Surface semi-geostrophic turbulence is examined in this study. In our simulations, the strength of the ageostrophic component of the flows is controlled by the Rossby number ε, varying from 0.01 to 0.2. The flows manifest a cyclone-anticyclone asymmetry with a cyclonic preference for cold vortices and an anticyclonic preference for warm filaments. This asymmetry becomes especially pronounced in the flows with large ε, where an abundance of warm filaments is observed. Strong vertical motions concentrate in the small-scale filaments and at the periphery of the vortices. There, the lateral divergence becomes significant. A negative correlation between the divergence and the relative vorticity is identified using joint probability density functions. Slopes of the kinetic and potential energy spectra vary between -2.2 and -1.7 at intermediate scales. Analyses of spectral fluxes demonstrate an inverse kinetic energy cascade and a forward cascade of potential energy. As ε increases, the filaments become more numerous in the flows. They wrap around cyclones, weakening their interactions and subsequent mergers, thus suppressing the inverse cascade of kinetic energy. We characterize lateral dispersion in the SSG flows using the finite-scale Lyapunov exponents (FSLEs). They are used to identify Lagrangian coherent structures, such as those created by the interaction of vortices. The FSLEs are also used to investigate the regimes of dispersion at different scales. The results show a smooth transition from hyper-ballistic diffusion at small scales to normal diffusion at large scales.

This is a laboratory zonal-jet study using a rotating water tank. The bottom topography has a tent-shaped radial cross section designed to generate two critical latitudes, i.e. two positions where βe, the radial gradient of the potential vorticity (PV), changes sign. This configuration is motivated by observations indicating Jupiter and Saturn have not only multiple zonal jets, but multiple stable critical latitudes. It is known that “supersonic” critical latitudes (with respect to Rossby waves) are stable, whereas “subsonic” critical latitudes are posited to be unstable. Because Rossby waves are uni-directional, “supersonic” critical latitudes come in two varieties: Rossby Mach number MR > 1 and MR < 0, where the latter holds when the waves are directed downstream. Experiments focus on: i) how do zonal jets emerge from localized forcing in a system with alternating PV gradients? and ii) what differences are there between the evolution of various types of critical latitudes? The water is forced by mass injection along one radius. Laboratory altimetry provides accurate, unobtrusive records of the circulations that reveal the emergence of counter-propagating β-plumes (Rossby-wave envelopes), which expand into tank-encircling zonal jets. The tank’s negative βe annulus is characterized by MR ~ 1, which is the condition surmised for Jupiter and Saturn. The weaker critical latitude (in terms of jumps in the PV-gradient) adjusts its position by ~4% of the tank radius and maintains MR ~ 1. In contrast, the stronger one vacillates while maintaining |MR| << 1, and may be relevant to steep oceanic seamounts.