Boussinesq up-down symmetry

With mechanically and thermally equivalent upper and lower boundaries, the Boussinesq approximation permits reflection through the layer midplane together with reversal of the temperature perturbation and vertical velocity. In a reduced convection temperature equation this induces temperature inversion. A quadratic term which changes differently from the linear terms breaks this symmetry; a cubic term can preserve it. The Boussinesq approximation alone does not impose symmetry on unequal boundary conditions.