Investigation on internal solitary waves breaking for geophysical applications

Nonlinear internal waves are a spectacular phenomenon taking place in many parts of the world ocean. They consist in oscillations that travel along the pycnocline, i.e., the portion of the water column separating the surface layer from relatively more dense underlying fluid. They are mostly generated by the interaction between tidal flow and bottom topography features, such as underwater sills and the continental shelf. Nonlinear internal waves can take the shape of a special waveform called internal solitary wave (ISW), a class of nonsinusoidal waves that has the ability to retain its form over long distances and extended periods of time. In the present work, we investigate the propagation, shoaling and breaking of ISWs in a two–layer stratified fluid system through analytical and numerical methods. We study the propagation of ISWs over a varying bathymetry through variable coefficients KdV–type equations, which are widely used to model weakly–nonlinear waves in the oceanic context. We study the shoaling and breaking of ISWs along a sloping bathymetry, and we build an anaytical model to derive the ISWs breaking location. Theoretical results are validated by laboratory experiments performed in a wave tank. We then apply KdV–type equations to describe both numerically and analitically the evolution of ISWs generated in the Messina Strait (Mediterranean Sea) propagating northward, towards the frontal slope of a headland, i.e., Capo Vaticano. Finally, we apply our wave–breaking model to predict breaking location of ISWs along this frontal slope. We also focus on the mixing process induced by the ISWs breaking, defining the potential energy, the background potential energy and the available potential energy (APE) of an ISW in a two–layer fluid. Through the Thorpe and Ozmidov length scales we build a theoretical model to predict the values of mixing efficiency involved in ISWs breaking and we validate the model through laboratory experiments.