On the Turbulent Far-Wake in Incompressible Axi-Symmetric Flow

Abstract

The arguments that lead to the x(expn (1/3)) dependence of wake width and the x(expn (-2/3)) dependence of axial velocity on axial distance in the far turbulent wake are reviewed. Assuming similarity of mean velocity profiles, the dominant terms in the Navier-Stokes equations for turbulent wake flow are used to derive these profiles with the help of Boussinesq's and Prandtl's hypotheses. The resulting profile has the same form as in the better known two-dimensional case. It is compared with an assumed Gaussian profile and both are compared with the Gaussian profile that results in the corresponding laminar case. The form of the eddy viscosity is also obtained in the two cases: for the former it is zero on the axis and rises to a maximum before falling to zero again on the wake boundary; whereas for a Gaussian profile it is constant across a cross section of the turbulent wake. In addition, the eddy viscosity has an x(expn (-1/3)) dependence in both cases, which is absent in the two-dimensional wake.

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Document Details

Document Type
Technical Report
Publication Date
Nov 10, 1961
Accession Number
AD0266943

Entities

People

  • A. W. Kenneth Metzner

Organizations

  • Massachusetts Institute of Technology

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Layer
  • Cartesian Coordinates
  • Computational Fluid Dynamics
  • Equations
  • Flow
  • Fluid Dynamics
  • Fluid Mechanics
  • Lepidoptera
  • Mechanical Properties
  • Mechanics
  • Navier Stokes Equations
  • Pressure Distribution
  • Reynolds Number
  • Steady Flow
  • Turbulence
  • Viscosity

Fields of Study

  • Physics

Readers

  • Fluid Dynamics.
  • Fluid Mechanics and Fluid Dynamics.