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Submitted on 1 Jan 1979
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PARAMETRIC ARRAYS IN SHALLOW WATER.
L. Bjørnø, J. Folsberg, L. Pedersen
To cite this version:
L. Bjørnø, J. Folsberg, L. Pedersen. PARAMETRIC ARRAYS IN SHALLOW WATER.. Journal de
Physique Colloques, 1979, 40 (C8), pp.C8-71-C8-82. �10.1051/jphyscol:1979814�. �jpa-00219519�
JOURNAL DE PHYSIQUE Colloque C8, supplement au n°ll, tome 40, novembre 1979, page c8- 71
PARAMETRIC ARRAYS IN SHALLCW WATER,
L. BJ0RN0, J. FOLSBERG and L. PEDERSEN
Department of Fluid Mechanics Technical University of Denmark Building 404 DK-2800 Lyngby Denmark.
Résumé. - On donne un bref compte rendu des principaux résultats obtenus lors de précédents essais de laboratoire à petite échelle, concernant la propagation acoustique dans l'eau en faible profon- deur, en comparant les modes de propagation résultant d'une excitation linéaire ou paramétrique.
A p a r t i r , d'une fréquence porteuse de 4 MHz avec une modulation d'amplitude de 100 % égale à la fréquence différence (400 kHz) on a réalisé l ' e x c i t a t i o n paramétrique du mode inférieur (le premier) dans un bassin peu profond et sous différentes conditions d'environnement, dans le guide d'onde acoustique constitué par une couche d'eau douce isovitesse de 60 mm d'épaisseur et ses parois.
Les modifications des conditions d'environnement comportent :
a) l'application de différents matériaux sur le fond du bassin (béton, tapis de caoutchouc, sable).
b) la mise en place d'obstacles de géomëtries variées sur le t r a j e t de propagation des modes.
c) l'introduction d'un fond i n c l i n é .
Abstract. - A brief account of the most essential results obtained by some earlier small-scale laboratory tests on underwater sound propagation in a shallow-water area is given comparing both linearly and parametrically excited mode propagation. Using a 100 % amplitude-modulated carrier (4 MHz) with a modulation frequency equal to the difference frequency (400 kHz) the parametric excitation of the lowest (first) mode has been performed in a shallow-water basin under the in- fluence of various environmental conditions in the acoustic waveguide formed by the 60 mm deep isovelocity, fresh water layer and its boundaries. The changes is environmental conditions in- clude : (a) the application of various botton materials, concrete, rubber mats and sand, (b) the placing of obstacles of various geometries in the propagation path of the modes, (c) the introduc- tion of a sloping bottom.
1. INTRODUCTION. - Long range underwater communica- tion systems naturally have to operate at low fre- quencies due to the strong increase in signal ab- sorption with frequency generally observed. Another restriction on sound propagation arises from limi- tations in the water depth which on continental shelves and in shallow-water areas as for instance the North Sea, the Baltic and the Mediterranean frequently is no more than 10 to 100 wave lengths of the underwater sonar signal. In this situation the water column becomes an acoustic waveguide the signal propagation in which is strongly influenced by the bottom and the surface. The transmission of parts of the signal into the bottom, for instance when the botton structure allows the transmission of strong shear waves, may lead to a great loss of energy during signal propagation in the water co- lum, the scattering from the roughnesses along the waveguide boundaries, for instance from surface waves and from varying topography of the bottom, leads to further losses, and the establishment of thermal and salinity gradients refracts the sound beams. Moreover, most conventional (linear), low- frequency sound sources produce multimode excita-
tation where several modes simultaneously excited interfere with each other.
This very complicated nature of underwater sound propagation may be strongly simplified by the use of parametric acoustic arrays. The super- directivity of the parametric beam and its lack of sidelobes, for instance will make the signal propa- gation more uniform, more coherent and less subject to multipath propagation and to modal interference.
Moreover, the choice of a parmetric system instead of a conventional linear one will seem desirable due to its frequency agility and bandwidth and in particular due to the fact that it opens up possi- bilities of selective excitation of discrete nor- mal modes which allows one to concentrate the pro- pagation of acoustic energy along ray paths corres- ponding to natural spactial resonances of the wave- guide formed by the shallow water /l/, / 2 / , /3/, /4/.
The principle of decomposition of the shallow water wave propagation into orthogonal modes has been known for a long time /5/. Physically the for- mation of a mode can be considered the result of an interference between a down-going and an up-
6
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:1979814
C8- 72 JOURNAL DE PHYSIQUE
going wave of equal, b u t o p p o s i t e i n c l i n a t i o n w i t h t h e v e r t i c a l d i r e c t i o n . The angle o f i n c l i n a t i o n increases w i t h t h e mode number and i t decreases w i t h t h e frequency. Unattenuated propagation o f a mode over a d i s t a n c e demands p e r f e c t r e f l e c t i o n o f t h e two i n t e r f e r i n g waves a t t h e s u r f a c e
-
due t oimpedance mismatch
-
and a t the bottom-
due t o t o - t a l i n t e r n a l r e f l e c t i o n o f waves i n c i d e n t beyond t h e c r i t i c a l angle- ,
which leads t o a v e r t i c a l d i s t r i b u t i o n o f pressure associated w i t h t h e mode represented by a succession of zero and maxima and w i t h a phase i n v e r s i o n o f o c c u r r i n g a t each zero crossing. The number of zero crossings b e t - ween t h e s u r f a c e and t h e bottom represents t h e mode order and t h e f i r s t zero w i l l always be s i t u a t e d a t t h e water surface.The d i s t r i b u t i o n w i t h depth o f the a c o u s t i c pressure i n each o f t h e normal modes o f propagation i s a s e n s i t i v e f u n c t i o n o f t h e v e r t i c a l sound speed p r o f i l e . T i d a l c u r r e n t s , fresh water r u n o f f from a d j a c e n t l a n d masses, and d i u r n a l h e a t i n g and c o o l i n g , being c h a r a c t e r i s t i c o f shallow-water areas o f t h e sea, tend t o produce sound speed pro- f i l e s which vary w i d e l y w i t h time and l o c a t i o n .
The f i r s t mode, i . e . t h e l o w e s t mode, i s t h e most i m p o r t a n t f o r l o n g range sound propagation i n shallow water. I f more than one mode i s present, mode i n t e r f e r e n c e can be expected. The mode i n t e r - ference i s s t r o n g e s t when o n l y two modes o f compa- r a b l e s t r e n g t h a r e present.
The experimental i n v e s t i g a t i o n s o f sound pro- pagatfon i n shallow water have d u r i n g t h e p a s t mainly been performed as f u l l - s c a l e t e s t s a t sea o r as modal-tank l a b o r a t o r y experiments. Both procedu- res have advantages and disadvantages. Model -tank experiments make i t e a s i e r t o c o n t r o l t h e parame- t e r s i n f l u e n c i n g t h e sound propagation, thus g i v i n g more f l e x i b i l i t y i n t h e choise of t e s t parameters.
Moreover, they are frequently l e s s expensive than f u l l - s c a l e t e s t s , t h e manual o p e r a t i o n s d u r i n g t h e measurements can e a s i e r be performed, the necessary instruments are a t hand etc., b u t model-tank experi- ments are f r e q u e n t l y beset w i t h s c a l i n g problems which can l e a d t o serious d e v i a t i o n s between small- s c a l e and f u l l - s c a l e r e s u l t s and conclusions based thereon.In s p i t e of t h i s f a c t model-tank experiments have l o n g been recognized as an i m p o r t a n t method t o o b t a i n valuable i n f o r m a t i o n about underwater sound propagation,but i t should be emphasized t h a t model- tank r e s u l t s m a i n l y a r e o f a q u a l i t a t i v e character.
A.B. Wood /6/ gave an example of outstanding use o f model-tank technique i n t h e i n v e s t i g a t i o n o f shallow-watersound propagation. Through t h e use o f an a r b i t r a r i l y chosen s c a l i n g f a c t o r of 1 : 1000, approximately, he s t u d i e d mode propagation under i n f l u e n c e of bottom m a t e r i a l s , o f surface waves, o f temperature s t r a t i f i c a t i o n and o f depth v a r i a t i o n s due t o a s l o p i n g bottom. Th'rough t h i s masterpiece o f a l a b o r a t o r y experiment he showed how whole se- r i e s o f v a l u a b l e i n f o r m a t i o n i n d e t a i l i l l u m i n a t i n g t h e n a t u r e of mode propagation i n shallow water could be obtainsd by some r e l a t i v e l y simple model- t a n k measurements.
L i k e Wood, a l s o Eby e t a1 /7/ used conven- t i o n a l sound sources f o r t h e i r model s t u d i e s . Mo- reover, t h e y i n c l u d e d a b s o r p t i o n e f f e c t s t o g e t h e r w i t h shear waves i n a bottom model c o n s i s t i n g o f a Hycar rubber s l a b s i m u l a t i n g t h e s t r e s s wave pro- pagation c a p a b i l i t i e s o f a sedimentary bottom. F o r Hycar they found t h e same l i n e a r a b s o r p t i o n depen- dence on frequency as found l a t e r f o r a broad v a r i e - t y o f sediments /81. One of the e s s e n t i a l f e a t u r e s o f t h e i r work was t h e i m p o r t a n t conclusion, t h a t a f i r s t mode can be generated and r e c e i v e d w i t h lit- t l e o r no admixture o f second o r higher modes by a p p r o p r i a t e adjustments o f t h e s i g n a l source and t h e r e c e i v e r depths. This simple technique w i l l , u n f o r t u n a t e l y , n o t work f o r t h e g e n e r a t i o n o f t h e secpnd mode alone. Eby e t a1 a l s o showed how mode conversion may be caused by an abrupt change i n t h e water depth w h i l e a random d i s t r i b u t i o n o f small roughnesses produced no h i g h e r modes. Attempts t o e x c i t e , t o s t i m u l a t e and t o r e c e i v e s i n g l e , prese- l e c t e d , i n d i v i d u a l modes by an a p p r o p r i a t e " t a i l o - r i n g " o f l i n e a r t r a n s m i t t i n g o r r e c e i v i n g a r r a y s have r e c e n t l y been shown g r e a t i n t e r e s t by various s c i e n t i s t s /91, 1101, 1111, 1121, /131. These transducer a r r a y s must however be t a i l o r e d t o a s p e c i f i e d combination o f water depth, a c o u s t i c frequency, sound-speed p r o f i l e y bottom qua1 i t i e s , and mode number and w i l l t h e r e f o r e s u f f e r from an i n h e r e n t l a c k o f f l e x i b i l i t y .
Only r e c e n t l y successful attempts t o e x c i t e i n d i v i d u a l modes u s i n g p a r a m e t d c a r r a y s have been done /I/, /2/, /3/, /4/, /14/. The pioneer work i n t h i s f i e l d has been done by t h e group around Dr. T.G. M u i r i n t h e Applied Research L a b o r a t o r i e s a t t h e U n i v e r s i t y o f Texas a t Austin. Through t h e o r e t i c a l and experimental s t u d i e s t h e y proved i t t o be p o s s i b l e t o e x c i t e preselected s i n g l e modes
1. BJ$RNP and a1
by an a p p r o p r i a t e t i l t i n g o f t h e a r r a y a x i s an an- g l e 4 being c h a r a c t e r i s t i c f o r t h e mode t o be e x c i t e d by t h e narrow d i f f erence-frequency beam.
A good agreement between c a l c u l a t e d and experimen- t a l depth f u n c t i o n s f o r t h e lowest ( f i r s t ) mode difference-frequency sound pressure l e v e l a t va- r i o u s source distances was obtained by Dr. M u i r ' s group. Through experiments performed i n a shallow- water tank f a c i l i t y and i n a shallow-water lagoon a l l o w i n g l o n g range propagation over approximately constant water depth t h e y showed t h e s u p e r i o r i t y o f the parametric a r r a y over a conventional source when multimode e x c i t a t i o n should be avoided and t h e echo/reverberation r a t i o should be improved.
Very r e c e n t l y t h e simultaneous e x c i t a t i o n o f t h e v e r t i c a l and h o r i z o n t a l lowest modes were s t u d i e d i n a w a t e r - f i l l e d channel i l l u m i n a t i n g mode i n t e r - a c t i o n problems /14/.
2. EXPERIMENTAL EQUIPMENT AND EXPERIMENTAL PROCE- DURES.
-
An airbacked p i s t o n source-
PZT-26, ma- nufactured by Ferroperm A/S, Vedbaek, Denmark-
t r a n s m i t t e d s 100 % amplitude modulated c a r r i e r wave, modulation frequency equal t o t h e d i f f e r e n c e frequency, i n t o a l a y e r o f i s o v e l o c i t y f r e s h water.
The n a t u r a l frequency o f t h e p i s t o n source, fo = 4 MHz, formed t h e c a r r i e r frequency and a mo- d u l a t i o n frequency o f 400 kHz was used f o r most experiments, and t h e i n t e r a c t i o n o f each sideband, thus formed, w i t h t h e c a r r i e r produces a d i f f e - rence-frequency component f s a t t h e modulation frequency. As shown p r e v i o u s i y /15/, /16/, t h e d i f f e r e n c e - f r e q u e n c y pressure amp1 i tude achieved using 100 % amplitude modulation o f a c a r r i e r exceeds t h e value achieved w i t h a two-component primary wave system by 2.5 dB, i f t h e primary s i g n a l i n each case has t h e same t o t a l power.
The e f f e c t i v e diameter o f t h e p i s t o n source was 10 mm and t h e speed o f sound i n t h e water was approximately a constant (= 1487 m/s) d u r i n g a l l experiemnts. The d a t a f o r the a c o u s t i c parameters o f t h e a r r a y used f o r t h e experiments a r e :
1) C a r r i e r frequency :
4 .
600 kHz
2) D i f f e r e n c e frequencies : 400 kHz (used i n kHz most s e r i e s
o f e x p e r i
-
ments) 3) C a r r i e r half-power beamwidth : 1°.08 (angle
between h a l f - power p o i n t and a c o u s t i c a x i s )
4) P i s t o n source d i r e c t i v i t y index : 38.5 d~
( a t 4 MHz)
5) Half-power beamwidth of p i s t o n source r u n n i n g l i n e a r l y a t f S = 400 kHz : 21°.8.
6) Primary source l e v e l : 202 dB r e 1 uPa a t 1 m ( 4 MHz).
7) Parametric source l e v e l : 152.6 dB r e 1 uPa a t 1 m (400 kHz).
8 ) ' ~ u l s e l e n g t h : 100 p s . 9) Array l e n g t h : L = 1.45 m.
10) Rayleigh d i s t a n c e : Rr = 0.21 m. ( a t 4 MHz).
Table I .
-
Half-power beamwidths 0 f o r v a r i o u s difference-frequent* fs o f t h e parametric a r r a y . Modal s e p a r a t i o n angle 4d and c y c l e d i s t a n c e D( f i r s t mode).
The predominantly spreading l o s s 1 im i t e d a r - r a y w i l l have t h e difference-frequency half-power beamwidths Bh g i v e n i n Table I. Oh denotes here angle between t h e half-power p o i n t s and t h e a r r a y a x i s . This t a b l e moreover g i v e s t h e modal separation angle 4d and t h e c y c l e d i s t a n c e D { f i r s t mode) /14/, /15/, f o r mode propagation un- d e r the experimental c o n d i t i o n s , i s o v e l o c i t y f r e s h water w i t h a constant depth H = 60 mm. Except f o r f s = 600 kHz t h e c o n d i t i o n o f
e,,
6 $d i s s a t i s - f i e d i n order t o concentrate t h e maximum amount of parametric energy i n t o a g i v e n mode.I n f l u e n c e of phase r e v e r s a l s d u r i n g r e f l e c - t i o n s a t t h e surface and t h e bottom w i l l o n l y be v e r y weak due t o a l l f i r s t r e f l e c t i o n s t a k i n g p l a c e f a r beyond t h e 3 dB-distance of t h e p r i m a r i e s f o r t h e t i l t - a n g l e s used i n t h e experiments.
Measurements of t h e p r i m a r y and d i f f e r e n c e - frequency sound pressure l e v e l were performed using a mini-hydrophone showing a s e n s i t i v i t y a t 400 k ~ z o f 0.4 uV/llbar /16/.
A l l experiments were performed i n a shallow- water basin. This basin, having t h e dimensions : 12 x 1.6 x 0.15 m, c o n s i s t e d o f a wooden frame mounted on a concrete f l o o r an l i n e d w i t h a t h i c k - w a l l e d p o l y e t h y l e n e f o i l i n o r d e r t o o b t a i n water tightness,
C8- 74 JOURNAL DE PHYSIQUE
The acoustic waveguide boundary c o n d i t i o n s by t h e bottom c o u l d be changed by t h e i n t r o d u c t i o n o f m a t e r i a l s l i k e a rubber s l a b o r a l a y e r o f sand t o simulate seabed c o n d i t i o n s . Moreover, t h e b a s i n f a - c i l i t y was provided w i t h a f a c i l i t y f o r generation of waves on t h e water surface.
The p i s t o n source was mounted on a c a r a l l o - wing i t t o be moved along t h e l o n g i t u d i n a l and t r a n s v e r s a l a x i s o f t h e basin and t o be moved i n depth. Furthermore, i t c o u l d be r o t a t e d 360" i n t h e h o r i s o n t a l plane and i t could be t i l t e d w i t h an accuracy b e t t e r than 0.1' u s i n g a t h r e a d gear.
C a l i b r a t i o n o f t h e h o r i z o n t a l p o s i t i o n of t h e a r - r a y a x i s was performed u s i n g a l a s e r beam t o be r e f l e c t e d by t h e p i s t o n source surface. The t i 1 t angles used were c a l i b r a t e d u s i n g t h e same proce- dure.
The r e c e i v e r , a m i n i hydrophone produced i n F u n c t i o n
G e n e r a t o r E x a c t Type 516
a
t h e Department o f F l u i d Mechanics, was mounted on a c a r being f r e e t o move on r a i l s i n t h e l o n g i t u - d i n a l d i r e c t i o n o f t h e basin. I n order t o achieve a continuous and automatic r e g i s t r a t i o n o f t h e sound pressure l e v e l v a r i a t i o n i n depth and i n the t r a n s v e r s a l d i r e c t i o n o f t h e b a s i n the hydrophone movements i n these d i r e c t i o n s were c o n t r o l e d by a step-motor governed by a preset-index device.
The e l e c t r o n i c instruments used f o r t h e beam- forming, t h e s i g n a l processing and t h e r e g i s t r a - t i o n on o s c i l l o s c o p e s and on paper tape a r e shown i n F i g u r e 1.
R e g i s t r a t i o n s o f depth f u n c t i o n s and sound pressure l e v e l v a r i a t i o n i n t h e t r a n s v e r s a l b a s i n d i r e c t i o n were performed a t various p i s t o n source distances through 6 s e r i e s o f measurements. These measurement s e r i e s comprised p a r a m e t r i c a l l y gene- r a t e d s i g n a l s propagated i n t h e f o l l o w i n g environ-
M e a s u r i n g A m p l i f i e r Type 2607
' i
Type HP 312 A
Krohn-Hite P h i l i p s
P h i l i p s
Power A m p l i f i e r EN1 Type 240L R F
E N 1 Type 300L R F
Hydrophone
T r a n s m i t t e r tieceiver
Fig. 1.
-
Block diagram f o r e l e c t r o n i c equipment used by t h e experiments.L. BJPRN0 and a1
LINEAR TRANSMISSION ( LOO kHz ) TRANSDUCER T I L T ANGLE: 0
10 dB BOTTOM MATEK!AL: CONCRETE
1
I m 7 m 3 m L m 5 rn 6 m 7 m 8 m Qrn 9.7rn
TRANSDUCER T l LT ANGLE: o
'
10 d B BOTTOM MATERIAL' CONCRETEF i g . 2,
-
L i n e a r and parametric transmission o f 400 kHz i n t o a water column o f constant h i g h t , 60 mm, over a concrete bottom. A l l distances are measured from t h e p i s t o n sources surface.ments :
1) Concrete bottom and constant water depth.
2) Rubber mat bottom and constant water depth.
3) Sand bottom and constant water depth.
4) Items of v a r i o u s geometries s i t u a t e d on sand bottom by constant water depth.
5) Sloping sand bottom w i t h o u t and w i t h items on t h e bottom.
6) Transversal scannings by constant water depth over sand bottom.
3. EXPERIMENTAL RESULTS AND DISCUSSION.
-
A l lexperiments were performed i n f r e s h water a t cons- t a n t temperature, 22 O C , i n order t o avoid t h e i n f l u e n c e on t h e mode propagation a r i s i n g from a v e r t i c a l sound speed p r o f i 1 e.
During a l l experiments t h e p i s t o n source was i n middepth i n order t o e x c i t e t h e f i r s t ( l o - west) mode being t h e most i m p o r t a n t f o r l o n g range propagation.
F i g u r e 2 shows a comparison between l i n e a r l y and p a r a m e t r i c a l l y produced depth f u n c t i o n s i n t h e mode propagation over a concrete bottom a t a cons- t a n t water depth o f 60 mm. The frequency i s i n both cases 400 kHz. The l i n e a r l y produced depth
f u n c t i o n s show t h e usual effects o f multimode i n - t e r f e r e n c e w h i l e t h e parametrical l y produced depth f u n c t i o n s are smooth, i n d i c a t i n g a s t r o n g reduc- t i o n i n multimode i n t e r f e r e n c e and a s t r o n g l y pre- v a l i n g energy propagation i n t h e lowest mode. Some weak i n f l u e n c e o f t h e bottom' a b s o r p t i o n
-
probablydue t o propagation o f shear waves i n t h e concrete
-
may be seen o f t h e parametric curves a t g r e a t e r source distances.
Increased a b s o r p t i o n by t h e bottom m a t e r i a l s can be observed i n F i g u r e 3 when a 3 mm t h i c k , s o f t rubber mat i s covering t h e concrete bottom.
I n s p i t e o f t h e ti 1 t angle being kept on 0' t h e complex wave number of t h e rubber seems t o have a n o t vanishing i n f l u e n c e on t h e parametric depth f u n c t i o n s . This i n f l u e n c e i s on a par w i t h t h e one observed by Wood /6/ and Eby e t a1 /7/.
Even i f some r e d i s t r i b u t i o n o f energy i n t h e depth takes p l a c e w i t h i n c r e a s i n g source distance, most energy i s propagated along i n t h e lowest mode A weak i n f l u e n c e o f higher modes
-
probably t h e 3 r d mode-
can be seen over t h e rubber mat a t source distances 5 and 6 m.The i n f l u e n c e of a 15 mm t h i c k l a y e r o f sand
C8- 76 JOURNAL DE PHYSIQUE
TRANSDUCER T I L T ANGLE : 0 BOTTOM MATERIAL : RUBBER I 3 mm
10 dB CONCRETE
TRANSDUCER T l L T ANGLE: 0
10 dB BOTTCM MATERIAL CONCRETE
Fig. 3.
-
Comparison between parametric depth functions measured over a f r e e concrete bottom and a concrete bottom covered by a 3 mm ,thick rubber mat.SAND I 15 rnm 1 TRANSDUCER T L L T ANGLE : O 0 BOTTOM MATERIAL: RUBBER ( 3 m m l
10 d B CONCRETE
I
TRANSDUCER T l L T ANGLE: 0
10 dB BOTTOM MATERIAL: CONCRETE
Fig. 4.
-
Comparison between parametric depth functions f o r a f r e e concrete bottom and f o r a concrete bottom covered by rubber mat and 15 mm t h i c k l a y e r o f medium sand.L.
BJPRNP
and a1 c8- 77c o v e r i n g t h e rubber mat and t h e concrete bottom on i s shown i n F i g u r e 5 f o r negative, i.e. downward t h e p a r a m e t r i c a l l y generated depth f u n c t i o n s f o r p o i n t i n g , tilt angles :
-
0.5',-
1.0' and -1.5'.tilt angle 0" i n a w a t e r column o f 60
mn
may be A s t a b i l i z a t i o n of energy propagation i n t h e l o - seen i n Figure 4. The presence o f h i g h e r modes due west mode, i n p a r t i c u l a r a t-
l o , seem t o t a k e t o t h e i n f l u e n c e o f t h e sand bottom may c l e a r l y be p l a c e by t h e n e g a t i v e t i l t angles. By p o s i t i v e seen i n t h e f i g u r e . The speed o f sound and t h e ab- t i l t angles of t h e same magnitude as t h e n e g a t i v e s o r p t i o n c o e f f i c i e n t f o r t h e medium sand used was ones, F i g u r e 6 shows d e s t a b i l i z a t i o n of t h e lowest measured t o be : 1765 m/s and 22 Np/m ( a t 400 kHz) mode t o occur and a mode i n t e r f e r e n c e w i t h propa-/IT/.
g a t i o n d i s t a n c e takes place, presumably between The i n f l u e n c e o f t h e tilt angle on t h e para- t h e 3-
4 lowest modes. Changes in t h e environmen- m e t r i c depth f u n c t i o n s over t h e sand covered bottom t a l c o n d i t i o n s i n an a c o u s t i c waveguide may strong-SAND ( 15mrn )
TRANSDUCER T I L T ANGLE : - 0 . 5 ~ BOTTOM M A T L H I A L ' RUBBER ( 3 m m I 10 dB
C_I CONCRETE
1 rn 2 m 3 m L m 5rn 6rn 6.5m
SAND 1 15 rnrn ) TRANSDUCER T l L T ANGLE :
-
1 BOTTOM MATERIAL: RUBBER 1 3 mm10 dB
C---r
CONCRETE
I rn 2rn
. . . . ,
--
SAND { 15rnm )
TRANSDUCER T I L T ANGLE
-
1.5 BOTTOM M A T E R I A L : RUBBER ( 3 mrn I 10 d Bc_. CONCRETE
1 rn 2 m 3 rn L m 5m b m 6.5rn
F i g . 5.
-
The i n f l u e n c e of n e g a t i v e t i l t angles on t h e parametric depth f u n c t i o n s over the sand bottom a t constant w a t e r depth 60mm.
JOURNAL DE PHYSIQUE
SAND ( 1 5 m m 1 TRANSDUCER T I L T A N G L E . + 1 . 5 ~ BOTTOM M A T E R I A L : RUBBER ( 3 mm I
10 d B
C_ CONCRETE
I m ? *n 3 m L rn 5 m 6 m 6.5m
SAND 1 15 m n i I
TRANSDUCER T l L T ANGLE : + l o BOTTOM MATERIAL: RUBBER I 3 rnm 1 10 d B
--
CONCRETESAND 1 15mm 1 TRANSDUCER T I L T ANGLE + 0.5 B O T T O M M A T E R I A L RUBBEK 1 3 m m l
10 d B
-
CONCRETE1 m 2 m 3 rn L m 5 m 6 m 6.5m
F i g . 6.
-
The i n f l u e n c e of p o s i t i v e tilt angles on t h e parametric depth f u n c t i o n s over t h e sand bottom a t constant water depth 60 mm.l y i n f l u e n c e the mode propagation. Obstacles, which son between t h e mode c o n d i t i o n s w i t h o u t t h e i r o n due t o t h e i r p o s i t i o n i n t h e shallow water and due tube, and w i t h t h e i r o n tube a t p o s i t i o n s
t o t h e i r s p e c i f i c a c o u s t i c impedance d i f f e r i n g from R = 2.10 m and R = 4.10 m. The d i s t u r b i n g i n f l u e n c e t h e one o f t h e environment, may l e a d t o mode i n t e r - on t h e depth f u n c t i o n s a r i s i n g from t h e presence ,
ference and t o r e - d i s t r i b u t i o n of modes. These chan- o f t h e i r o n tube seems t o be present even i n depth ges w i l l be r e f l e c t e d i n m o d i f i c a t i o n s i n t h e cour-
se o f t h e depth functions, which i n a v e r y convin- c i n g way i s shown i n F i g u r e 7. This f i g u r e shows a w a t e r - f i l l e d i r o n tube, o u t e r diameter 17 mm, p o s i - t i o n e d on t h e sand bottom a t v a r i o u s distances from the p i s t o n source. The tube a x i s , forms a r i g h t an- g l e w i t h t h e parametric a r r a y a x i s . The t h r e e se- r i e s o f depth f u n c t i o n s i n F i g u r e 7 show a compari-
f u n c t i o n s f a r "down-stream" from t h e tube. Also t h e depth f u n c t i o n "up-stream", i.e'. a t R = 3.0 my from t h e tube on p o s i t i o n R = 4.1 m seems t o be exposed t o some r e f l e c t i o n i n f l u e n c e . The s t r o n g e s t i n - f l u e n c e of an o b s t a c l e on t h e course o f t h e depth f u n c t i o n s should be expected when i t s p o s i t i o n c o i n c i d e s w i t h a n u l l i n t h e depth f u n c t i o n o f t h e s p e c i f i c mode considered thus p r e v e n t i n g t h e f i e l d
L.
BJ0RN0
and a1 C8- 79SAND ( 1 5 m m ) TRANsOUCER T l LT AXGLE 1.5' BOTTOM MATERIAL: RUBBER ( 3 mm I
10 d B
-
CONCRETE0
SAND 1 15 n m I TRLUSDUCER T I L J ANGLE. 1.5 BOTTOM MATERIAL. RUBBER 1 3 rnm i
10 dB
-
CONCRETE0
- -~
----7 , ,, ,/,,,
.
,, r ,, , , ,,, , ,, , , , , ,, , ,,,,,,,, ,, , r ,,, - , , , I , / I , / / /,,-/, ,//,,////////////,/////IRON TUBE 1 0 17rn1n distance from transducer: 2.1 Om
SAND 1 1 5 m m ) TRANSDUCEF; T l L T ANGLE : 1.5
'
BOTTOM MATERIAL: QUBBER 1 3 mm I10 d 6 CONCRETE
0
-- A___-- .A-
-
7. ,,,,,,, , ,, r , , , , ,,,,,, , ,, , ,,,,,,,,r,,,,,,/,//,,,,,/~,,,/,/,C,//,,/ /,,,// / /
--
IRON TUBE 1 0 17mm I / r 7 d ~ s t a n c e from transducer: C,lOm
F i g . 7.
-
I n f l u e n c e of an i r o n tube on t h e sand bottom on t h e depth f u n c t i o n s measured a t v a r i o u s distances from t h e p i s t o n source.s t r e n g t h o f t h e mode t o go down t o zero.
A s o l i d b l o c k o f i r o n p o s i t i o n e d a t v a r i o u s distances from t h e p i s t o n source i n F i g u r e 8 shows some o f t h e same f e a t u r e s i n i t s i n f l u e n c e on t h e depth f u n c t i o n s as observed by t h e i r o n tube. A s t r o n g r e d i s t r i b u t i o n o f t h e propagating a c o u s t i c modes i s t h e r e s u l t l e a d i n g t o a p e r s i s t e n t change o f shape by t h e depth f u n c t i o n s .
Change i n environmental c o n d i t i o n s f o r t h e mode propagation may a l s o a r i s e from a s l o p i n g sea- bed. F i g u r e 9 shows a comparison between depth f u n c t i o n s measured above a s l o p i n g bottom o f sand
( s l o p e angle :
lo)
w i t h o u t and w i t h obstacles i n - f l u e n c i n g t h e course o f t h e depth f u n c t i o n s . A c e r - t a i n f o c u s i n g e f f e c t seems t o be present above t h e s l o p i n g bottom, i n s p i t e of t h e increased absorp- t i o n t o be a c t i n g on t h e modes due t o t h e i n c r e a - s i n g number o f r e f l e c t i o n s by t h e bottom m a t e r i a l . A considerable mode, conversion which i s f u r t h e r am- p l i f i e d due t o t h e presence of t h e obstacles can be seen i n F i g u r e 9.A l l depth f u n c t i o n s p r e v i o u s l y shown a r e measured through t h e a c o u s t i c a x i s o f t h e parame- t r i c beam. Measurements o f depth f u n c t i o n s o f f - a x i s
JOURNAL DE PHYSIQUE
SAND I 15 mm I TRANSDUCER T I L T A N G L E : + 1 " BOTTOM M A T E R I A L : RUBBER ( 3 mm I
10 d B C O N C R f T E
m
SAND I 15 rnm 1 TRANSDUCER T l L T A N G L E . + 1 BOTTOM M A T E R I A L . RUBBER ( 3 m m )
10 dB C O N C R E T E
. . , , - -- --
I , , , , , , , I
,.,,
,.,,
,,,,,,,,,,,,/,/,,,,,,,,,,,,/, / /,,,,,//,,/// / / / / / / / / / / / /I R O N BLOCK (i htgth 1 6 m m , w ~ d t h . 31.5 mm 1 d ~ s t o n c e from tromducer 2 , l O r n
SAND I 15mrn
TRANSDUCER T I L T A N G L E . + 1 " BOTTOM M A T E R I A L : RUBBER I 3 m m I @ 10 dB
--
CONCRETE1 rn 2 rn 3 rn 4 rn 5 rn 6 m 6.5m
6 crn
. .
. , , . , .
. . , .
. - - - . ... _.__-_ . . --
7 , . . , r / / / r , / / / /I//////,////////////// / / / / / / / /,,/ / - , I
- -
>I R O N BLOCK l h ~ g t h 1 6 m m , w i d t h ; 31.5mm 1 d ~ s t a n c e from tronsducer L , l Om
Fig.
8.- Influence of a solid iron block situated on the sand bottom on the depth functions measured at various distances from the piston source.
at various transversal positions at a piston source distance
R = 3.5m are shown in Figure
10.Well- developed transversal symmetry in the distribution of sound pressure level with depth around the peak value in the beam-axis depth function are shown in Figure
10.This symmetry was in general found at all other piston source distances in the shal low-water basin.
4. CONCLUSIONS. - The experimental results presen-
ted in .this paper seem to support the applicability
of the parametric array in a shallow-water area
even if obstacles on a sloping bottom changes the
environmental conditions in the acoustic wave
guide. In spite of the mode conversions observed
caused by changed environmental conditions the
parametrically excited lowest mode seems to sur-
vive over longer distances of propagation carrying
most of the acoustic energy along even if a limited
L. BJ0RN0 and a1 c8- 81
5 A N D ( s l o p e angle . 1";
TRANSDUCtR TILT ANGLE: 0 BOTTOM MATERIAL: RUBBER i 3mm 1
10 d B
-
CONCRETE5 m 5 . 5 m 6 m 6.5 m 7 m 7.5 m 8 m 8 5 m
SAND ( slope angle l e i
TRANSDULER TILT ANGLE. o 0 BOTTOM MATERIAL RUBBER 1 3mm )
10 dB
a* LONCRETE
5 m 5 . 5 m 6 m 6.5 m 7 m 7 5 m 8 m 8 5 m
\
IRON TUBE 1 0 l l m m Id ~ s t a n c e from transducer. 5.5m
SAND { slope angle 1') 1 WANSDUCER TILT ANGLE: 0 BOTTOM M A ~ ~ R I A L RUBBER 1 3mm )
10 d B
t--.l CONCRETE
5 m 5 5 m 6 m 6.b m 7 m 7 5 m 8 m 8 5 m
6 cm
. .
'
IRON BLOCK ( h f g t h . I d m m.
w i d t h . 31.5mm l d ~ s t a n c e from transducer. 5 . 5 mFig. 9 .
-
The i n f l u e n c e o f a s l o p i n g sand bottom ( s l o p e a n g l elo)
on t h e depth f u n c t i o n s measured i n t h e water wedge.number of h i g h e r modes a r e simultaneously present. /2/ Clynch, J.R. & Muir, T.G., " A p p l i c a t i o n o f pa- The course o f t h e measured depth f u n c t i o n s shows r a m e t r i c a r r a y s t o shallow water propagation".
J. Acoust. Soc. Amer.,
57,
1975, 564.t h a t t h i s number o f h i g h e r modes introduced by mo'
d i f i e d environments i s much lower than t h e number /3/ Mufry T.G. & Clynch, J .R., "Propagation o f pa- r a m e t r i c waves i n shallow water". Proceedings o f modes l i n e a r l y e x c i t e d under t h e same c o n d i t i o n s of t h e I n s t i t u t e of Acoustics, Underwater
i n a shal low-water waveguide. Acoustics Group Meeting, Portland, G.B. A p r i l
1976.
REFERENCES /4/ Ctynch I.R. & M u i r T.G., "Parametric a r r a y i n shallow water". Paper presented a t 7 t h I n t e r - n a t i o n a l Symposium on Nonlinear Acoustics, /1/ M u i r T.G., White, R.L. & Clynch, J.R., "Experi- Blacksburg, Va., Aug
.
1976.mental model s t u d i e s o f n o n l i n e a r e f f e c t s i n
normal mode propagation". O.F. Hastrup & /5/ Tolstoy, I. & Clay, C.S., "Ocean Acoustics", O.V. Olesen, (Eds.) Sound Propagation i n Shal- McGraw-Hill, New York, 1966,
low Water. Vol. 2, S p e
,
Conference Proceedings no. 14, Nov. 1974.
JOURNAL DE PHYSIQUE
F i g . 10.
-
O f f . - a x i s depth f u n c t i o n s measured a t various t r a n s v e r s a l p o s i t i o n s a t a p i s t o n source d i s t a n c e R = 3.5 m./6/ Wood A.B., "Model experiments on sound propa- /12/ King L.A., "Enhancement techniques i n t r a n s - g a t i o n i n shallow water". J. Acoust. Soc. m i t t i n g and r e c e i v i n g underwater a c o u s t i c Amer.,
3,
( 9 ) , 1959, 1213-
1235. modes". I b i d Ref. 1./7/ Eby R.K., W i l l i a m s Jr., A.O., Ryan R.P. & / I 3 1 I n g e n i t o F. & Wolf, S.N., "Acoustic propaga- Tamarkin P., "Study o f a c o u s t i c propagation t i o n i n s h a l l o w water o v e r l y i n g a consolida- i n a two-layered model". J. Acoust. Soc. Amer., t e d bottom". J . Acoust. Soc. Amer.,
60,
( 3 ) , 32, ( I ) , 1960, 88-
99.-
1976, 611-
617./8/ Hamilton E.L., "Com~ressional-wave a t t e n u a t i o n
.
.i n marine sedimentsi1. Geophysics,
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(4),1972, 620
-
646./9/ F e r r i s R.H., "Comparison o f measured and c a l - c u l a t e d normalmode amplitude f u n c t i o n s f o r a c o u s t i c waves i n shallow water". J. Acoust.
Soc. Amer.,
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( 3 ) , 1972, 981-
988./lo/ Ingeni t o R., "Measurements o f mode attenua- t i o n c o e f f i c i e n t s i n shallow water".
J. Acoust. Soc. Amer.,
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(3), 1973, 858-
863.
/11/ W i l l i a m s Jr., A.O. & Novak, B.M., "Normal- mode a n a l y s i s o f underwater-sound propagation w i t h d i r e c t i o n a l sources and r e c e i v e r s " . J. Acoust. Soc. Amer.,
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( I ) , 1974, 80-83./14/ Bjmrnd L., " E x c i t a t i o n of s e l e c t e d modes i n shallow-water sound propagation". Proceedings o f U l t r a s o n i c s I n t e r n a t i o n a l 1977, IPC Science and Technology Press, Ltd., G u i l d f o r d , England, 1977, 285
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298./15/ Weston D.E., "Rays, modes, i n t e r f e r e n c e and t h e e f f e c t o f shear f l o w i n underwater a c o u s t i c s "
.
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89./16/ Lewin P.A., "Threshold f o r u l t r a s o n i c expo- sure o f b i o l o g i c a l t i s s u e and t h e b i o l o g i c a l e f f e c t s o f ultrasound". Department o f F l u i d Mechanics, Technical U n i v e r s i t y o f Denmark.
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Acustica,
