Transition to Turbulence in Plane Poiseuille and Plane Couette Flow,

Abstract

Direct numerical solutions of the three-dimensional time-dependent Navier-Stokes equations are presented for the evolution fo three-dimensional finite-amplitude disturbances of plane Poiseuille and plane Couette flows. Spectral methods using Fourier series and Chebyshev polynomial series are used. It is found that plane Poiseuille flow can sustain neutrally stable two-dimensional finite-amplitude disturbances at Reynolds numbers larger than about 2800. No neutrally stable two-dimensional finite amplitude disturbances of plane Couette flow were found. Three-dimensional disturbances are shown to have a strongly destabilizing effect. It is shown that finite-amplitude disturbances can drive transition to turbulence in both plane Poiseuille flow and plane Couette flow at Reynolds numbers of order 1000. Details of the resulting flow fields are presented. It is also shown that plane Poiseuille flow can not sustain turbulence at Reynolds numbers below 500.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1978
Accession Number
ADA148554

Entities

People

  • L. C. Kells
  • S. A. Orszag

Tags

DTIC Thesaurus Topics

  • Boundary Layer
  • Channel Flow
  • Chebyshev Polynomials
  • Computational Fluid Dynamics
  • Computational Science
  • Couette Flow
  • Fluid Dynamics
  • Fluid Mechanics
  • Hydrodynamics
  • Navier Stokes Equations
  • Poiseuille Flow
  • Reynolds Number
  • Standing Waves
  • Stratified Fluids
  • Three Dimensional
  • Turbulent Flow
  • Two Dimensional

Fields of Study

  • Physics

Readers

  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Fluid Dynamics.