Linearized spin-up in vortex flows

Abstract

Transient motions of contained laminar vortex flows are investigated by solving a linearized (low Rossby number) spin-up problem for arbitrary primary flow circulation distribution. If the local Ekman number is of the order of one or larger, spin-up occurs solely by viscous diffusion (Rayleigh layers), but if the local Ekman number is small compared with one, spin-up occurs by the action of an Ekman layer induced secondary flow in a time much less than the viscous diffusion time. The unsteady motion is superimposed on a steady state secondary flow which compensates for diffusion of primary flow vorticity.