On the relation between adjacent inviscid cell type solutions to the rotating-disk equations

Abstract

Over a large range of the axial coordinate a typical higher-branch solution of the rotating-disk equations consists of a chain of inviscid cells separated from each other by viscous interlayers. In this paper the leading-order relation between two adjacent cells will be established by matched asymptotic expansions for general values of the parameter appearing in the equations. It is found that the relation between the solutions in the two cells crucially depends on the behaviour of the tangential velocity in the viscous interlayer. The results of the theory are compared with accurate numerical solutions and good agreement is obtained