Studies of steady convection in compressible layers extending over
several scale heights find the motion to be dominantly in large cells
extending over the bulk of the layer, rather than breaking down into
cells of the order of the local scale height. We here give a simple
explanation of this phenomenon. In a steady state the rate of production
of entropy in a closed stream tube must be zero, which requires the stream
tube to link the lower half of the zone where entropy production is
positive with the upper half where it is negative.