NOTE ON A HETEROGENEOUS SHEAR FLOW,

Abstract

Goldstein has considered the stability of a shear layer within which the velocity and the density vary linearly and outside which they are constant. Rayleigh had found that the corresponding, homogeneous shear flow is unstable in and only in a finite band of wave-numbers. Goldstein concluded that a small density gradient renders the flow unstable for all wave-numbers. This conclusion appears to depend on the acceptance of all possible branches of a multi-valued eigenvalue equation, and it is shown that the principal branch of this eigenvalue equation yields one and only one unstable mode if and only if the wavenumber lies in a band that decreases from Rayleigh's band to zero as the Richardson number increases from 0 to 1/4. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 26, 1964
Accession Number
AD0613123

Entities

People

  • John W. Miles

Organizations

  • Australian National University

Tags

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Eigenvalues
  • Equations
  • Flow
  • Fluid Dynamics
  • Fluid Mechanics
  • Mechanics
  • Richardson Number
  • Shear Flow
  • Turbulent Mixing

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Fluid Dynamics.