The temporal evolution of a geostrophic flow in a rotating stratified basin

Abstract

A laboratory study in a rotating stratified basin examines the instability and long time evolution of the geostrophic double gyre introduced by the baroclinic adjustment to an initial basin-scale step height discontinuity Δ H in the density interface of a two-layer fluid. The dimensionless parameters that are important in determining the observed response are the Burger number S = R / R 0 (where R is the baroclinic Rossby radius of deformation and R 0 is the basin radius) and the initial forcing amplitude ɛ = Δ H / H 1 ( H 1 is the upper layer depth). Experimental observations and a numerical approach, using contour dynamics, are used to identify the mechanisms that result in the dominance of nonlinear behaviour in the long time evolution, τ > 2 ɛ − 1 (where τ is time scaled by the inertial period T I = 2 π / f ). When the influence of rotation is moderate ( 0.25 ≤ S ≤ 1 ), the instability mechanism is associated with the finite amplitude potential vorticity (PV) perturbation introduced when the double gyre is established. On the other hand, when the influence of rotation is strong ( S ≤ 0.1 ), baroclinic instability contributes to the nonlinear behaviour. Regardless of the mechanism, nonlinearity acts to transfer energy from the geostrophic double gyre to smaller scales associated with an eddy field. In the lower layer, Ekman damping is pronounced, resulting in the dissipation of the eddy field after only 40 T I . In the upper layer, where dissipative effects are weak, the eddy field evolves until it reaches a symmetric distribution of potential vorticity within the domain consisting of cyclonic and anticyclonic eddy pairs, after approximately 100 T I . The functional dependence of the characteristic eddy lengthscale L E on S is consistent with previous laboratory studies on continuously forced geostrophic turbulence. The cyclonic and anticyclonic eddy pairs are maintained until viscous effects eventually dissipate all motion in the upper layer after approximately 800 T I . The outcomes of this study are considered in terms of their contribution to the understanding of the energy pathways and transport processes associated with basin-scale motions in large stratified lakes.