Oscillations of a stratified rotating fluid in a cylindrical cavity

DOI: 10.34759/trd-2023-130-09

Аuthors

Yan N. O.

Bauman Moscow State Technical University, MSTU, 5, bldg. 1, 2-nd Baumanskaya str., Moscow, 105005, Russia

e-mail: yno64528@gmail.com

Abstract

In this paper, the problem of free oscillations of an ideal stratified rotating incompressible fluid filling a cylindrical cavity in a solid is considered. The normal oscillations of a stratified fluid at a low rotational speed are studied in the case of full or partial filling of a cylindrical round tank with liquid. Recently, there has been interest in the study of oscillations of a stratified fluid filling a vessel of finite dimensions (oscillations of oil and other liquids in various reservoirs). The study of the motion of a rotating ideal stratified fluid in a limited volume leads to very peculiar boundary and initial problems. In this paper, we investigate the problem of oscillations of an ideal incompressible stratified fluid whose density at rest varies along the vertical axis. The questions of the interaction of an ideal stratified fluid and the cavity of a moving solid body are considered, and solutions to problems of normal (natural) oscillations of a fluid with boundary conditions are presented. To study the vortex motion of a rotating homogeneous fluid, the method of state functions of S.L. Sobolev or the method of generalized potentials of F.L. Chernousko is usually used. The method of generalized potentials, which uses some restriction on the change of variables from time, is more convenient in this sense. The method of F.L. Chernousko makes it possible to emphasize the hydrodynamic problem from the general problem of the mechanics of the body-liquid system in the most complete way. Numerical results of determining the eigenvalues and eigenfunctions of normal fluid oscillations are given at a constant buoyancy frequency in the form of tables and graphs.

Keywords:

stratified fluid, normal fluid oscillations, cylindrical cavity

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