Abstract

Many interesting free-surface flow problems involve a varying bottom. Examples of such flows include ocean waves propagating over topography, the breaking of waves on a beach, and the free surface of a uniform flow over a localized bump. We present here a formulation for such flows that is general and, from the outset, demonstrates the wave character of the free-surface evolution. The evolut on of the free surface is governed by a system of equations consisting of a nonlinear wave-like partial differential equation coupled to a time-independent linear integral equation. We assume that the free-surface deformation is weakly nonlinear, but make no a priori assumption about the scale or amplitude of the topography. We also extend the formulation to include the effect of mean flows and surface tension. We show how this formulation gives some of the well-known limits for such problems once assumptions about the amplitude and scale of the topography are made.

LanguageEnglish
Pages95-106
Number of pages12
JournalStudies in Applied Mathematics
Volume100
Issue number1
DOIs
StatusPublished - 1 Jan 1998

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Water waves
Water Waves
Topography
Free Surface
Formulation
Free Surface Flow
Nonlinear Waves
Surface Tension
Ocean
System of equations
Linear equation
Integral Equations
Beaches
Partial differential equation
Partial differential equations
Integral equations
Surface tension
Demonstrate

ASJC Scopus subject areas

  • Applied Mathematics

Cite this

A formulation for water waves over topography. / Milewski, Paul A.

In: Studies in Applied Mathematics, Vol. 100, No. 1, 01.01.1998, p. 95-106.

Research output: Contribution to journalArticle

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