Convective Motions in Water: Linear and Nonlinear Models, Criteria of Convection Onset

Abstract

The problem of convective motions adequate description on the base of linear or nonlinear mathematic models is considered. The criterion of convection onset is formulated in the form $\vert \mathbf{J}_{conv}\vert /\vert \mathbf{J}_{cond}\vert >1$ where the $\vert \mathbf{J}_{conv}\vert$ and $\vert \mathbf{J}_{cond}\vert$ are the convective and conductive fluxes of heat correspondingly. As a result of governing equations solution for initial time moments of the problem the characteristic scales are chosen. It is shown that for Rayleigh-Bénard convection the Rayleigh number $Ra=\alpha g\vert \nabla T\vert d^4/\chi \nu$ should be attributed not to the onset, but to the intensity of convection and to the rate of its development after the onset.