Some analytical solutions for propagation of gravity waves along a small-scale frontal surface

Abstract

Propagation of the gravity waves along a small-scale frontal surface is considered. The simplified perturbation perturbation equations, which can be applied to describe this phenomenon, are introduced and a method to solve them is exposed.

The main difficulty in finding analytical solution to the resulting initial value problem is in taking into account the frontal inclination towards ground. It is shown how this problem can be overcome by an approximate solution in form of a Bessel-Fourier series, provided the inclination is partially ignored in the governing equations.

In order to demonstrate the role of the frontal inclination in the propagation of disturbances along the frontal surface, some properties of the exact solution, which can be obtained after substitution of the wavelike solution in the complete system, are analysed. It is shown that inclination leads to the appearance of an instability of downstream propagating waves. This phenomenon is further described and discussed.