Section: Scientific Foundations
Introduction
Geophysical flows generally have a number of particularities that make it difficult to model them and that justify the development of specifically adapted mathematical and numerical methods:

Geophysical flows are nonlinear. There is often a strong interaction between the different scales of the flows, and smallscale effects (smaller than mesh size) have to be modeled in the equations.

Every geophysical episode is unique: a field experiment cannot be reproduced. Therefore the validation of a model has to be carried out in several different situations, and the role of the data in this process is crucial.

Geophysical fluids are non closed systems, i.e. there is always interactions between the different components of the environment (atmosphere, ocean, continental water,etc.). Boundary terms are thus of prime importance.

Geophysical flows are often modeled with the goal of providing forecasts. This has several consequences, like the usefulness of providing corresponding error bars or the importance of designing efficient numerical algorithms to perform computations in a limited time.
Given these particularities, the overall objectives of the MOISE projectteam described earlier will be addressed mainly by using the mathematical tools presented in the following.