Canonical System of Integrodifferential Equations Arising in Resonant Nonlinear Acoustics

摘要

In general, weakly nonlinear high frequency almost periodic wave trains for systems of hyperbolic conservation laws interact and resonant to leading order. Simplified asymptotic equations have been developed describing this resonant interaction. In the important special case of compressible fluid flow in one or several space dimensions, these simplified asymptotic equations are essentially two inviscid Burgers equations for the nonlinear sound waves, coupled by convolution with a known kernel given by the sum of the initial vortex strength and the derivative of the initial entropy. Some of the remarkable new properties of the solutions of this system are derived for resonant acoustics. These new features include substantial almost periodic exchange of energy between the nonlinear sound waves, the eliminating or suppressing the strong temporal decay of sawtooth profile solutions of the decoupled inviscid Burgers equations. The approach combines detailed numerical modeling. Reprints. (jhd)