The figure above was produced using a Godunov/Projection method applied to the two-dimensional equations for Boussinesq convection. The initial conditions for this computation were taken from a paper by E and Shu and consist of a smooth "bubble" of density in a zero flow field. As the bubble begins to rise, strong fronts in the density field form (shown by the contour lines in the figure) and vorticity is baroclinically produced along this front (shown by the color shading). As the numerical method begins to under-resolve the flow, the density front destabilizes and rolls up under the influence of the vorticity. Because of the experience gained from studying the appearance of spurious vortices in under-resolved flows the correctness of the front roll-up is questionable despite the fact that it is consistent with the evolution of the bubble. In order to investigate this problem further I have developed adaptive mesh refinement techniques for the Boussinesq equations. Below is an example of a simulation using initial conditions from the paper of Siggia and Pumir.