The unsteady laminar boundary layer on a rotating disk in a counter-rotating fluid

Abstract

The growth of the unsteady boundary layer on an infinite rotating disk in a counter-rotating fluid is examined numerically and analytically. The numerical computations indicate that the boundary layer breaks down when ωt* ≈ 2·36 in a novel way: the displacement thickness, as well as all the velocity components, becomes infinite. This numerical solution is fitted to an asymptotic expansion which contains the singularities found in the numerical integrations, and it is concluded that the solution of the unsteady similarity equations does break down at a finite time as the numerical results indicate. This problem is placed in a physically more realistic context by considering numerically the unsteady boundary layer which develops on a finite rotating disk in a counter-rotating fluid. It is found that the breakdown of the solution occurs at the axis at the same time, and thus the concept of a thin boundary layer in this more realistic problem is also destroyed in a finite time.