Premium
The Interaction of a Strong Bore with Small Disturbances in Shallow Water
Author(s) -
Yu J.,
Kevorkian J.
Publication year - 1994
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm1994913247
Subject(s) - froude number , disturbance (geology) , amplitude , waves and shallow water , trajectory , nonlinear system , mechanics , mathematics , work (physics) , mathematical analysis , physics , geology , flow (mathematics) , optics , thermodynamics , paleontology , quantum mechanics , astronomy
This paper gives an extension of previous work [2] on weakly nonlinear shallow water waves over a variable bottom to include the effects of strong bores and small surface disturbances. We first consider the interaction of a strong bore with quiescent water over an isolated bottom disturbance to highlight some of the modifications that are introduced in our results for both noncritical and transcritical Froude numbers. We also exhibit the secular effect on the bore trajectory of a bottom disturbance that has a nonzero average. In a second example, we consider the interaction of a strong bore with a small amplitude periodic surface disturbance upstream. We show that downstream of the bore, the wave length of this disturbance increases, whereas its amplitude increases (decreases) depending on whether the bore speed is larger (smaller) than a critical value. We also use this example to illustrate the derivation of the solution and bore trajectory to second order accuracy. All our asymptotic results, obtained in the form of multiple scale expansions, are compared with numerical solutions for a number of illustrative cases.