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Vestnik KRAUNC. Fiziko-Matematicheskie Nauki, 2023, Volume 43, Number 2, Pages 111–125
DOI: https://doi.org/10.26117/2079-6641-2023-43-2-111-125
(Mi vkam604)
 

PHYSICS

Two types of waves in a two-layer stratified fluid

A. I. Rudenko

Department of applied mathematics and information technology, Kaliningrad State Technical University
References:
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 $\frac{\Delta\rho}\rho$, i.e. it is very small.
Keywords: two-layer liquid, Boussinesq approximation, dispersion relation, potential oscillations.
Document Type: Article
UDC: 517.958
MSC: 35Q35
Language: English
Citation: A. I. Rudenko, “Two types of waves in a two-layer stratified fluid”, Vestnik KRAUNC. Fiz.-Mat. Nauki, 43:2 (2023), 111–125
Citation in format AMSBIB
\Bibitem{Rud23}
\by A.~I.~Rudenko
\paper Two types of waves in a two-layer stratified fluid
\jour Vestnik KRAUNC. Fiz.-Mat. Nauki
\yr 2023
\vol 43
\issue 2
\pages 111--125
\mathnet{http://mi.mathnet.ru/vkam604}
\crossref{https://doi.org/10.26117/2079-6641-2023-43-2-111-125}
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