Models and equations encountered in geosciences (typically the free surface Navier-Stokes equations) are very complex to analyse and solve. For multi-scale and multi-physics systems, a key point is often to derive reduced complexity models for which mathematical/numerical analysis and simulation can bring significant benefits. This is a strong point of the team and it is worth noticing that few teams in the applied mathematics community pay attention to this aspect of mathematical modelling. Among physicists, several teams contribute to the modeling of complex rheology flows. The mathematical modelling in biology is more developed and we especially collaborate with BIOCORE, LOV4, IFREMER, INRA, …
During the last 10 years, for the study of geophysical and environmental phenomena, there has been an impressive growth of the available measurements. These data reveal complex and sophisticated phenomena (interactions, couplings, wave propagation, …) e.g. the seismic noise generated by the atmosphere-ocean coupling. Thus it is necessary to propose rigorously derived reduced complexity models endowed with minimal stability properties – conservativity, energy balance, … – and easily calibrated. As examples let us mention the problem of transition between the static and flowing behaviour of granular matter and also the approximation of the non-hydrostatic Euler system using shallow water or multi-layer type models.
