ON THE STABILITY OF AXISYMMETRICAL FLOWS

Abstract

The stability equation of an axisymmetrical flow of an incompressible fluid subjected to rotationally-symmetric disturbances is derived and studied. It is shown that the axisymmetrical flow is always stable with respect to disturbances of the tangential velocity component. Hence, the stability equation for axisymmetrical disturbance is then investigated in detail for arbitrary basic velocity profiles. It was found that the stability of an axisymmetrical flow may be reduced approximately to the corresponding problem of two-dimensional flow by proper transformations. The comparison of stability of an axisymmetrical flow with that of a corresponding two-dimensional flow is discussed according to an equivalent principle. It is found that the minimum critical Reynolds number of an axisymmetrical wake, or jet, is of the same order of magnitude as that of a two-dimensional boundary layer flow which is much higher than the value for a two-dimensional wake, or jet.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1962
Accession Number
AD0286028

Entities

People

  • S. I. Pai

Organizations

  • General Electric

Tags

Communities of Interest

  • Air Platforms
  • Space
  • Weapons Technologies

DTIC Thesaurus Topics

  • Air Force
  • Analytic Functions
  • Boundary Layer
  • Boundary Layer Flow
  • Boundary Value Problems
  • Couette Flow
  • Differential Equations
  • Equations
  • Flow
  • Flow Fields
  • Fluid Dynamics
  • Government Procurement
  • Poiseuille Flow
  • Reynolds Number
  • Space Sciences
  • Two Dimensional
  • Two Dimensional Flow

Fields of Study

  • Physics

Readers

  • Fluid Dynamics.