Boundary Layers on Characteristic Surfaces for Time-Dependent Rotating Flows

Abstract

Time-dependent motion of a fluid in a container rotating at Ω is characterized by boundary layers on the container surfaces if ν/Ω, where ν denotes kinematic viscosity, is small compared to the square of a typical length of the container. Let the frequency of the motion, measured in a corotating coordinate system, be ωΩ. If ω ~ 1, then the length scale of the boundary layer is (ν/Ω)1/2 , unless |ω| is equal to twice the normal component of the unit rotation vector. If |ω| does equal twice the normal component of the unit rotation vector, scales of (ν/ΩL2 )1/3 L and (ν/ΩL2 )1/4 L are possible. If the normal vector and rotation vectors are parallel, the former scale vanishes.