On the spectral properties of operators describing normal oscillations in 3-dimensional rotating stratified fluid (Spectra of Random Operators and Related Topics)
Andrei Giniatoulline · Institutional Repositories DataBase (IRDB) · 2015
We consider mathematical properties ofthe three-dimensional compressible rotating fluid in a homogeneous gravity field, which may find an application in the study ofthe Atmosphere and the Ocean.In particular, we investigate the structure and localization ofthe spectrum of internal oscillations for differential operators generated by such flows.This spectrum may be very useful for studying the stability ofthe flows, since it is closely related to the non-uniqueness of the limit amplitude ofthe stabilized flow.Also, it is important in the investigation ofweakly non-linear flows, since the bifurcation points where the small nonlinear solutions arise, belong to the spectrum oflinear normal oscillations.We consider both inviscid and viscous fluid for various boundary conditions.The novelty ofthis research is to consider simultaneously the effects ofrotation and stratification, which has been studied separately in previous works.