[A-CG38] Dynamics of Oceanic and Atmospheric Waves, Vortices, and Circulations

[ACG38-P03] On the structure of the spectrum of internal waves and the distribution of the eigenvalues for stratified rotating flows in various domains.

*andrei giniatoulline¹ (1.Department of Mathematics, Los Andes University, Bogota, Colombia, South America)

Keywords:Dynamical systems, Internal waves, Turbulence, Spectral analysis, Climate

We study a system of Partial Differential Equations which describes linearized flows with the consideration of rotation over the vertical axis, as well as non-homogeneous distribution of density due to the gravitational force. The three-dimensional model is applied either to the Ocean flows or the Atmosphere flows. For arising internal waves we find the structure of the spectrum of inner oscillations in general domains. For the particular cases of cubes, circular cylinders, general cylinders and spheres, we find the explicit eigenvalues and their corresponding eigenfunctions. We prove that the set of the eigenvalues consists of two parts, one of which is composed of isolated points, and the other is represented by limit points which belong to the essential spectrum. Since the found eigenfunctions form an ortonormal complete set in L₂, the results may be used in numerical modelling of more general problems in the Ocean or the Atmosphere.