Comparison of  Turbulence in the RNL and DNS Systems

We have been working on extending S3T to higher Reynolds number flows which requires implementing an approximation in which the restriction on the dynamics of S3T to involve only the nonlinear interaction of the perturbation field with the streamwise mean flow is retained while the infinite ensemble Reynolds stress solution of S3T is approximated by an average in the streamwise direction of the Reynolds stresses of a realization.  If there are sufficient statistically independent structures in the streamwise direction this approximation, referred to as the restricted nonlinear system (RNL), works well.

This animation shows a simulation made using this approximation with its associated DNS.  The similarity in the turbulence obtained implies that the fundamental dynamics of turbulence is retained in this severely restricted dynamical system.  This greatly simplifies our study of the mechanism of turbulence in wall-bounded shear flows.