Large-Time Behavior of Viscous Surface Waves.

Abstract

We consider the mathematical behavior of a viscous, incompressible fluid bounded above by an atmosphere of constant pressure and below by a horizontal bottom. After reviewing the existence and regularity theory for the equations governing the motion, we establish rates of decay for solutions near equilibrium. The function describing the height of the free surface decays like 1/square root of t; the velocity field decays like 1/t. These estimates are shown first for the linearization about equilibrium and then for the full nonlinear problem. Complete details will be given elsewhere. Keywords include: viscous incompressible flow, surface waves, free surface.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1985
Accession Number
ADA154805

Entities

People

  • J. T. Beale
  • Toshikazu Nishida

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Classification
  • Contracts
  • Differential Equations
  • Equations
  • Flow
  • Formulas (Mathematics)
  • Incompressible Flow
  • Mathematical Analysis
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Stratified Fluids
  • Surface Waves
  • Theorems
  • United States
  • Universities
  • Waves

Fields of Study

  • Mathematics

Readers

  • Fluid Dynamics.
  • Theoretical Analysis.