Small Probability Events for Two-layer Geophysical Flows under Uncertainty

The stochastics two-layer quasi-geostrophic flowmodel is an intermediate system between the single-layer two dimensional barotropic flow model and the continuously stratified three dimensional baroclinic flow model. This model is widely used to investigate basic mechanisms in geophysical flows, such as baroclinic effects, the Gulf Stream and subtropical gyres. A large deviation principle for the two-layer quasi-geostrophic flow model under uncertainty is proved. The proof is based on the Laplace principle and a variational approach. This approach does not require the exponential tightness estimates which are needed in other methods for establishing large deviation principles.