Relations Between Solutions of the Navier-Stokes Equations and of the Boundary Layer Equation,

Abstract

The relations between solutions of the full Navier-Stokes equations and of the boundary layer equations are explored by a discussion of the eigensolutions of a model equation which retains the essential features of the problem. Important are the following results. The system of eigensolutions for the full Navier-Stokes equations is not well suited to represent numerically the concentration of vorticity occurring in the boundary layer. Restriction of the viscosity effect to a layer close to the wall is therefore desirable from a numerical point of view. With this provision the boundary layer equation, including a subsequent correction for its displacement thickness, reproduces perturbations of the Navier-Stokes equations which correspond to potential flow solutions (with wall corrections) and to vorticity effects propagating downstream. The Navier-Stokes equations allow for effects propagating upstream; they are confined to a narrow layer close to the wall within the boundary layer and die out very quickly. In the vicinity of a separation point these solutions gain greater importance. (Author)

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1973
Accession Number
AD0773183

Entities

People

  • Karl G. Guderley
  • Shih-liang Wen

Tags

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Displacement
  • Equations
  • Flow
  • Layers
  • Mathematics
  • Navier Stokes Equations
  • Perturbations
  • Potential Flow
  • Thickness
  • Viscosity

Fields of Study

  • Physics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Fluid Mechanics and Fluid Dynamics.