Rare events in the Boussinesq system with fluctuating dynamical boundary conditions

Abstract

The Boussinesq system models various phenomena in geophysical and climate dynamics. It is a coupled system of the Navier–Stokes equations and the salinity transport equation. Due to uncertainty in salinity flux on fluid boundary, this system is subject to random fluctuations on the boundary. This stochastic Boussinesq system can be transformed into a random dynamical system. Rare events, or small probability events, are investigated in the context of large deviations. A large deviations principle is established via a weak convergence approach based on a recently developed variational representation of functionals of infinite dimensional Brownian motion.