Asymptotic analysis of diffraction effects in the radiation of underwater sound by interesting configurations of laser-generated heat deposition

Abstract

A previously proposed ideal configuration [J. Acoust. Soc. Am. Suppl. 1 77, S104 (1985)] for optimal laser-generated heating of water to achieve strong farfield acoustic signals with desirable properties suggests a number of pertinent boundary value problems in thermoacoustics. These progress in complexity and are analyzable with varying degrees of simplicity and thoroughness using mathematical physics techniques such as Fourier transforms, contour deformation, and the saddle point method. A simple class of such models assumes that the source term (associated with heat addition) of the wave equation is independent of the horizontal coordinate y, is a sinusoidal progressing wave in the horizontal coordinate x, and dies out exponentially with depth coordinate z. The source extent in the x direction is either taken as unlimited in the simplest idealization or non-zero only over a fixed length L. The pressure disturbance is described as a Fourier integral over wavenumber kx and angular frequency ω. The ordinary differential equation for the integrand is readily solved, and the resulting integrals are evaluated for positions and times of interest using complex variable techniques. [Work supported by ONR, Code 425-UA.]