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

[ACG38-P02] Essential spectrum of internal waves arising in rotating stratified fluid

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

Keywords:Dynamical systems, Internal waves, Resonance effect, Rotational fluid, Stratified fluid, Essential spectrum

For viscous and inviscid compressible fluid, we consider the three-dimensional models which involve simultaneously the stratification and rotation of the fluid. The rotation corresponds to the rotation of the Earth over the vertical axis, and the stratification corresponds to the non-homogeneous distribution of density due to the gravitational force. We find the structure and the localization of spectrum of normal vibrations of the inner waves for various boundary conditions. We prove that, when the spectral parameter belongs to the essential spectrum, there arises the resonance effect of non-uniqueness of the limit amplitude of internal waves. The results may find application in the study of the Ocean and Atmosphere.