In this study, the interactions between an offshore wind farm, upper-ocean currents, and stratification are examined under shallow water conditions from a two-dimensional modeling standpoint. The modeling results from two numerical simulation runs provide new insights on the formation of downwind vortex streets and the adjustment of coastal processes, such as upwelling and stratification. The distorted farm-induced wind deficits are calculated by the concept of single- and multiple-wake models. By assuming farm geometry as a large rigid rectangle, the numerical results of a shallow water model demonstrate the formation of vortex shedding wakes in the downwind of the wind farm. The slice model simulation runs, as the second numerical experiment, will address the coastal upwelling and geostrophic adjustment of density fronts in the presence of wind farm effects over a sloping bathymetry. We apply gravity wave effects using a wave-dependent aerodynamic roughness length when assuming the wind farm as an array of multiple turbines. Despite dynamical differences between simulation runs assuming farm as a rigid element and those considering farm as a cluster of single turbines, the results show some aspects of the farm-induced modulations on the pycnocline displacements and on the spatial-temporal evolution of the coastal upwelling. Although each simulation run has a unique scientific focus, the overall achieved numerical results are greatly able to improve the understanding of physical coupling between the wind farms and upper ocean dynamical processes.