Mellor, G. L., M. G. McPhee, and M. Steele, 1986: Ice-seawater turbulent boundary layer interaction with melting or freezing. Journal of Physical Oceanography, 16 (11), 1829-1846.

Abstract: A second-moment, turbulence closure model is applied to the problem of the dynamic and thermodynamic interaction of sea ice and the ocean surface mixed layer. In the case of ice moving over a warm, ocean surface layer, melting is intrinsically a transient process; that is, melting is rapid when warm surface water initially contacts the ice. Then the process slows when surface water is insulated from deeper water due to the stabilizing effect of the melt water, and the thermal energy stored in the surface layer is depleted. Effectively, the same process prevails when ocean surface water flows under stationary ice in which case, after an initial rapid increase, the melting process decreases with downstream distance. Accompanying the stabilizing effect of the melt water is a reduction in the ice-seawater interfacial shear stress. This process and model simulations are used to explain field obervations wherein ice near the marginal ice zone diverges from the main pack.
When the surface ice layer is made to grow by imposing heat conduction through the ice, the surface ocean layer is destabilized by brine rejection and mixing in the water column is enhanced. The heat flux into the water column is a small percentage of the heat conduction through the ice.