Near the vicinity of 30 latitude, the coincidence of the period of sea breeze and the inertial period of the ocean leads to a maximum near-inertial ocean response to sea breeze. This produces a propagating inertial internal (Poincare) wave response that transfers energy laterally away from the coast and provides significant vertical mixing. In this paper, the latitudinal dependence of this wave propagation and its associated vertical mixing are investigated primarily using a nonlinear numerical ocean model. Three-dimensional idealized simulations show that the coastal oceanic response to sea breeze is trapped poleward of 30 latitude; however, it can propagate offshore as Poincare waves equatorward of 30 latitude. Near 30 latitude, the maximum oceanic response to sea breeze moves offshore slowly because of the near-zero group speed of Poincare waves at this latitude. The lateral energy flux convergence plus the energy input from the wind is maximum near the critical latitude, leading to increased local dissipation by vertical mixing. This local dissipation is greatly reduced at other latitudes. The implications of these results for the Gulf of Mexico (GOM) at 30N is considered. Simulations with realistic bathymetry of the GOM confirm that a basinwide ocean response to coastal sea-breeze forcing is established in form of Poincare waves. Enhanced vertical mixing by the sea breeze is shown on the model northern shelf, consistent with observations on the TexasLouisiana shelf. Comparison of the three-dimensional and one-dimensional models shows some significant limitations of one-dimensional simplified models for sea-breeze simulations near the critical latitude.