Vibration Effect on a Thermal Front Propagation in a Square Cavity Filled with Incompressible Fluid

We investigate numerically the effect of a linearly polarized, harmonic vibration on a 2-D incompressible fluid confined in a square cavity when a sudden change of temperature is imposed at the walls under zero static gravity. A thermal front propagates from the wall, which can become unstable and develop as fingers. The study is performed in the framework of the Boussinesq approximation where the density variations are taken into account only in the vibrational force. The calculations carried out by finite difference method show that the direction of vibrations has a major impact on the thermal front propagation. When vibrations are parallel to the wall, the flow is induced in the same direction and a thermal vibrational instability develops. In contrast, when vibrations are normal to the wall, it is observed a parametric instability is observed.