Zonal jets over small-scale topography: jet properties and energy transfers

Small-scale topography can significantly influence large-scale motions in geophysical flows, but the dominant mechanisms underlying this complicated process are poorly understood. Here, we present a systematic experimental study of the effect of small-scale topography on zonal jets. The jet flows form under the conditions of fast rotation, a uniform background $\beta$ -effect, and sink–source forcing. The small-scale topography is produced by attaching numerous small cones on the curved bottom plate, and the height of the cones is much smaller than the water depth. It is found that for all tested cases, the energy fraction in the zonal mean flow consistently follows a scaling $E_{uZ}/E_{uT}=C_1 l_f^2\epsilon _{\textit{up}}^{-2/5}\beta _{\textit{eff}}^{6/5}$ , where $l_f$ is the forcing scale, $\epsilon _{\textit{up}}$ is the upscale energy transfer rate, and $\beta _{\textit{eff}}$ measures the effective $\beta$ -effect in the presence of topography. The presence of the small-scale topography weakens the jet strength notably. Moreover, the effect of topography on energy transfers depends on the topography magnitude $\beta _\eta$ , and there exist three regimes. At small $\beta _\eta$ , the inverse energy transfers are remarkably diminished while the jet pattern remains unchanged. When $\beta _\eta$ increases, a blocked flow pattern forms, and the jet width reaches saturation, becoming independent of the forcing magnitude and $\beta$ . At moderate $\beta _\eta$ , the inverse energy fluxes are surprisingly enhanced. A further increase of $\beta _\eta$ leads to a greater reduction of the energy fluxes. We finally examine the effect of topography from the perspective of turbulence–topography interaction.