Coherence and chaos in a model of turbulent boundary layer

The dynamics of coherent structures in the wall region of a turbulent channel flow is considered. The Karhunen–Loève eigenfunctions and Galerkin procedure are used to derive the dynamical description. In a previous treatment of this problem by Aubry et al. [J. Fluid Mech. 192, 115 (1988)] the analysis required an inhomogeneous pressure term to be supplied from outside the theory. In the first part of this paper this theory is reconsidered on the basis of the construction of wall eigenfunctions that have a full channel validity. As a result of the methods developed here, a well-posed Hermitian theory is developed and convergence questions do not arise. Among a number of important consequences is the fact that no exterior pressure is required by the present theory. In the second part of this paper it is shown that the behavior of the resulting model equations include intermittency, quasiperiodic, and chaotic solutions. In the final part of this paper three-dimensional effects are introduced into the dynamics in order to produce a physically more realistic dynamical theory. It is felt that the bursting and ejection events in turbulent boundary layers is given a more satisfactory explanation within this framework.