On the eigenvalues of internal waves of rotating exponentially stratified three-dimensional fluid

andrei giniatoulline

Presentation information

[E] Poster

A (Atmospheric and Hydrospheric Sciences ) » A-CG Complex & General

[A-CG36] Dynamics of Oceanic and Atmospheric Waves, Vortices, and Circulations

Thu. Jun 2, 2022 11:00 AM - 1:00 PM Online Poster Zoom Room (13) (Ch.13)

convener:Kunihiro Aoki(Japan Agency for Marine Earth Science and Technology), convener:Shane R Keating(University of New South Wales), Yukiharu Hisaki(University of the Ryukyus), convener:Norihiko Sugimoto(Keio University, Department of Physics), Chairperson:Kunihiro Aoki(Japan Agency for Marine Earth Science and Technology), Shane R Keating(University of New South Wales), Yukiharu Hisaki(University of the Ryukyus), Norihiko Sugimoto(Keio University, Department of Physics)

11:00 AM - 1:00 PM

[ACG36-P03] On the eigenvalues of internal waves of rotating exponentially stratified three-dimensional fluid

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

Keywords:Oceanic waves, Atmospheric waves, Internal vibrations of the fluid, Eigenvalues and Eigenfunctions, Essential spectrum

We study a model of fluid dynamics which describes three-dimensional flows in the Ocean or Atmosphere with the consideration of non-homogeneous initial density due to the gravitational force, together with the consideration of the rotation of the Earth. For the internal waves caused by the Coriolis force and the gravitational force, we find the spectrum of normal vibrations and investigate its structure and localization. We find the eigenvalues and the corresponding eigenfunctions of the spectrum for the domains of the sphere, cylinder and parallelepiped. We also prove that the essential spectrum of internal waves is composed of the limit points of the found eigenvalues.