Harmonic Solutions for the Reflection and Refraction of Finite-Amplitude Acoustic Waves in Two Fluids

摘要

This paper deals with the reflection and refraction of finite-amplitude acoustic waves obliquely incidents to a plane interface between two lossless fluids. The study is based on the second-order harmonic wave equations in term of displacement potential in Lagrangian coordinate system. Variable parameter separation method is used to get the special solutions of the wave equations. Source conditions and boundary conditions are applied to determine the parameters in the special solutions. Results show that the amplitudes of the incident, the reflected and the transmitted harmonic waves all depend on coordinates a and b. The solution of incident fluid is composed by three parts: the first part corresponds to the nonlinear interactions of the first acoustic field, with amplitude stimulating along coordinates a and b; the second part corresponds to the linear reflection of the second incident wave on the interface and it remains constant when propagation; the third part induced by the interaction between the first incident and reflected waves propagates parallel to the interface with constant amplitude. The special solutions are applicable to wave incidence with any incident angle, not only 0° and 90° as mentioned in previous research.