a p p l i c a t i o n s r e a l i z e d t o date are p r o f i l i n g o f the p l a n e t a r y boundary l a y e r t o study a i r mass i n v e r - sions, t h e s u b s i s t e i c e o f i n v e r s i o n layers, mixing,

0 0

0

I<

⁰

1 " "10 " " " 1 1 ' 15 20

RANGE - m

thermal plumes

,

and g r a v i t y ( i n t e r n a l ) waves. These s t u d i e s a r e q u i t e s i g n i f i c a n t i n t h e a i r p o l l u t i o n and meteorologic d i s c i p l i n e s . Also i m p o r t a n t a r e p r a c t i c a l a p p l i c a t i o n s t o Doppler sensing o f wind speed, v e r t i c a l p r o f i l i n g o f wind v e l o c i t y , t h e measurement o f wind shear and t h e development of sensors f o r shear induced turbulence. These devices have been developed and t e s t e d f o r use a t a i r p o r t s , as have combination a c o u s t i c and electromagnetic sensors which a r e a l s o amenable t o a i r c r a f t a p p l i - c a t i o n s f o r t h e d e t e c t i o n o f c l e a r a i r turbulence.

The a t t r a c t i v e n e s s o f a c o u s t i c sensors l i e s i n t h e f a c t t h a t t h e a c o u s t i c cross s e c t i o n f o r turbulence i s some 10 times g r e a t e r than t h a t f o r 6 electromagnetic waves ( 6 ) . I t i s predominantly t h e temperature d i f f e r e n t i a l s i n t h e t u r b u l e n t atmosphere t h a t i n f l u e n c e t h e a c o u s t i c cross section.

Atmospheric sounders can be deployed i n several c o n f i g u r a t i o n s (6). Simple monostatic sounders a r e u s u a l l y mounted on a v e r t i c a l a x i s and a r e operated l i k e a depth sounding sonar t o probe t h e atmosphere on t h e b a s i s o f echo amplitude. T h i s c o n f i g u r a t i o n i s modeled by t h e echosonde equation (8) 5

(4)

' O r

dimensional triangulation

(6,8).

4

t

I I I 1 1 1 1 1 1 I I

2 3 4 6 8 1 0 20

RANGE - rn ( 0 )

d & 70

,,I 2

g

gg

^60-

:

_2::

* 5:

50-

U ' i! I lU

d 50-

L

RANGE - rn (b)

-.-sP

4. Applicability of parametric sources. As i n any

- -uE@lc4c

---.2ee4',

analysis there a r e advantages and disadvantages

-.LNG

-. --. with each a l t e r n a t e approach. The q u i t e a t t r a c t i v e

-o

-O

l o parametric radiation patterns, generated from small

\ o

apertures, warrant a consideration of the nonlinear

0 MEASURED

DATA 2

\ approach t o atmospheric sounding. This i s appropria-

302

- -

^ro

4 A p AP

t e and timely as side lobe r e f l e c t i o n s from t e r r e s -

Fig.

3 :

The acoustic f i e l d of difference frequency radiation, a ) propagation curve, b) half-power spot s i z e of the beam.

where the received power P R , transmitted power

PT,

t r i a l features have recently been i d e n t i f i e d as sources of f a l s e structures in sounder records (10).

Other potential advantages of parametric sounders e x i s t .

The diurnal variations i n ambient temperature and humidity a f f e c t the absorption and consequently the properties of the parametric array. Some typi- cal values are plotted in Fig.

4.

Over the range

RELATIVE HUMIDITY - ^%

PARAMETRIC ARRAY LENGTH - m 20

18 10% +

PARAMETRIC 3 . 5 m 1 0 %

3 dB BEAM O 0

WIDTH

-

^deg ^3,0 107.

,

range

R ,

pulselength

T ,

aperture area

A

a r e s t r a i -

^10%^a

PARAMETRIC

ghtforward parameters. The e f f e c t i v e aperture

SOURCE LEVEL

VARIATION - dB

+

^{- 1}

l w

IOY.

o

f a c t o r

G

a r i s e s from the transducer d i r e c t i v i t y .

^NIGHT DAY NIGHT

The acoustic cross section oois frequently appro- ^ximated

^{( 9 )}

^by _1/3

_C:

-

^TIME

^-

^h

cr =

0.0039

k

(2) Fig. 4

:

Diurnal variations in parametric array

o properties over a typical summer day in

To Texas.

where

k

i s the wave number,

To

the mean temperatu- of values shown, the night time decrease in tempe- r e , and ct2 i s the temperature s t r u c t u r e parameter, rature and increase i n humidity increases the which frequently varies from t o parametric array length,

LA =

1 / ( 2 a 0 ) , and decrea-

Several models have been developed f o r ses the half-power beamwidth,

O 3 dB =

4 (ao/ks) 1/2 ,

Doppler sensing of wind f i e l d s , ranging from the while the e f f e c t i v e source level i s simultaneously

simple monostatic case t o those involving three- increased. Since the 24 hour variation i n array

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C8- 92 JOURNAL DE PHYSIQUE

p a r a b o l i c horn, 2 m i n diameter. The e x t r a p o l a t e d

source l e v e l i s approximately 157 dB r e 20 pPa rms ^0!0 ^1b0

l l o

¹ⁱ⁰

l l o

^1;0 ^2&

MEAN PRIMARY SOURCE LEVEL

-

dB ^re20 P P ~ rms at 1 m

a t 1 m. Although i t would be l u d i c r o u s t o s e r i o u s l y

l e n g t h o n l y spans

+

13%, t h e beam w i d t h

+

7%, and ₁₆₀ t h e source l e v e l

+

12%, t h e d i u r n a l e f f e c t s do n o t

appear s i g n i f i c a n t , e s p e c i a l l y since t h e y can be

accounted f o r . This may be more d i f f i c u l t i n ¹⁴⁰ periods o f t r a n s i t i o n from calm t o v i o l e n t weather,

o r f o r use o f t h e same a r r a y one day i n a r a i n

-

_E₁₂₀

f o r e s t , the n e x t on a desert.

-

Y)

Perhaps a more serious concern i s t h e r e l a t i v e

i n e f f i c i e n c y o f parametric a r r a y s and t h e i r conse-

5

¹⁰⁰

0

quent low source l e v e l . T h i s u s u a l l y r e s t r i c t s para-

>

_m

m e t r i c a p p l i c a t i o n s t o problems where t h e low _-o _{8 0} e f f i c i e n c y i s n o t an issue, such as ocean depth A _W

>

sounding and propagation i s shallow water. The _w_A e f f i c i e n c y i s s u e i s n o t t r i v i a l f o r a p p l i c a t i o n s U ^WE ^{6 0 -}

t o atmospheric sounding. ³

B

F o r purposes o f discussion, we can consider

y

^{4 0 -}

source l e v e l requirements f o r an e x i s t i n g wind shear Y, C

<

sounder deployed a t D u l l e s I n t e r n a t i o n a l A i r p o r t i n

2

²⁰

Washungton D.C. by t h e National Oceanic and Atmos- p h e r i c A d m i n i s t r a t i o n , Wave Propagation Laboratory.

The main t r a n s m i t t e r o f t h i s system r a d i a t e s 120 ¹⁰ Watts i n a 9' half-power beam a t 1250 Hz from a

compare t h i s system t o t h e simple experiment i l l u s -

r

-

- -

1 -4

EXPERIMENT

-

rp

⁼ ¹⁶^HZ ^f, ⁼^{1 kHz}

-

T = 25.C H = 7 7 ~ .

t r a t e d i n t h e present paper, s i n c e i t r a d i a t e s l e s s

Fig. : High amplitude response of the parametric than a Watt ( a t t h e primary frequencies), t h e f r e - a r r a y experiment.

quencies are nonetheless s i m i l a r w h i l e t h e beam- w i d t h and source diameter o f t h e experiment a r e about 2 t o 3 times smaller, r e s p e c t i v e l y .

The question o f increased r a d i a t e d power now a r i s e s . There a r e l i m i t s t o a r b i t r a r y increases as t h e p r i m a r i e s e v e n t u a l l y go i n t o shock which means harmonic generation, increased absorption, and eventual acoustic s a t u r a t i o n . A u s e f u l model f o r a l a r g e l y plane wave parametric a r r a y i n shock has been discussed i n reference 11, and r e s u l t s con- c e r n i n g t h e parametric source l e v e l f o r t h e present experiment a r e shown i n Fig. 5. I t can be seen t h a t a1 though t h e slope o f the amplitude response curve changes from q u a d r a t i c t o l i n e a r i n t h e shock region, t h e amplitude o f t h e d i f f e r e n c e frequency r a d i a t i o n continues t o increase w i t h increase i n primary power.

T h i s i s accompanied by an increase i n parametric beamwidth, (11) and simply means t h a t a c o u s t i c s a t u r a t i o n u l t i m a t e l y l i m i t s t h e a t t a i n a b l e source l e v e l s , a r r a y lengths, and beamwidths (12).

5.

-

Sel f-demodulation o f t r a n s i e n t s .The transmis- s i o n of an i n t e n s e cw p u l s e i s accompanied by t h e i n t e r a c t i o n o f i t s sideband components t o produce a d i r e c t i v e parametric t r a n s i e n t o f low frequency content. The o r i g i n a l model (13) p r e d i c t i n g t h i s e f f e c t was d e r i v e d f o r t h e a x i a l pressure response i n t h e time domain. I t shows a dependence on t h e second time d e r i v a t i v e o f t h e square o f t h e primary p u l s e envelope f u n c t i o n f ( t

-

^x/cO),i n t h e form

- -

2

Experimental v e r i f i c a t i o n o f t h i s e f f e c t i n l i q u i d s has been p u b l i s h e d (14).

The question a r i s e s as t o t h e existence and p o t e n t i a l u t i l i t y o f t h e self-demodulation t r a n - s i e n t i n a i r . The a x i a l time domain data o f F i g . 6

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- F i g . 6 : Experimental demonstration o f t h e s e l f - demodulation e f f e c t i n a i r . Top t r a c e : primary p u l s e ; bottom t r a c e : self-demo- d u l a t i o n t r a n s i e n t .

was acquired d u r i n g t h e course o f t h e present measurements t o i l l u s t r a t e the e f f e c t . A dual beam o s c i l l o s c o p e was used t o d e p i c t both t h e primary and demodulated s i g n a l s r e s u l t i n g from transmission

o f an 18 kHz p u l s e a t a range o f 9.3 m. The d i f f e - rence i n a r r i v a l times f o r these two s i g n a l s i s due t o t h e geometry o f t h e frequency s e l e c t i v e r e c e i v e r .

I t can be seen t h a t a demodulated t r a n s i e n t was here obtained, i n reasonable consonance w i t h

theory, d e s p i t e the low power l e v e l o f t h e present experiment. Systems producing hundreds o f w a t t s o f r a d i a t e d p u l s e power should be expected t o generate f a i r l y s t r o n g self-demodulation t r a n s i e n t s i n t h e medium. T h e i r bandwidths can be made q u i t e l a r g e , w i t h frequency responses extending down t o t h e i n f r a s o n i c region. T h e i r d i r e c t i v i t y a t these f r e - quencies c o u l d be remarkably high. I t i s suggested t h a t e x i s t i n g sounders be examined f o r t h i s e f f e c t .

A l s o o f p o t e n t i a l i n t e r e s t i s t h e a p p l i c a t i o n o f d i r e c t i v e parametric t r a n s i e n t s t o turbulence research. Use o f t h e parametric t r a n s i e n t would appear t o l e a d instantaneous wideband sensing through impulse response techniques. Other p o s s i b i - l i t i e s e x i s t .

6.- Conclusions. The n a t u r e o f parametric a r r a y s i n t h e atmosphere has been examined w i t h theory and experiment. P r a c t i c a l a p p l i c a t i o n s have been suggested and considered from t h e f e a s i b i 1 i ty stand- p o i n t . I t was shown t h a t d i u r n a l v a r i a t i o n s i n temperature pose no g r e a t problems i n parametric a r r a y generation. The low e f f i c i e n c y and source l e v e l o f t h i s process i s n o n t r i v i a l . A p p l i c a t i o n s

r e q u i r i n g h i g h source l e v e l s should employ s p h e r i - c a l l y d i v e r g i n g p r i m a r i e s t o circumvent t h e 1 im i t i n g e f f e c t s of a c o u s t i c s a t u r a t i o n w i t h i n t h e i n t e r a c - t i o n volume. The generation o f d i r e c t i v e , low requency t r a n s i e n t s through t h e s e l f -demodul a t i o n o f primary pulses was i d e n t i f i e d as a v i a b l e process f o r a i r acoustics w i t h p o s s i b l e i m p l i c a t i o n s f o r a p p l i c a t i o n s i n i n f r a s o n i c s and turbulence research.

E x i s t i n g atmospheric sounders should be examined as sources o f parametric t r a n s i e n t s .

7.- Acknowledgements. M. Vestrheim's c o n t r i b u t i o n was made p o s s i b l e by t h e Royal Norwegian Council f o r S c i e n t i f i c and I n d u s t r i a l Research. T.G. M u i r acknowledges h e l p f u l discussions w i t h E.M. Brown, D.W. Beran, and W.D. N e f f o f t h e Wave Propagation Laboratory, N a t i o n a l Oceanic and Atmospheric A d m i n i s t r a t i o n , Boulder, Colorado, and w i t h D.W. Thompson o f t h e Pennsylvania S t a t e U n i v e r s i t y and Risb N a t i o n a l Laboratory, Copenhagen.

References

/1/ Westervelt, P.J., J . Acoust. Soc. Am., 1963, 35, 535.

-

/2/ B e l l i n , J.L.S., and Beyer, R.T., J. Acoust.

Soc. Am., 1962,

3,

1051.

/3/ Brinkmann, K., Acustica, 1968,

20,

92.

/4/ Bennett, M.B., and Blackstock, D.T., J . Acoust., Soc. Am., 1975,

2,

^562.

/5/ Muir, T.G., i n F i n i t e - a m p l i t u d e wave e f f e c t s i n f l u i d s , proc. 5 t h ISNA (IPC Science and

"Pchnology Press, Ltd.) 1974, p. 119 /6/ Brown, E.H., and H a l l , F.F., Rev. Geophys.

and Space Phys.

,

1978,

16,

47.

/7/ Vestrheim, M., i n F i n i t e - a m p l i t u d e wave e f f e c t s i n f l u i d s , proc. 5 t h ISNA IPC Science and Technology Press, L t d . 1974, p. 140.

/8/ Hal 1, F.F.

,

i n Remote Sensing o f t h e Tropos- phere, (U.S. Gov. P r i n t i n g O f f i c e ,

Washington, D.C.) 1972, ch. 18.

/9/ N e f f

,

^W.^D.

,

i n Proc. 15 3,; Radar Meteor01 ogy Conf.

,

(Aner. Meteor. Soc. Boston) 1975, p. 263.

/ l o /

Brown, E.H., L i t t l e , C.G., and Wright, W.M.

J. Acoust. Soc. Am. 1978,

63,

694.

/11/ Bartram, J.F., J. Acoust. Soc. Am., 1972, 52, 1042.

-

/12/ Shooter, J.A., Muir, T.G., and Blackstock, D.T., J. Acoust. Soc. Am., 1974,

55,

^54.

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JOURNAL DE PHYSIQUE

/13/ Berktay, H.O., J. Sound Vib., 1965,

2

(4), 435.

/14/

M o f f e t t , M.B., Westervelt, P.J., and Beyer, R.T., J. Acoust. Soc. Am., 1971,

49,

^339.

HAL Id: jpa-00219521