Wind-driven ice-ocean interaction in the marginal ice zone has been shown to contribute to enhanced entrainment when the winds are favorable for upwelling at the ice edge. If a strong surface heat loss is present, formation of a deep convective region is possible resulting from an ever decreasing buoyancy and a rapid deepening of the mixed layer, i.e., a ''chimney''. This chimney does not extend to the bottom, but loss of buoyancy would indicate eventual overturning to the bottom in the studied two-layer ocean model where initially a ''fresh'' and cold (freezing) mixed layer lies above a stagnant, warm and saline lower layer. A catalyst for the convection is the ice (and especially the existence of the ice edge), which has both a dynamic and thermodynamic interaction with the ocean in the coupled ice-ocean model. The entrainment between the mixed layer and the lower layer consists of both the wind mixing component (involving the frictional velocity at the ocean surface, a Kraus-Turner parameterization) and the convectively induced entrainment (no dissipation of convective turbulence). The latter is necessary in producing the chimney. The results are an extension to the earlier and model results (H¿kkinen, 1987) which did not include the convective component of entrainment.