Two-dimensional Boussinesq convection is studied numerically using two different methods: a filtered pseudospectral method and a high order accurate Essentially Nonoscillatory (ENO) scheme. The issue whether finite time singularity occurs for initially smooth flows is investigated. The numerical results suggest that the collapse of the bubble cap is unlikely to occur in resolved calculations. The strain rate corresponding to the intensification of the density gradient across the front saturates at the bubble cap. We also found that the cascade of energy to small scales is dominated by the formulation of thin and sharp fronts across which density jumps. Weinan, E. and Shu, Chi-Wang Unspecified Center NAS1-18605; NAS1-19480; DAAL03-89-K-0039; DAAL03-91-G-0123; AF-AFOSR-0090-90; NSF DMS-91-00383; NAG1-1145; RTOP 505-90-52-01...