When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic pressure balance. In this thesis we discuss the internal Poincare waves and Kelvin waves in a rotating, continuously stratified, flat-bottom, circular lake with fully nonlinear and non-hydrostatic effects. An analytical solution is derived for the linearized system and it provides initial conditions used in the MIT General Circulation Model (MITgcm). This model is chosen due to its non-hydrostatic capability. Both Poincare waves and Kelvin waves are considered. The analytical solution of the linear system is verified numerically when the wave amplitude is small. As the wave amplitude increases the waves become more nonlinear. Poincare waves steepen and generate solitary-like waves with shorter wavelengths, but most of the energy contained in these waves is transferred back and forth between the parent wave and the solitary-like waves. Kelvin waves, on the other hand, steepen and lose their energy to solitary-like waves. The appearance of the solitary-like waves is not absolutely clear and higher resolution is required to clear up the details of this process. This conclusion agrees with de la Fuente et al (2008) who discussed the internal waves in a two-layer model. Moreover, in the Kelvin waves case, unexpected small waves are generated at the side boundaries and travel inwards. The wave amplitude and wavelength of these spurious waves become smaller as the horizontal resolution increases. One possible reason to explain these waves is the use of square grids to approximate the circular lake.

When wind blows over a stratified lake an interface tilt is often generated, and internal waves usually appear after the wind stops. Internal waves in lakes are studied in many literatures, but most assume a hydrostatic pressure balance. In this thesis we discuss the internal Poincare waves and Kelvin waves in a rotating, continuously stratified, flat-bottom, circular lake with fully nonlinear and non-hydrostatic effects. An analytical solution is derived for the linearized system and it provides initial conditions used in the MIT General Circulation Model (MITgcm). This model is chosen due to its non-hydrostatic capability. Both Poincare waves and Kelvin waves are considered. The analytical solution of the linear system is verified numerically when the wave amplitude is small. As the wave amplitude increases the waves become more nonlinear. Poincare waves steepen and generate solitary-like waves with shorter wavelengths, but most of the energy contained in these waves is transferred back and forth between the parent wave and the solitary-like waves. Kelvin waves, on the other hand, steepen and lose their energy to solitary-like waves. The appearance of the solitary-like waves is not absolutely clear and higher resolution is required to clear up the details of this process. This conclusion agrees with de la Fuente et al (2008) who discussed the internal waves in a two-layer model. Moreover, in the Kelvin waves case, unexpected small waves are generated at the side boundaries and travel inwards. The wave amplitude and wavelength of these spurious waves become smaller as the horizontal resolution increases. One possible reason to explain these waves is the use of square grids to approximate the circular lake.

The spatial structure and temporal evolution of sea breeze and the latitudinal distribution of propagation and mixing of sea breeze driven near-inertial ocean response in the Gulf of Mexico are investigated using comprehensive data sets and a non-linear numerical model. Near 30�N, inertial oceanic response is significantly enhanced by a near-resonant condition between inertial and diurnal forcing frequencies. Observational results indicate that sea breeze variability peaks in summer and extends at least 300 km offshore with continuous seaward phase propagation. The maximum near-inertial oceanic response occurs in June when there is a shallow mixed layer, strong stratification, and an approximately 10-day period of continuous sea breeze forcing. Near-inertial current variance decreases in July and August due to the deepening of the mixed layer and a more variable phase relationship between the wind and current. River discharge varies interannually and can significantly alter the oceanic response during summer. During 1993, the ?great flood? of the Mississippi River deepens the summer mixed layer and reduces the sea breeze response. The near-inertial currents can provide considerable vertical mixing on the shelf in summer, as seen by the suppression of bulk Richardson number during strong near-inertial events. 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 vertical mixing. This local dissipation is greatly reduced at other latitudes. Simulations with realistic bathymetry of the Gulf of Mexico confirm that a basin-wide ocean response to coastal sea breeze forcing is established in the form of Poincare waves. This enhanced vertical mixing is consistent with observations on the Texas-Louisiana 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.