This study is aimed at modeling mesoscale processes such as upwelling/downwelling and ice edge eddies in the marginal ice zones. A two-dimensional coupled ice-ocean model is used for the study. The ice model is coupled to the reduced gravity ocean model through interfacial stresses. The parameters of the ocean model were chosen so that the dynamics would be nonlinear. The model was tested by studying the dynamics of upwelling. Winds parallel to the ice edge with the ice on the right produce upwelling because the air-ice momentum flux is much greater than air-ocean momentum flux; thus the Ekman transport is greater under the ice than in the open water. The stability of the upwelling and downwelling jets is discussed. The downwelling jet is found to be far more unstable than the upwelling jet because the upwelling jet is stabilized by the divergence. A constant wind field exerted on a varying ice cover will generate vorticity leading to enhanced upwelling/downwelling regions, i.e., wind-forced vortices. Steepening and strengthening of vortices are provided by the nonlinear terms. When forcing is time-varying, the advection terms will also redistribute the vorticity. The wind reversals will separate the vortices from the ice edge, so that the upwelling enhancements are pushed to the open ocean and the downwelling enhancement are pushed underneath the ice.