Wave motion in a random hydroacoustic medium using boundary integrals/elements methods

Abstract

Two algorithms for solving the general problem of wave propagation, radiation and/or scattering in a random hydroacoustic medium using the boundary element method are presented here. The formulation is based on an observation about the predominant type of randomness in a hydroacoustic medium, i.e. the dominance of sound velocity fluctuations over density fluctuations, that allows employment of a single perturbation scheme. Perturbations may be applied at either the differential or the integral operator level. In the former case, each of the resulting nth order governing differential equations, n = 1,2…, preserves the deterministic nature of the original wave operator with the randomness appearing as a forcing function (inhomogeneity). The differential equations are subsequently recast as integral equations with both surface and volume type integrals that are solved using routine boundary element techniques. In the latter case, a random integral equation statement is written and the random kernels are expanded using perturbations. Only surface type integrals result, but different expressions must be evaluated at each perturbation order level n. Second-order moment statistics are finally computed once the total solution has been reconstituted from the perturbed solutions. Random forcing functions and /or boundary conditions are included in the development of these approaches but these are taken as deterministic in the applications. The methodology is for steady-state waves. Finally, a numerical example involving a pulsating sphere in a random fluid under stationary conditions serves to illustrate the method.