Nonlinear Mathematical Modeling in Atmosphere and Ocean

The purpose of this monograph is to provide illustrative examples of nonlinear modeling of oceanic and atmospheric dynamics and associated energetic. Particularly,exact solutions for the Navier-Stokes equations and the corresponding energy balance associated with an atmospheric motion around the Earth are presented. Additionally,nonlinear internal gravity waves forming a column of stratified fluid affected by the Earth's rotation are considered. In terms of linear modeling,the energy density was visualized as spinning patterns that appear to be rotating in an anticlockwise sense. Such spinning patterns were compared with the flow around a low-pressure area that is usually being linked with a modeling of hurricanes. In terms of nonlinear analysis,several classes of exact solutions were found.One particular class was visualized as funnels having something in common with the geometric structure of oceanic whirlpools. Up to the present,it remains an open issue where the whirlpools came from and what surprises they may bring to. However,it is recognized that the oceanic whirlpools play a key role in global climate. Additionally,such whirlpools show influence on the atmosphere.

Ranis N. IBRAGIMOVAssociate ProfessorDepartment of Mathematics University of Texas at Brownsville Research areas and expertise- Applied and Interdisciplinary Mathematics- Mathematical Modeling in Physical and Environmental Siences- Atmosphere and Ocean Modeling