Abstract
We obtained steady solutions to the two-dimensional Boussinesq approximation equations without a mean temperature gradient. This system is referred to as free convection in this paper. Under an external flow described by the stream function Ψ=−Ayf(x), steady solutions are found. They are kept steady by the balance between the strain of Ψ and the diffusion. In this sense, they are similar to the Burgers vortex layer solution. Two examples other than f(x)=x are shown to have steady solutions. We discuss the relation between these solutions and long-lived fine scale coherent structures observed in direct numerical simulations of two-dimensional free convection turbulence.
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