Nonlinear Gravity-Capillary Waves on a Compressible Viscous Fluid with Edge Constraints.

Abstract

An asymptotic method is developed for the study of gravity-capillary waves in a compressible viscous fluid with edge constraints in an inclined, straight channel. The Navier-Stokes equations subject to free surface and rigid bottom conditions are reduced to a sequence of elliptic boundary problems over a cross section of the channel. Their solutions are used to determine the wave speed and to construct the Burgers equation for the evolution of the gravity-capillary waves. The Burgers equation may become ill-posed when the Reynolds number exceeds some critical value. A criterion for the stability of the flow is then defined in terms of the critical Reynolds number. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1983
Accession Number
ADA130545

Entities

People

  • Meichang Shen

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Asymptotic Series
  • Boundary Value Problems
  • Capillary Waves
  • Equations
  • Equations Of Motion
  • Flow
  • Fluid Flow
  • Mathematics
  • Navier Stokes Equations
  • Reynolds Number
  • Sequences
  • Surface Properties
  • Surface Tension
  • Two Dimensional
  • United States
  • Viscous Flow
  • Wisconsin

Fields of Study

  • Mathematics

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