The Continuous Spectrum of the Orr-Sommerfeld Equation. Part 1. The Spectrum and the Eigenfunctions

Abstract

It is shown that the Orr-Sommerfeld equation governing the stability of any mean shear flow in an unbounded domain which has finite energy under some Galilean transformation has a continuous spectrum. This result applies to both the temporal and spatial stability problems. Formulae for the location of this continuum in the complex wave speed plane are given. The continuous spectrum and corresponding eigenfunctions are calculated for two samples problems: the Blasius boundary layer and the two-dimensional laminar jet. The nature of the eigenfunctions, which are very different from the Tollmien-Schlichting waves, are discussed. Three mechanisms are proposed by which these continuum modes could cause transition in a shear flow while bypassing the usual linear Tollmien-Schlichting stage.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1976
Accession Number
ADA035381

Entities

People

  • Chester E. Grosch
  • Harold Salwen

Organizations

  • Old Dominion University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Continuous Spectra
  • Cooperation
  • Differential Equations
  • Eigenvectors
  • Equations
  • Flow
  • Layers
  • Mathematics
  • Shear Flow
  • Spectra
  • Transitions
  • Two Dimensional

Readers

  • Fluid Dynamics.
  • Solar Physics