Oscillations of a stratified rotating fluid in the field of centrifugal forces of inertia

Аuthors

Temnov A. N.^*, Yan N. O.^**

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

*e-mail: antt45@mail.ru
**e-mail: yno64528@gmail.com

Abstract

In this paper, free oscillations of an ideal stratified incompressible fluid in a rotating cylindrical vessel are considered under the assumption that the equilibrium motion of the fluid is the rotation of a solid body. The problem of oscillations of an ideal incompressible rotating stratified fluid in the field of centrifugal inertia forces is studied. Rotating fluids are not only of scientific interest, but are also important in nature and technical applications. In technical applications, rotating liquids are found in centrifuges, in the hollow shafts of liquid-cooled turbines, in stabilization of rocket rotation, in zone-melting processes of single crystal growth. Recently, there has been interest in studying the oscillations of a stratified fluid filling a vessel of finite dimensions used in various fields. In this paper, we focus our attention on the consideration of some issues related to the problems of oscillations in a stratified fluid. Some results obtained by us in the study of the problem of natural oscillations of an inhomogeneous rapidly rotating fluid that partially fills a cylindrical cavity and completely fills a coaxial cylindrical cavity of a solid body are presented. The eigenfunctions of a fluid and the eigenvalues of free oscillations of a stratified fluid filling a cylindrical cavity of a solid rapidly rotating around its vertical axis of symmetry are obtained. For sufficiently large values of the angular velocity of motion of a solid body with a liquid, the case under consideration is equivalent to the case of rotation in conditions of complete weightlessness. Numerical calculations of the eigenvalues of normal fluid oscillations at a constant buoyancy frequency are presented in the form of tables and graphs with boundary conditions for internal and surface waves.

Keywords:

stratified fluid, free oscillations, internal waves, surface waves

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