Rayleigh-Bénard and schwarzschild instability in a supercritical fluid

Due to the density stratification, the convection onset criterion in a supercritical fluid layer heated from below includes a stabilizing effect known as the Schwarzschild criterion, which requires an adaptation of the classical low Mach number approximation. We numerically solve the mathematical model describing the motion of a supercritical fluid in the classical Rayleigh-Bénard configuration and we bring to the fore two main events: (i) the reverse transition of an unstable layer to stability without any external intervention; (ii) the convection onset according to the Schwarzschild criterion. In addition, the 3D extension of the study is briefly described.