Turbulent solution of the NavierStokes equations for uniform shear flow
Abstract
To study the nonlinear physics of uniform turbulent shear flow, the unaveraged NavierStokes equations are solved numerically. This extends our previous work in which mean gradients were absent. For initial conditions, modified threedimensionalcosine velocity fluctuations are used. The boundary conditions are modified periodic conditions on a stationary threedimensional numerical grid. A uniform mean shear is superimposed on the initial and boundary conditions. The three components of the meansquare velocity fluctuations are initially equal for the conditions chosen. As in the case of no shear the initially nonrandom flow develops into an apparently random turbulence at higher Reynolds number. Thus, randomness or turbulence can apparently arise as a consequence of the structure of the NavierStokes equations. Except for an initial period of adjustment, all fluctuating components grow with time. The initial equality of the three intensity components is destroyed by the shear, the transverse components becoming smaller than the longitudinal one, in agreement with experiment. Also, the shear creates a smallscale structure in the turbulence. The nonlinear solutions are compared with linearized ones.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 1981
 Bibcode:
 1981STIN...8232634D
 Keywords:

 Boundary Layer Flow;
 NavierStokes Equation;
 Numerical Analysis;
 Reynolds Number;
 Shear Flow;
 Turbulence;
 Uniform Flow;
 Analysis (Mathematics);
 Boundary Conditions;
 Fluid Flow;
 Problem Solving;
 Reynolds Stress;
 Turbulent Flow;
 Fluid Mechanics and Heat Transfer