On nonlinear transient free-surface flows over a bottom obstruction

Publisher Website
Google Scholar
Abstract
A fully nonlinear integral-equation model based on the potential theory is used to study transient free-surface flow induced by a bump moving along a flat bottom. Comparison is made between the large-time solution of the transient model and the fully nonlinear steady-state solution in Zhang and Zhu [J. Eng. Math. 30, 487 (1996)] for both subcritical and supercritical flows, and asymptotic agreement between the two is observed. For the transcritical flow, some features associated with the resonant flow motion previously found by approximate theories are confirmed. A diagram of the parameter space is presented showing the regions of different solution categories including wave breaking. Through this diagram, a discrepancy between two previous steady-state models can now be clearly explained. Interestingly, the dividing line separating those solutions with or without wave breaking levels out asymptotically for very large Froude numbers, indicating that there is a limiting dimension of the bump, beyond which physically meaningful steady-state solutions do not exist, although they may well be obtained mathematically.

This publication has 18 references indexed in Scilit: