FOR 5528:  Mathematical Study of Geophysical Flow Models: Analysis and Computation

• Subject Area: Mathematics ; Geosciences
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 500072446

Turbulence is identified by the scientific community to be one of the most challenging classical scientific problems. It is commonly believed that turbulent flows are governed by the Navier-Stokes equations. In oceanic and atmospheric dynamics the Navier-Stokes equations are driven by buoyancy forces due variations in density and temperature as it is modeled by the Boussinesq approximation. 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 vapour and the way it affects, and is affected by, the evolution of the temperature field. Realistically, 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 in addition to other effects such as sea-ice dynamics. It is proposed here to develop rigorous mathematical analytical and numerical/computational tools to investigate the various oceanic and atmospheric models and their coupling. 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 real-life 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. The aims and breadth of the proposed projects are beyond the reach of individual proposals requiring a unique team and intense exchange and cooperation. The present team, with its wide range of expertise in geophysical modeling, mathematical and numerical analysis and scientific computing, seems in an excellent position to accomplish the stated ambitious goals.

• DFG Programme: Research Units
• International Connection: United Kingdom

Projects

• A Coupled Atmosphere-Ocean-Sea-Ice Model: Mathematical Analysis, Numerics and Computations (Applicants Klein, Rupert ;  Korn, Peter )
• Analysis, Thermodynamics and Numerics of Hibler’s Sea-Ice Model (Applicants Disser, Karoline ;  Hieber, Matthias ;  Korn, Peter )
• Computational Convex Integration (Applicants Korn, Peter ;  Székelyhidi, László )
• Coordination Funds (Applicant Hieber, Matthias )
• Coupling Moisture with Atmospheric Dynamics (Applicant Titi, Ph.D., Edriss )
• Interaction of Deterministic or Stochastic Forces on Flat or Moving Interfaces (Applicants Hieber, Matthias ;  Titi, Ph.D., Edriss )
• Scale Analysis and Asymptotic Reduced Models for the Atmosphere (Applicant Klein, Rupert )

• Spokesperson: Professor Dr. Matthias Hieber