Project Details
Projekt
Coupling Moisture with Atmospheric Dynamics
Applicant
Professor Edriss Titi, Ph.D.
Subject Area
Mathematics
Term
since 2023
Project identifier
Deutsche Forschungsgemeinschaft (DFG) - Project number 500072446
Atmospheric dynamics is governed by the Navier-Stokes equations driven by buoyancy forces due to variations in density and temperature as it is modeled by the Boussinesq approximation. 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. In this project it is proposed to investigate the solvability of the coupling of atmospheric fluid motion with moisture dynamics with phase changes for warm clouds, where water is present in the form of water vapor and in the liquid state as cloud water and rain water. The moisture dynamics contains closures for the phase changes condensation and evaporation, as well as the processes of auto conversion of cloud water into rain water and the collection of cloud water by the falling rain droplets. The structure of the nonlinearity in the saturation/source terms in moisture dynamics forms a challenge for establishing the uniqueness of solutions. Therefore, it is proposed to investigate, first, the solvability of various transport dynamics moisture models with a given velocity field. Secondly, it is proposed to investigate the solvability of the coupling of the moisture dynamics with different atmospheric dynamics models. The proposed fluid models include the hydrostatic primitive equations and the Quasi-Geostrophic model. These models are derived using a systematic asymptotic approach and are designed to capture underlying geophysical phenomena at the relevant scales. Thirdly, it is proposed to investigate the rigorous justification of the asymptotic derivation of the coupled reduced fluid models with moisture. In the case of lack of uniqueness of solutions in certain transport moisture model it is also proposed to investigate the coupling of such moisture model to the full three-dimensional Boussinesq approximation system and establish global existence (without uniqueness) of weak solutions.
DFG Programme
Research Units
International Connection
United Kingdom
Co-Investigators
Professorin Dr. Karoline Disser; Professor Dr.-Ing. Rupert Klein
