Quasilinear Approximation for Modeling Difference-Frequency Acoustic Wave in a Diffracting Pump-Wave Beam

Abstract

A quasilinear approach is considered to simulate generation of a difference-frequency acoustic wave by the interaction of two intense high-frequency diffracting pump beams with close frequencies. The boundary condition corresponds to dual-frequency excitation of an existing parametric source used for underwater research. It is shown that the linear field of primary waves has a high directivity with a total beam divergence angle of several degrees; therefore, the nonlinear-diffraction problem is solved numerically in the parabolic approximation. The pump wave field is calculated in the linear approximation; the solutions obtained at each step of the numerical grid along the beam axis are used to calculate nonlinear sources in the equation for a three-dimensional difference-frequency beam. The one- and two-dimensional distributions of the pressure field and the directivity pattern are analyzed for three values of a difference frequency. Numerical solutions obtained with realistic boundary conditions at the source and description of diffraction effects are compared with the known approximate analytical results for the quasilinear approach.