An experimental study of multiple zonal jet formation in rotating, thermally driven convective flows on a topographic beta-plane

A series of rotating, thermal convection experiments were carried out on the Coriolis platform in Grenoble, France, to investigate the formation and energetics of systems of zonal jets through nonlinear eddy/wave-zonal flow interactions on a topographic ß-plane. The latterwas produced by a combination of a rigid, conically sloping bottom and the rotational deformation of the free upper surface. Convection was driven by a system of electrical heaters laid under the (thermally conducting) sloping bottom and led to the production of intense, convective vortices. These were observed to grow in size as each experiment proceeded and led to the development of weak but clear azimuthal jet-like flows, with a radial scale that varied according to the rotation speed of the platform. Detailed analyses reveal that the kinetic energy-weighted radial wavenumber of the zonal jets, k_{J y}, scales quite closely either with the Rhines wavenumber as k_{J y} ≃ 2(β_T/2u_rms)^1/2, where u_rms is the rms total or eddy velocity and β_T is the vorticity gradient produced by the sloping topography, or the anisotropy wavenumber as k_{J y} ≃ 1.25(β³_T ε{lunate})^1/5, where ε{lunate} is the upscale turbulent energy transfer rate. Jets are primarily produced by the direct quasi-linear action of horizontal Reynolds stresses produced by trains of topographic Rossby waves. The nonlinear production rate of zonal kinetic energy is found to be strongly unsteady, however, with fluctuations of order 10-100 times the amplitude of the mean production rate for all cases considered. The time scale of such fluctuations is found to scale consistently with either an inertial time scale, Τ_p ~ 1.√u_rms β_T, or the Ekman spin-down time scale. Kinetic energy spectra show some evidence for a k^-5/3 inertial subrange in the isotropic component, suggestive of a classical Kolmogorov-Batchelor-Kraichnan upscale energy cascade and a steeper spectrum in the zonal mean flow, though not as steep as k^-5, as anticipated for fully zonostrophic flow. This is consistent with a classification of all of these flows as marginally zonostrophic, as expected for values of the zonostrophy parameter R_β ≃ 1.6-1.7, though a number of properties related to flow anisotropy were found to vary significantly and systematically within this range.