A level 2 second-order turbulent closure model is employed to study the surface mixed layer developing between sea ice and a relatively warmer background water in the marginal ice zone. The model is driven by a suddenly imposed ice-water stress and warming in the water. The mixed layer rapidly develops in 1 day and afterwards is gradually eroded at its bottom mainly by an inertial oscillation. The ice velocity is larger with the stronger stress, but the mixed layer is thicker. Hence the length scale of ice travel before complete melting is nearly independent of the ice-water stress. Higher temperature of the background water gives more heat to ice but produces a thinner mixed layer. The product of the travel distance and (the background temperature minus the freezing point) is larger for the warmer water. Heat flux through the ice due to atmospheric forcing is a minor mechanism for melting in the marginal ice zone.