Abstract

D.V. Strunin and A.J. Roberts

We study an expansion of a turbulent layer generated by a steep initial velocity profile occurring in a narrow zone. Of interest to us is asymptotic dynamics of the layer at large times when the layer is much wider than its initial size. Dimensional analysis reveals possible self-similar forms of distributions of the turbulent energy and average velocity across the layer. By applying the k-l model of fully developed turbulence we prove numerically that the turbulent layer indeed exhibits self-similar dynamics. At all times the turbulent area has a sharp boundary (the layer persists) which is well resolved by a numerical scheme. Using computer algebra we derive useful analytical approximations of a solution. We also consider a situation where the turbulent layer develops in a channel and, after reaching its boundaries, eventually becomes steady-state. We demonstrate that the k-l model results in reasonable solutions satisfying no-slip conditions on channel bottom.

Full Paper (Size: 224 KB)