Oscillatory model for wall-bounded turbulence

A three-dimensional oscillatory model is proposed to represent the main features of the transition from laminar to turbulent flow and of turbulent flow along a wall. The model is based on the Strouhal law f = U/2pi(delta), giving the frequency f of periodic perturbations within the boundary layer as a function of the boundary layer thickness delta and of the outer velocity U. The validity of this law for the main boundary-layer features is proved. Experimental evidence suggests the presence of a traveling wave and an associated standing wave, both of length lambda = 2pi(delta), by which bursting activity is controlled and coherent turbulent structures are shaped and timed. Other waves at wall appear to account for the production, spacing and length of viscous-sublayer longitudinal streaks. The model provides means for a quantum mechanics approach to turbulent motion. This is shown through an example in which the turbulent energy spectrum is obtained by deterministic considerations.