On the spectrum of internal oscillations of rotating stratified fluid

摘要

We consider mathematical properties of the three-dimensional compressible rotating fluid in a homogeneous gravity field, which may find an application in the study of the Atmosphere and the Ocean. In particular, we investigate the structure and localization of the spectrum of internal oscillations for differential operators generated by such flows. This spectrum may be very useful for studying the stability of the flows, since it is closely related to the non-uniqueness of the limit amplitude of the stabilized flow. Also, it is important in the investigation of weakly non-linear flows, since the bifurcation points where the small nonlinear solutions arise, belong to the spectrum of linear normal oscillations. We consider both inviscid and viscous fluid for various boundary conditions. The novelty of this research is to consider simultaneously the effects of rotation and stratification, which has been studied separately in previous works.