Internally cooled convection: A fillip for Philip

We discuss a simplified mathematical description of internally cooled convection that includes a constant adiabatic lapse rate and an internal energy sink. The latter provides a representation of radiative cooling and, in combination, these two effects break the up-down symmetry of the vertical motions by making the convection penetrative in the upper portion of the fluid layer. At large enough turbulent intensity of the motion, the dynamics is dominated by intense convective updrafts that generate a strongly skewed distribution of vertical velocities. The numerical exploration of this model system exhibits a qualitatively useful description of atmospheric convection.