Run-Up and Nonlinear Propagation of Oceanic Internal Waves and Their Interactions

Citation

Lin, Duo-min (1996) Run-Up and Nonlinear Propagation of Oceanic Internal Waves and Their Interactions. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rgkn-4g56. https://resolver.caltech.edu/CaltechETD:etd-12192007-084353

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.

A weakly nonlinear and weakly dispersive oceanic internal long wave (ILW) model, in analogy with the generalized Boussinesq's (gB) model, is developed to investigate generation and propagation of internal waves (IWs) in a system of two-layer fluids. The ILW model can be further derived to give a bidirectional ILW model for facilitating calculations of head-on collisions of nonlinear internal solitary waves (ISWs). The important nonlinear features, such as phase shift of ISWs resulting from nonlinear collision encounters, are presented. The nonlinear processes of reflection and transmission of waves in channels with a slowly varying bottom are studied.

The terminal effects of IWs running up submerged sloping seabed are studied by the ILW model in considerable detail. Explicit solution of the nonlinear equations are obtained for several classes of wave forms, which are taken as the inner solutions and matched, when necessary for achieving uniformly valid results, with the outer solution based on linear theory for the outer region with waves in deep water. Based on the nonlinear analytic solution, two kinds of initial run-up problems can be solved analytically, and the breaking criteria and run-up law for IWs are obtained. The run-up of ISWs along the uniform beach is simulated by numerical computations using a moving boundary technique. The numerical results based on the ILW model are found in good agreement with the run-up law of ISWs when the amplitudes of the ISWs are small.

The ILW model differs from the corresponding KdV model in admitting bidirectional waves simultaneously and conserving mass. This model is applied to analyze the so-called critical depth problem of ISWs propagating across a critical station at which the depths of the two fluid layers are about equal so as to give rise to a critical point of the KdV equation. As the critical point is passed, the KdV model may predict a new upward facing ISW relative to a local mean interface is about to emerge from the effects of disintegrating original downward ISW. This phenomenon has never been observed in our laboratory. Numerical results are presented based on the present ILW model for ISWs climbing up a curved shelf and a sloping plane seabed. It is shown that in the transcritical region, the behaviour of the ISWs predicted by the ILW model depends on the relative importance of two dimensionless parameters, s_w, the order of ISW wave slope, and s, the beach slope. For s >> s_w, the wave profile of ISWs exhibits a smooth transition across the transcritical region; for s <s_w, ISWs emerge with an oscillatory tail after passing across the critical point. Numerical simulations based on the ILW model are found in good agreement with laboratory observations.

Finally, conclusions are drawn from the results obtained in the present study based on the ILW model.

Thesis Files