 Penetrative convection in an ice-covered lake

ID: 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} = \frac{3}{5} (T_{w} - T_{m})

and a maximum upward heat flux proportional to

(T_{w} - T_{m})^{5/3}

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