Penetrative convection

Penetrative convection occurs when an unstable convecting region extends into, or is capped by, a stably stratified region. Water near its temperature of maximum density provides a common example: a cold stable layer can lie above a warmer turbulent convecting layer.

Fresh water reaches maximum mass density near $4{}^{\circ }\mathrm{C}$ at atmospheric pressure. A useful local equation of state isso water becomes less dense when its temperature moves either above or below $T_m$.

In an ice-covered freshwater lake, a stagnant layer colder than the density-maximum temperature can cap a warmer turbulent region. Maximizing the boundary-layer heat flux obtained from a Local Rayleigh-number closure gives an interface temperature $T_h$ satisfyingand a maximum upward heat flux proportional to $(T_w-T_m{)}^{5/3}$.