Behavior of coherent structures in the wall region by dynamical systems theory

Objective analysis of experimental measurements indicates that there are recurrent streamwise rolls present in the wall region, at least in the quadratic mean sense. Representation theorems permit optimal expansion of the instantaneous velocity field in the wall region in terms of these streamwise rolls. Without involving ourselves in the question of the source of these rolls, we ask how they will behave dynamically. Severely truncating our system, and using Galerkin projection, we obtain a closed set of non-linear ordinary differential equations with ten degrees of freedom. The methods of dynamical systems theory are applied to these equations.