Eddy–wave duality in a rotating flow

Abstract

A series of experiments with rotating, electromagnetically forced, turbulent flows were carried out at the Sapienza University of Rome to investigate the eddy–wave duality in flows with a β-effect and the electromagnetic force acting in the westward direction. When the β-effect is significant, i.e., as in planetary atmospheric and oceanic circulations, nonlinear eddy/wave interactions facilitate flow self-organization into zonal patterns in which Rossby waves and westward propagating cyclonic and anticyclonic eddies coexist. Upon time averaging, eddies disappear and the flow pattern transforms into a system of alternating zonal jets. What is the relationship between eddies, jets, and Rossby waves? To address this issue, we designed a laboratory experiment in which a westward zonal flow is produced by applying an electromagnetic small-scale forcing to a thin layer of a rotating fluid. In order to investigate different levels of flow zonality and a wider range of zonal modes, we varied the forcing intensity and the area of the forced sector. The zonal flow evolves as a system of westward propagating, large scale, cyclonic, and anticyclonic eddies. The propagation speed of the traveling structures was calculated from the Hovmöller diagrams of both the streamfunction and the centroids of clusters of different types (cyclonic and anticyclonic eddy cores and saddle point neighborhoods) obtained via an Okubo–Weiss analysis. The results were compared with the theoretical phase speed of a Rossby wave. The correspondence between these two characteristics at the radius of maximum shear corresponding to the epicenter of the barotropic instability is quite good, particularly after including the radial variation of the zonal velocity in the β-term. It is concluded that the Rossby waves and eddies are inseparable as the former maintain the instability that sustains the latter. This symbiosis visually resembles the Rossby soliton.