DFG Research Unit FOR 5528

Mathematical Study of Geophysical Flow Models: Analysis and Computation

In oceanic and atmospheric dynamics, the underlying primitive and Navier-Stokes equations are driven by buoyancy forces due to variations in density and temperature. The dynamical changes in the salinity and temperature are the main causes for such variations of density in oceanic dynamics. In the atmosphere, the presence of moisture implies the additional challenge of modeling the thermodynamics of the phase change dynamics between water and vapor.

The atmosphere and oceans are also coupled through the exchange of stress forces and heat transfer at the interfaces that separate them. Therefore, comprehensive global climate models must take this coupling into account along with the other effects such as sea-ice dynamics.

In addition, the group aims to advance a systematic asymptotic methodology for the derivation of reduced models that capture underlying geophysical phenomena at the relevant scales and to rigorously justify such reduced models. This mathematical Research Unit is thus motivated by important applications. In pursuing its projects, it aims to demonstrate that rigorous mathematical research and application-oriented theoretical developments in geophysical fluid dynamics can join forces to their mutual benefit: While formal theoretical developments in geophysical flows gain credibility when underpinned by proven mathematical theorems, real-life applications trigger important advances in the mathematics of partial differential equations and associated fields. It is this kind of constructive bridge-building between abstract mathematics, and concrete applications, which this Research Unit is to foster and establish within the field of geophysical fluid dynamics.

The methods used range from scale analysis, evolution equations, convex integration and PDE analysis to the numerical treatment of geophysical models such as the ICON model.