On the numerical simulation of buoyant convection

The two-dimensional turbulent vortex generated by release of buoyant fluid from an instantaneous thermal line source has been simulated by machine numerical solution of a complete set of Eulerian gas equations. The equations included turbulent eddy exchange tern, similar to those used by Smagorinsky, which made possible the generation of computationally stable solutions qualitatively and quantitatively resembling the convective "thermals" studied and described by Scorer and Richards. The results of a number of numerical experiments, performed with varying computational approximations, lead to conclusions as to the importance of various sources of numerical errors and the validity of the eddy exchange formulation. The formulation leads to qualitatively good results with the resolution provided by about 1600 grid points, but it has not yet been possible to exhibit the shape-preserving stage assumed in theoretical treatments and found approximately by laboratory experiments. This is probably due in large part to the neglect of the effects of eddies in the third dimension.