Title: Dynamical systems theory and extra rates of strain in turbulent flows
Abstract: Peter Bradshaw has shed considerable light on turbulent flows with extra rates of strain. Here we apply a different approach to two of the flows that Bradshaw studied. We begin with a brief introduction reminding the reader of our application of dynamical systems theory to the flat-plate boundary layer. There we constructed a low-dimensional model that simulated the bursting in the boundary layer, in qualitative agreement with experiment. The bursting frequency responded to modeled polymer additives and flow accelerations by decreasing, resulting in a decreased skin friction, in agreement with experiment. Now we consider the application of this same technique to incompressible turbulent shear flows with streamline curvature in the direction of the mean flow, and to such flows with a transverse strain rate. We show qualitatively how the additional physical effects in these two flows will result in a changed rate of bursting, which will result in a change in the skin friction, likewise in agreement with experiment.