Two Types of Waves in a Two-Layer Stratified Fluid

Abstract

Within the framework of the linear theory of small potential oscillations the article studies the structure and characteristics of internal and surface waves in a two-layer stably stratified fluid. Dispersion relations have been obtained and analyzed. The Boussinesq approximation has been studied. We have determined the existence of two types of waves: a fast wave and a slow wave. The fast wave differs little from a surface wave in a homogeneous fluid. The main results of studying the case of n=1 are as follows: obtaining expressions for fluid particles velocity components and hydrodynamic pressure in the upper layer of the considered two-layer fluid, as well as obtaining relations, which connect the oscillation amplitudes of the free surface and the interface of the considered two-layer fluid. The main results of studying the case of n=2 are as follows: obtaining expressions for fluid particles velocity components and hydrodynamic pressure in the lower layer of the considered two-layer fluid, as well as obtaining dispersion relations in the considered two-layer fluid. In the case of implementing the Boussinesq approximation, the fast wave differs little from a surface wave in a homogeneous fluid, andthe velocity of slow waves is proportional to the square root of the squared ratio ρ/Δρ​, i.e. it is very small.

Keywords

• two-layer liquid
• boussinesq approximation
• dispersion relation
• potential oscillations
• двухслойная жидкость
• приближение буссинеска
• дисперсионное соотношение
• потенциальные колебания