On the (non-linear) foundations of boussinesq approximation applicable to a thin layer of fluid. (II). viscous dissipation and large cell gap effects

Abstract

We present here a generalization of the Boussinesq approximation of interest in the thermohydrodynamic study of a horizontal fluid layer heated from below (Rayleigh-Bénard problem) when the depth of the layer is important. A straightforward dimensional analysis of the problem shows under which conditions one cannot neglect, however small, the isothermal compressibility. We discuss also the role played by viscous dissipation and by an adiabatic temperature gradient