Large deviation and averaging for multi-scale stochastic tidal dynamics equation

In this paper, we study the asymptotic behavior of multi-scale stochastic tidal dynamics equation. We first derive a strong averaging principle for the multi-scale stochastic tidal dynamics equation. Specifically, we show the solution to the multi-scale stochastic tidal dynamics equation can be approximated by the solution to averaged stochastic system in the sense of mean square. Next, in order to investigate the probability of deviations away from the limiting process, we establish a large deviation principle by utilsing the weak convergence approach.