## Abstract

Periodic disturbances of rigidly rotating inviscid flow of suitable frequency are controlled by a hyperbolic equation (Gortler 1944). In a completely enclosed container, discontinuities of velocity or velocity gradient can result whose location is physically random. The effect of viscosity is here examined for a particular configuration. The inviscid solutions are confirmed as true approximations to the flow at high Reynolds number R, for cases in which the internal inviscid velocity (but not velocity gradient) is continuous. The internal discontinuities become layers of thickness O(R$^{-\frac{1}{3}}$) in which the shears are O(R$^\frac{1}{6}$). The extreme sensitivity of the pattern of internal shear layers to the container's dimensions remains. Provided R$^\frac{1}{6} \ll$ ln R, the rough location of the strongest shears is insensitive to cell dimensions. A minute height change causes the original layers to split into a large number of parallel layers, with the strongest shears on layers near the original, and with a decay as n$^{-\frac{2}{3}}$ on the nth singular surface numbered from the original.