Mathematical and numerical delicacies in coupled ocean-atmosphere simulations

International audienceAtmospheric and oceanic simulation models are widely used for weather, general/regional circulation, and climate, as well as for many idealized processes. In this context, the simulated flows are fundamentally chaotic and spectrally broad band across global to micro scales. A full representation in different scales is uncomputable even with the continuous increase of computing power. To cope with this problem, numerical models contain ad-hoc parameterizations to account for unresolved (subgrid scale) processes. The parameterization schemes are essential to maintain a reasonable level of plausibility, but their math- ematical formulation is devised empirically, and often impairs the regularity of the associated solutions. This problem is even more acute when considering coupled ocean-atmosphere models because the number of parameterizations present in the problem increases which substantially increase the task load. In this talk, it is showed that this complexity has to be taken into account to devise mathematically consistent and efficient coupling algorithms. In existing coupled models, deficiencies appear both in the formulation of the physical parameterizations and in the algorithmic approach used for the coupling. This problem is here addressed from the point of view of Schwarz-like domain decomposition methods. Using a hierarchy of examples, from highly simplified to three-dimensional fully-realistic cases, the delicacies associated with ocean-atmosphere coupling are illustrated both theoretically and numerically. In particular, a focus is on the proper design of air-sea interface conditions in the presence of turbulent boundary layers. Fi- nally, numerical results showing the benefits of a carefully designed coupling strategy for regional coupled models will be presented