Free oscillations of a viscous stratified fluid in limited containers

Аuthors

Yue Z. ^*, Temnov A. N.^**

Baumann Moscow State Technical University, 105005, Moscow, 2nd Baumanskaya St., b. 5, c. 1

*e-mail: zhang274234111@yandex.ru
**e-mail: antt45@mail.ru

Abstract

The paper investigates the effect of viscosity on the natural frequencies of small oscillations of an incompressible stratified fluid completely filling a stationary vessel. Using functional analysis methods, general spectral properties are derived for cavities of arbitrary shape, including the distribution of eigenvalues and the conditions for the existence of oscillatory modes. For the numerical analysis of low‑viscosity fluid oscillations, the boundary layer method is employed. This approach enables the calculation of first‑order corrections to both the oscillation frequencies and the damping decrements. Exact and approximate solutions are presented for vessels shaped as rectangular cylinders, circular cylinders, and rotational ellipsoids. The study demonstrates that fluid stratification gives rise to long‑lasting internal waves characterized by small damping decrements. These findings highlight the significant role of stratification in sustaining internal wave motion over extended periods.

Keywords:

boundary layer method; Poincaré wave equation; S. L. Sobolev problem; stratification; spectrum; viscosity

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