On the mathematical modeling of the Reynolds stress's equations
Abstract
By considering the Reynolds stress equations as a possible descriptor of complex turbulent fields, pressurevelocity interaction and turbulence dissipation are studied as two of the main physical contributions to Reynolds stress balancing in turbulent flow fields. It is proven that the pressure interaction term contains turbulence generation elements. However, the usual 'return to isotropy' element appears more weakly than in the standard models. In addition, convectionlike elements are discovered mathematically, but there is no mathematical evidence that the pressure fluctuations contribute to the turbulent transport mechanism. Calculations of some simple onedimensional fields indicate that this extra convection, rather than the turbulent transport, is needed mathematically. Similarly, an expression for the turbulence dissipation is developed. The end result is a dynamic equation for the dissipation tensor which is based on the tensorial length scales.
 Publication:

AIAA, Aerospace Sciences Meeting
 Pub Date:
 January 1990
 Bibcode:
 1990aiaa.meetQR...L
 Keywords:

 Computational Fluid Dynamics;
 Reynolds Equation;
 Reynolds Stress;
 Turbulence Models;
 Turbulent Flow;
 Computational Grids;
 Continuity Equation;
 Green'S Functions;
 NavierStokes Equation;
 Shear Flow;
 Fluid Mechanics and Heat Transfer