Direct numerical simulation of the time-dependent convection in a supercritical fluid layer: Temporal evolution of the convective structures in highly non-linear regimes

We present a numerical study of the hydrodynamic stability of a supercritic al fluid (more precisely CO2) contained in a 2D square bottom - heated cavi ty (Rayleigh - Benard configuration). The fluid is initially at rest, at th ermodynamic equilibrium and set at some Kelvins above its critical temperat ure. Due to the characteristic properties of near - critical fluids, the he ating of the lower wall induces the development of two thin boundary layers of temperature and density along the two (hot below and cold above) walls which are separated by a quasi isothermal bulk. We studied the stability of these two boundary layers by solving the time - dependent compressible Nav ier - Stokes equations written for a Van der Waals gas.