Rotating shallow water turbulence: Experiments with altimetry

Abstract

Results from a new series of experiments on turbulent flows in a rotating circular container are presented. Electromagnetic forcing is applied to induce flow in a layer of fluid of constant depth. Continuously forced and decaying flows are investigated. Optical altimetry is used to measure the gradient of the surface elevation field and to obtain the velocity and vorticity fields with high temporal and spatial resolution. Spectral analysis of the flows demonstrates the formation of dual cascade with energy and enstrophy intervals although the corresponding spectral fluxes of energy and enstrophy are not uniform in these intervals. The energy interval is characterized by the slope of ∼−5/3 in terms of wavenumber and is limited in extent by the finite radius of deformation effect. In the enstrophy range, the slope is steeper than −3 due to the presence of long-lived coherent vortices. The spatial patterns of fluxes to large or small scales in the flow indicate that inverse energy transfer and direct enstrophy transfer occur mainly in elongated vorticity patches. Cyclone/anticyclone asymmetry in favor of anticyclones is observed in our flows. Dominance of anticyclones is most clear during the decay phase of turbulence. The anticyclones remain circular, while cyclonic vorticity is stretched into elongated patches. Measurements show that skewness of vorticity distribution increases with increasing Froude number of the flow.