Effects of uniform suction on the stability of flow on a rotating disc

Abstract

The effects of uniform distributed suction on the cross-flow instability of the boundary layer on a rotating disc are considered. A vorticity-velocity formulation is used to obtain exact linear equations governing the development of infinitesimal disturbances to the steady flow on a rotating disc. A parallel flow approximation is made as a first step in determining the effect of suction on the instability. It is shown that suction has a stabilizing effect on the flow, whereas blowing is destabilizing. Small values of the suction parameter are found to increase significantly the critical Reynolds number associated with stationary modes of disturbance. The wave angle of the spiral vortices that precede turbulent flow is estimated from critical conditions and is shown to decrease with increase in suction rate. This is shown to be consistent with prediction based on an in viscid analysis. The corresponding estimate of the expected number of vortices is shown to increase with suction. Suction appears to make the second minimum on the neutral curve more pronounced, suggesting a possible increase in the relative importance of the associated low wavenumber mode of disturbance.