  Convection in astrophysical systems must be maintained against dissipation.
Although the effects of dissipation are often assumed to be negligible, theory
suggests that in strongly stratified convecting fluids, the dissipative heating
rate can exceed the luminosity carried by convection. Here we explore this
possibility using a series of numerical simulations. We consider
two-dimensional numerical models of hydrodynamic convection in a Cartesian
layer under the anelastic approximation and demonstrate that the dissipative
heating rate can indeed exceed the imposed luminosity. We establish a
theoretical expression for the ratio of the dissipative heating rate to the
luminosity emerging at the upper boundary, in terms only of the depth of the
layer and the thermal scale height. In particular, we show that this ratio is
independent of the diffusivities and confirm this with a series of numerical
simulations. Our results suggest that dissipative heating may significantly
alter the internal dynamics of stars and planets.
