Effect of normal blowing on the hydrodynamic flow between two differentially rotating infinite disks (Q1082968)

The effect of normal blowing on the linear, steady, axisymmetric flow of a homogeneous fluid confined between two differentially rotating infinite disks is investigated using asymptotic methods of analyses. For \(E^{1/2}\ll R\ll E^{1/3}\), where E is the Ekman number and R is the injection Rossby number, the suction boundary layer at the top disk is a modified Ekman layer while the injection boundary layer at the bottom disk loses its Ekman structure and becomes weakly viscous. The motion in the injection layer decays on a larger length scale, \(Z=O(R^ 3/E)\), but it oscillates on a smaller length scale, \(Z=O(R)\). Multiple length scale procedure is used to analyze the dynamics of injection layer. In addition to the steady state problem the transient problem is also discussed and the spin-up time is derived.