On the Smallest Scale for the Incompressible Navier-Stokes Equations.

Abstract

For solutions to the two and three dimensional incompressible Navier Stokes equations the minimum scale is inversely proportional to the square root of the Reynolds number based on the kinematic viscosity and the maximum of the velocity gradients. The bounds on the velocity gradients can be obtained for two dimensional flows, but have to be assumed in three dimensions. Numerical results in two dimensions are given which illustrate and substantiate the features of the proof. Implications of the minimum scale result to the decay rate of the energy spectrum are discussed. Keywords: Navier Stokes equations; Spectral method; Turbulence calculation.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1988
Accession Number
ADA192760

Entities

People

  • H. O. Kreiss
  • L. G. Reyna
  • W. D. Henshaw

Tags

DTIC Thesaurus Topics

  • Computational Fluid Dynamics
  • Computational Science
  • Computations
  • Differential Equations
  • Equations
  • Flow
  • Fluid Dynamics
  • Fourier Series
  • Inequalities
  • Navier Stokes Equations
  • Numbers
  • Simulations
  • Square Roots
  • Three Dimensional
  • Turbulence
  • Two Dimensional
  • Two Dimensional Flow

Fields of Study

  • Physics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)