Baroclinic geostrophic adjustment in a rotating circular basin

Abstract

Baroclinic geostrophic adjustment in a rotating circular basin is investigated in a laboratory study. The adjustment process consists of a linear phase before advective and dissipative effects dominate the response for longer time. This work describes in detail the hydrodynamics and energetics of the linear phase of the adjustment process of a two-layer fluid from an initial step height discontinuity in the density interface $\uDelta H$ to a final response consisting of both geostrophic and fluctuating components. For a forcing lengthscale $r_f$ equal to the basin radius $R_0$, the geostrophic component takes the form of a basin-scale double gyre while the fluctuating component is composed of baroclinic Kelvin and Poincaré waves. The Burger number $S\,{=}\,R/r_f$ ($R$ is the baroclinic Rossby radius of deformation) and the dimensionless forcing amplitude $\epsilon\,{=}\,\uDelta H/H_1$ ($H_1$ is the upper-layer depth) characterize the response of the adjustment process. In particular, comparisons between analytical solutions and laboratory measurements indicate that for time $\tau$: $1 \,{<}\, \tau \,{<}\, S^{-1}$ ($\tau$ is time scaled by the inertial period $2 \pi/f$), the basin-scale double gyre is established, followed by a period where the double gyre is sustained, given by $S^{-1} \,{<}\, \tau \,{<}\, 2\epsilon^{-1}$ for a moderate forcing and $S^{-1}\,{<}\, \tau\,{<}\,\tau_D$ for a weak forcing ($\tau_D$ is the dimensionless dissipation timescale due to Ekman damping). The analytical solution is used to calculate the energetics of the baroclinic geostrophic adjustment. The results are found to compare well with previous studies with partitioning of energy between the geostrophic and fluctuating components exhibiting a strong dependence on $S$. Finally, the outcomes of this study are considered in terms of their application to lakes influenced by the rotation of the Earth.