An oscillatory disturbance of rigidly rotating fluid

Abstract

Periodic disturbances of rigidly rotating inviscid flow of suitable frequency are controlled by a hyperbolic equation (Görtler 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 –⅓ ) in which the shears are O ( R 1/6 ). The extreme sensitivity of the pattern of internal shear layers to the container’s dimensions remains. Provided R 1/6 ≫ In 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 n ear the original, and with a decay as n –2/3 on then n th singular surface numbered from the original.