An Experimental and Theoretical Study of Barotropic Instability

Abstract

Abstract The barotropic instability of horizontal shear flows is investigated by means of a laboratory experiment. Two kinds of basic flows with different velocity profiles am examined, one a free-shear layer and the other a jet. It is found that for both flows the stability is described by a single nondimensional parameter, a Reynolds number R=VL/v where V is the characteristic velocity of the basic flow, L=(E/4)¼H is the characteristic length of the basic flow, v the kinematic viscosity, H the depth of the fluid layer, and E=v(ΩH2)−1 the Ekman number, with Ω the angular velocity of the basic rotation. The experimentally-determined critical Reynolds number Rc and critical wavenumber kc show excellent agreement with those predicted by a linear stability theory in which both Ekman friction and internal viscosity are incorporated. It is found that the internal viscosity plays an important role in explaining the observed values of Rc and kc. When R is larger than Rc, several organized eddies develop along th...