Feasible domain of Walker's unsteady wall-layer model for the velocity profile in turbulent flows

The present work studies, in detail, the unsteady wall-layer model of Walker et al. (1989, AIAA J., 27, 140 – 149) for the velocity profile in turbulent flows. Two new terms are included in the transcendental non-linear system of equations that is used to determine the three main model parameters. The mathematical and physical feasible domains of the model are determined as a function of the non-dimensional pressure gradient parameter (p⁺). An explicit parameterization is presented for the average period between bursts (), the origin of time () and the integration constant of the time dependent equation (A₀) in terms of p⁺. In the present procedure, all working systems of differential equations are transformed, resulting in a very fast computational procedure that can be used to develop real-time flow simulators.

law of the wall; turbulent boundary layer; unsteady model; feasible domain; asymptotic theory