SMALL-SCALE STRUCTURES IN BOUSSINESQ CONVECTION

Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high-order accurate ENO scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. In contrast to the finding s of Pumir and Siggia who reported finite time collapse of the bubble cap, the present numerical results suggest that the strain rate corres ponding to the intensification of the density gradient across the fron t saturates at the bubble cap. Consequently, the thickness of the bubb le decreases exponentially. On the other hand, the bubble experiences much stronger straining and intensification of gradients at its side. As the bubble rises, a secondary front also forms from its tail. Toget her with the primary front, they constitute a pair of tightly bound pl us and minus double vortex sheet structure which is highly unstable an d vulnerable to viscous dissipation.