Primary instabilities in convective cells due to non-uniform heating

Abstract

We study a convection problem in a container with a surface open to the air and heated by a long wire placed at the bottom. Coupled buoyancy and thermocapillarity effects are taken into account. A basic convective state appears as soon as a temperature gradient with horizontal component different from zero is applied. It consists of two big rolls that fill the convective cell and are parallel to the heater. A numerical solution allows us to determine this basic state. A linear stability analysis on this solution is carried out. For different values of the applied temperature gradient the basic rolls undergo a stationary bifurcation. The thresholds depend on the fluid properties, on the geometry of the heater, and on the heat exchange on the free surface. This confirms the results obtained in recent experiments.