Internal Solitons Generated by Moving Disturbances

Citation

Zhu, Jinlin (1986) Internal Solitons Generated by Moving Disturbances. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/pspg-vp83. https://resolver.caltech.edu/CaltechETD:etd-03122008-080220

Abstract

A new phenomenon of the generation of internal solitons is investigated in this thesis by applying theoretical models and is observed in both numerical and experimental results. By imposing an external disturbance, such as a top surface pressure or a bottom bump, that moves with a constant velocity within a trans critical range after an impulsive start from rest, upon a two-layered or a continuously stratified fluid system, a series of solitons are generated, one after another periodically, each surging ahead of the disturbance in turn. Two theoretical models, belonging to the generalized Boussinesq class, are developed to investigate the generation of weakly nonlinear and weakly dispersive long waves and their evolution in an inviscid, immiscible, and incompressible stratified fluid system under the forcing of the external disturbances. The top surface may be either free or covered by a rigid horizontal plate. For the generalized Boussinesq class for two-layered fluid systems, we have derived the FOUR-equation model for the free top-surface case and the THREE-equation model for the rigid horizontal top-surface case; these are extensions of the one-layer homogeneous fluid system previously considered by Wu (1979). For primarily unidirectional motions a forced KdV equation is obtained which represents each normal mode of a two-layer system or a continuously stratified fluid system. Numerical schemes have been successfully developed to solve these equations. Experiments were performed to investigate this phenomenon,henomenon using fresh water to form the upper layer and brine the lower layer. The relationship between the main properties (the amplitude and the period of generation) of the generated solitons and the forcing function configurations is discussed along with comparisons of theoretical, numerical and experimental results. Qualitatively all the results are consistent in exhibiting the salient features of the resulting motion. Quantitatively the numerical results based on the continuously stratified fluid model seem to be more satisfactory than those given by the two-layered fluid model in comparison with the present experiments. The discrepancy between the theory and experiment is supposedly due to the viscous effects, which will be left for future work.

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