Uniform Asymptotic Approximation for Viscous Fluid Flow Down an Inclined Plane.

Abstract

An asymptotic method is developed for the linearized Navier-Stokes equations governing the time-dependent motion of a viscous fluid flow down an inclined plane. A diffusion equation for the first order approximation of the fluid surface elevation in a perturbation scheme is derived and a critical Reynolds number is defined based upon the well-posedness of the equation. Under a set of sufficient conditions it is shown that the solution of the diffusion equation is a uniform asymptotic approximation to the generalized solution of the full equations for all time by means of various (L sub 2) and pointwise estimates.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1974
Accession Number
ADA003701

Entities

People

  • Meichang Shen
  • S. M. Shih

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Diffusion
  • Elevation
  • Equations
  • Flow
  • Fluid Flow
  • Mathematics
  • Navier Stokes Equations
  • Perturbations
  • Reynolds Number

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)