An Exponential Decay Estimate for the Stationary Perturbation of Poiseuille Flow.

Abstract

The author proves a decay estimate for the steady state incompressible Navier-Stokes equations. The estimate describes the exponential decay, in the axial direction of a semi-infinite tube, for an energy-type functional in terms of the perturbation of Poiseuille flow, provided that the Reynolds number does not exceed a critical value, for which we exhibit a lower and an upper bound. Since the motion is considered axi-symmetric we use a stream function formulation, and the results are similar to those obtained by Horgan for a two-dimensional channel flow problem. For the Stokes problem our estimate for the rate of decay is a lower bound to the actual rate of decay which is obtained from an asymptotic solution to the Stokes equations.

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Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1987
Accession Number
ADA193480

Entities

People

  • Gerardo A. Ache

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Dead Reckoning
  • Differential Equations
  • Elastic Properties
  • Equations
  • Flow
  • Incompressible Flow
  • Mechanics
  • Military Research
  • Navier Stokes Equations
  • Partial Differential Equations
  • Perturbations
  • Poiseuille Flow
  • Reynolds Number
  • Stationary
  • Steady State
  • Three Dimensional
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Approximation Theory.
  • Fluid Mechanics and Fluid Dynamics.
  • Operations Research