A KINETIC (NON-LINEAR) THEORY OF TURBULENCE IN INCOMPRESSIBLE FLUIDS

Abstract

In principle, a turbulence field is to be governed by the Navier- Stokes equations. In order to avoid the difficulty of treatment due to the non- linear characteristics of the Navier-Stokes equations, one begins with the assumption that a turbulence field may be represented by a proper distribution of many elementary vortex lines, each of which, being a particular solution of the Navier-Stokes equations, exhibits full characteristics of the non-linear equations. Based on this assumption, an equation is introduced which governs the distribution of those elementary vortex lines, in the same way as the Liouville equation governs the distribution of particles. With respect to a two-dimensional field, it is shown that Taylor's parabolic correlation mode for short distances and Kolmogoroff's 2/3-power correlation mode for moderate distances are unified to one correlation mode which is valid for the entire range of correlation distances. With respect to three-dimensional cases, introducing remarks are given. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 1968
Accession Number
AD0671835

Entities

People

  • Toyoki Koga

Organizations

  • New York University Tandon School of Engineering

Tags

Communities of Interest

  • Energy and Power Technologies
  • Space

DTIC Thesaurus Topics

  • Applied Mechanics
  • Boundary Layer
  • Equations
  • Flow Fields
  • Fluid Mechanics
  • Geometry
  • Hilsch Tubes
  • Kinetic Theory
  • Liouville Equation
  • Mechanics
  • Navier Stokes Equations
  • Particles
  • Probability
  • Probability Distributions
  • Three Dimensional
  • Turbulent Flow
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Fluid Mechanics and Fluid Dynamics.