Abstract

In this talk, we are interested in the study of geophysical fluids (like the atmosphere and oceans) on large scales. In this context, we observe the duality between the fast rotation (due to the Coriolis force), that drives the motion to horizontal planes, and the gravitation, that acts against this process by driving the fluid to a vertical stratification. Moreover, different scales, where some effects are predominant with respect to the others, interact and contribute to the average dynamics of the flow. We will review these features for a multi-scale and heat-conducting model (called Navier-Stokes-Fourier system) where we take into account the competition of several external forces as the Coriolis, the gravitational and the centrifugal forces. For this multi-scale problem, we have two main goals: the first aim is to understand the limit dynamics when the Coriolis term tends to infinity; the second one is to find a robust method that allows to deal with all the possible scenarios appearing due to the different scaling. In addition, our approach allows us also to handle a critical scaling in which some low stratification effects due to the gravity appear in the limit. This is a joint work with Daniele Del Santo, Francesco Fanelli and Aneta Wróblewska-Kamińska.