Previous numerical calculations of two-dimensional, compressible convection are extended to three dimensions, using a higher order Godunov scheme. The results show that the flow readily becomes supersonic in the upper boundary layer, where shock structures form intermittently in the vicinity of the strong downflow lanes. The convection as a whole is strongly time-dependent and evolves on a time scale comparable to the sound crossing time. The motions in the upper layers are characterized by the rapid expansion of the upward-moving fluid elements. In the interior, most of the heat is carried by a small fraction of the fluid residing in strong, highly coherent downflows. The remaining fluid is dominated by small-scale, disorganized turbulent motions.
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Malagoli et al. (1990) studied this question.