Rotating disk with uniform suction in streaming flow

We investigate the flow as it occurs above a single rotating disk when uniform suction is applied at the disk surface. It has been demonstrated by others that at zero suction repeated branching of the solution occurs as the parameter s is varied, where s is the ratio of the angular velocity of the fluid at infinity to the angular velocity of the disk. We show multiplicity of solution also at −0·82⩽α⩽1·15, where α is the suction parameter; for large absolute values of α the solution fails to turn back on itself and we obtain only the von Karman solution. We then generalize the von Karman solution for flow above a single rotating disk with uniform suction to include non‐axisymmetric solutions due to streaming at infinity. These solutions are continuous in an arbitrary parameter, the streaming velocity at infinity; for zero value of this parameter the asymmetric flow degenerates into the classical von Karman flow. Thus the classical solution is never isolated when considered within the framework of the Navier–Stokes equations: there are asymmetric solutions in every neighbourhood of the von Karman solution.