Author:
CHOI WOOYOUNG,CAMASSA ROBERTO
Abstract
Model equations that govern the evolution of internal gravity waves at the interface
of two immiscible inviscid fluids are derived. These models follow from the original
Euler equations under the sole assumption that the waves are long compared to the
undisturbed thickness of one of the fluid layers. No smallness assumption on the
wave amplitude is made. Both shallow and deep water configurations are considered,
depending on whether the waves are assumed to be long with respect to the total
undisturbed thickness of the fluids or long with respect to just one of the two
layers, respectively. The removal of the traditional weak nonlinearity assumption is
aimed at improving the agreement with the dynamics of Euler equations for large-amplitude waves. This is obtained without compromising much of the simplicity
of the previously known weakly nonlinear models. Compared to these, the fully
nonlinear models' most prominent feature is the presence of additional nonlinear
dispersive terms, which coexist with the typical linear dispersive terms of the weakly
nonlinear models. The fully nonlinear models contain the Korteweg–de Vries (KdV)
equation and the Intermediate Long Wave (ILW) equation, for shallow and deep
water configurations respectively, as special cases in the limit of weak nonlinearity
and unidirectional wave propagation. In particular, for a solitary wave of given
amplitude, the new models show that the characteristic wavelength is larger and
the wave speed is smaller than their counterparts for solitary wave solutions of the
weakly nonlinear equations. These features are compared and found in overall good
agreement with available experimental data for solitary waves of large amplitude in
two-fluid systems.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
357 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献