On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layer

Abstract

In this paper we establish some rigorous connections between the dynamics of coherent structures in the wall region of the turbulent boundary layer and the low-dimensional models of the type studied by Aubry et al. (1988). An important first step is to determine what sort of connection is feasible. We choose to study the energy budget of the models in comparison with the energy budget of the real flow. This is done by comparing the respective kinetic energy equations. In the process we reexamine some of the assumptions and approximations of Aubry et al. (1988) and perform order of magnitude analyses to determine when they hold. We find that, for the models developed in that paper, involving modes which do not vary in the streamwise direction, the energy production lies within positive, experimentally determined, bounds. Moreover, the dissipation due to neglected modes may be reproduced correctly with an order 1 value of the Heisenberg parameter α, as assumed by Aubry et al.