Onset of convection in a horizontal fluid layer in the presence of density inversion under given heat fluxes at its boundaries

The onset of convection in a horizontal fluid layer in the presence of density inversion is studied under given heat fluxes at the layer boundaries. The stability diagram is obtained and the nature of disturbances is studied in the linear approximation. Depending on the density maximum position within the layer the instability may be both long-wave and cellular in nature.