Penetrative convection in an ice-covered lake
= Penetrative convection in an ice-covered lake
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 $T_h$ satisfying
$$
T_m-T_h=\frac35(T_w-T_m)
$$
and a maximum upward <heat flux> proportional to $(T_w-T_m)^{5/3}$.