On the (non linear) foundations of Boussinesq approximation applicable to a thin layer of fluid

R. Perez Cordon , M. G. Velarde

A two-parameter perturbation scheme for the thermohydrodynamic description of a horizontal layer of a single component arbitrary fluid heated from below (Rayleigh-Bénard problem) is presented here. The first approximation leads to the Boussinesq-Oberbeck equations. This agrees with previous results obtained by Mihaljan [Astrophys. J. 136 (1962) 1126]. Contrary to Mihaljan's theory however, the series expansion given here is free from inherent difficulties in obtaining higher order approximations viz. non-Boussinesq effects. This is done by choosing a suitable adiabatic hydrostatic reference field and two parameters of the same order of magnitude. In a well defined limit the theory presented here recovers earlier results obtained by Malkus (as yet unpublished) for dilute ideal gas layers.

Mots clés: convection; hydrodynamics

Domaines: Articles anciens

R. Perez Cordon, M. G. Velarde. On the (non linear) foundations of Boussinesq approximation applicable to a thin layer of fluid. Journal de Physique, 1975, 36 (7-8), pp.591-601. ⟨10.1051/jphys:01975003607-8059100⟩. ⟨jpa-00208290⟩