Page 24 - Spring 2010

THE PARAMETRIC ARRAY AND LONG-RANGE OCEAN RESEARCH
Igor Esipov
Andreev Acoustics Institute Moscow, 117036 Russia
Konstantin Naugolnykh
Cooperative Institute for Research in Environmental Sciences
University of Colorado, Boulder, Colorado 80305 and
National Oceanic and Atmospheric Administration, Earth System Research Laboratory/Zel Technologies, LLC, Boulder, Colorado 80305
Vladimir Timoshenko
Taganrog Technological Institute
Southern Federal University, Taganrog, Russia 347928
“Parametric array systems are a promising tool for multi- frequency acoustical tomography techniques for monitoring range dependent temperatures and current distributions in a complex ocean environment.”
Introduction
The parametric array (PA) is a non-
linear transduction process that
can generate a narrow beam of low
frequency sound in a medium, through
the interaction of co-linear, intense, high
frequency sound waves,1,2 called pump
waves. The unique characteristic of a
parametric array is found in its extreme-
ly narrow directivity pattern (1°-3° angu-
lar resolution) for low frequency acousti-
cal signals. The effective width of the
directivity pattern remains practically
constant over a wide range of signal fre-
quencies. The parametric array has
become essentially a virtual acoustic
end-fire array that has been formed in the medium (water) by the non-linear interaction of the two high frequency waves at their sum and difference frequencies (Fig. 1). As a result, it radiates a sharp, low-frequency, directional signal at the inter- action frequency of its pump waves that propagates independ- ently of the pump waves. Due to the non-resonance property
of the low-frequency signal generation the parametric array can provide a sounding signal transmission in extremely wide frequency bands (more than two octaves).
The nonlinear interactions of sound waves are described by Burgers equation:
where u is the fluid velocity perturba- tions due to sound waves, x is the space coordinate, y=t-x/c0 is the retarded time, α = ε/c0 , ε is the nonlinear parameter of
the fluid, c0 is the sound velocity, and δ is the dissipation coef- ficient that is independent of frequency. The second term in the left-hand side and the term in the right-hand side take into account the nonlinear effects such as combination frequency generation and attenuation of the wave, respectively.
The ratio of the nonlinear term of the Burgers equation
Fig. 1. Parametric signal generation: 1—acoustic array that generates two co-linear high-frequency, intense sound waves in the near field volume; 2 – far field volume where parametric, low-frequency acoustic signals are generated. Directivity of parametrically generated, low-frequency signals are defined by the squared directivity pattern of high frequency pump, Ds(Θ)-(D20(Θ), where Ds is the directivity of the parametric signal and D0 is the directivity of the two primary signals.
20 Acoustics Today, April 2010