Nonlinear Interaction of Waves in a Two-Layer Density Stratified Fluid

This monograph presents selected analytical and direct simulation techniques for the problem of nonlinear wave interaction in a two-layer density stratified fluid. These techniques are specifically used to solve nonlinear wave-bottom and wave-wave interaction problems. In the first part of this book, a detailed analysis of the interaction of surface and interfacial waves with bottom topography, the so called Bragg resonance, is discussed. Second and third order resonances (triad and quartet) are considered and analytical results are obtained by perturbation techniques. A powerful spectral-based phase-resolved direct simulation scheme is also formulated, which is well suited for simulations over long spatial ranges as well as for taking into account high orders of nonlinearity. The book's second part discusses wave generation and propagation by a moving disturbance in stratified fluids. Techniques from the first part are used to demonstrate how stratification and nonlinearity can contribute to a significantly different surface/interface wave pattern about the disturbance. Presented techniques and results are of particular interest to ocean and coastal scientists and engineers.