We consider a fluid close to its gas-liquid critical point in a bottom-heated cavity. Due to strong density stratification, both the Schwarzschild and the Rayleigh stability criteria are relevant at the same space scale. Taking advantage of the competition between these two limits of the convection-onset criterion, we numerically exhibit striking non-Boussinesq effects: the reverse transition to stability through the Schwarzschild line of a heat diffusing layer subjected to convection, and the convection onset inside a few-millimeters-thick layer according to the Schwarzschild criterion.

This Note describes an acoustic filtering of the equations governing the supercritical fluid buoyant flow driven by a weak heating. The resulting low Mach number approximation takes into account the compressibility of the fluid with respect to the hydrostatic pressure. Using the direct numerical simulation of a supercritical fluid flow in the Rayleigh–Bénard configuration, we show that the density stratification may be taken into account without further numerical effort and is fundamental for the prediction of the convective instability threshold induced by a weak heating.