Simulation results

Introduction: this page describes some simulation results for the paper L. Tao, J. Wu, K. Zhao, and X. Zheng. Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion, Archive for Rational Mechanics and Analysis 237(585-630), 2020.

The governing equations are the perturbed Boussinesq-Navier-Stokes system (1.5) from the paper (see the paper for details):

Information of the simulation: Domain is [0,2pi]^2 and all variables are periodic in all directions. The initial perturbation for temperature is cos(x) sin(y), for velocity is (sin(x)cos(y), -cos(x)sin(y)).

This figure shows the decay of velocity in time, whose decay rate is roughly in the order of 1/t. This rate is better than the theoretical result 1/sqrt(t).

Movie 1: temperature evolution from time t=0 to t=15900, which shows the stratification of temperature