On the unsteady similarity equations for the flow above a rotating disc in a rotating fluid

The unsteady similarity equations for a large rotating disc immersed in an otherwise unbounded rigidly rotating incompressible fluid are investigated for several values of the parameter a, where a denotes the ratio of the angular velocity of the disc to that of the rigidly rotating fluid above it. Numerical computations for a =- 0- 5,-0-25,-0-20,- 0 1 5 and- 0 1 0 show that the appropriate steady-state solutions are not obtained even though they are known to exist. For a<—0-15 the computations break down for a finite value of fit * with all the velocity components as well as the displacement thickness becoming unbounded. However, for a = —0-10 and —0-15 a limit cycle solution is obtained. The results indicate that the steady-state similarity solutions are physically unacceptable for a«—0-10 since they cannot be reached via a time-dependent process. Further it is deduced that the concept of a rotating core of fluid with a thin unsteady boundary layer is destroyed and we can expect that thereafter the core flow must be modified in a serious way. 1