A local closure condition for developed turbulent shear flows
Abstract
Instead of momentum, heat, or material transport equations for the characteristic turbulence parameters, in the present work vorticity transport equations are used for obtaining a closed system of equations for developed turbulent shear flows. This approach is taken for steady, rectilinear, planar shear layers with boundary layer characteristics, for an incompressible, isothermal, Newtonian medium. The vorticity transport equation is obtained by applying the rotation operator to the NavierStokes equations with time averaging and boundary layer simplification. Local turbulence structure is then characterized by a local turbulence Reynolds number and local ratios of relevant vorticity viscosities and characteristic lengths. The equations can be closed by empirically determined relations between these parameters. This is illustrated for the case of turbulent Couette flow.
 Publication:

Zeitschrift Angewandte Mathematik und Mechanik
 Pub Date:
 October 1976
 DOI:
 10.1002/zamm.19760561008
 Bibcode:
 1976ZaMM...56..415H
 Keywords:

 Closure Law;
 Shear Flow;
 Turbulent Flow;
 Vorticity Equations;
 Vorticity Transport Hypothesis;
 Couette Flow;
 Incompressible Fluids;
 Isothermal Flow;
 Steady Flow;
 Transport Properties;
 Fluid Mechanics and Heat Transfer