Plenary Lecture

On the Spectrum of Internal Oscillations of Rotating Stratified Fluid

Associate Professor Andrei Giniatoulline
Department of Mathematics
Los Andes University

Abstract: We consider mathematical properties of the three-dimensional 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 non-linear 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.

Brief Biography of the Speaker: Andrei Giniatoulline received his undergraduate, MSc, and PhD degrees from Friendship University in Moscow, Russia. Since 1993, he has taught undergraduate and graduate level courses at the Department of Mathematics of Los Andes University in Bogotá, Colombia, where he holds the position of Associate Professor. His research interests are in the areas of mathematical physics, with an emphasis on hydrodynamics and applied functional analysis. He has delivered invited lectures on the subject of Spectral Theory at universities in Bolivia, Brazil, Japan, Russia, Spain and other countries.