Unsteady Perturbation Solutions of 2D Anisotropic Boussinesq Systems in a Periodic Domain

This talk presents some unsteady solutions of the perturbed anisotropic Boussinesq system in a two dimensional periodic domain. In this Boussinesq system, the velocity has only the horizonal diffusion and the temperature has only the vertical diffusion. This corresponds to the Geophysical Reynolds-Averaged Navier-Stokes Equations, where the horizontal turbulent viscosity is far larger than the vertical turbulent viscosity. This work focuses on the perturbation around a particular solution with zero velocity and a linear temperature profile in the vertical coordinate. Some mathematical analysis has been performed to derive the stable steady state solutions of the perturbation system with thermal stratification. In contrast, this work presents some unsteady perturbation solution using numerical simulations, including periodic perturbation solutions in time.