Mathematical study on the reflection and refraction phenomena of three-dimensional plane waves in a structure with floating frozen layer

Abstract

A physically realistic mathematical problem has been modelled to discuss the reflection and refraction phenomena of three-dimensional (3-D) plane waves. The considered composite structure comprises of water layer of finite width lying between isotropic and ice substrate has been considered. The mathematical analysis pertaining to this problem has been addressed analytically. The closed form expressions for reflection and refraction coefficients of different reflected and refracted waves are derived. Mathematical expressions for the energy share associated with the various waves are also enlisted in a very concise form in connection with the reflection and refraction coefficients. The effects of various polar and azimuthal angles have been exhibited on the reflection and refraction coefficients. The energy conservation law is established to validate this model. Numerical examples and computations have been performed to illustrate the results of this model graphically. Further, as a particular case of the present problem, the deduced results are compared and validated with the pre-established classical results.