Source–sink turbulence in a rotating stratified fluid

Abstract

In a recent paper Boubnov, Dalziel & Linden (1994) described the response of a stratified fluid to forcing produced by an array of sources and sinks. The sources and sinks were located in a horizontal plane and the flow from the sources was directed horizontally so that fluid was withdrawn from, and re-injected at, its own density level. As a result vertical vorticity was imparted to the fluid with a minimum of vertical mixing. It was found that when the stratification was strong enough to suppress vertical motions an inverse energy cascade was observed leading to the establishment of a large-scale circulation in the fluid. Those experiments were restricted to eight source-sink pairs. The present paper extends this work in two ways. First, up to forty source-sink pairs are used to force the flow, thereby producing a much wider separation of scales between the forcing and the flow domain. An inverse cascade is again found, but in this case the energy transfer to large scales is more rapid. The basic pattern of the large-scale flow is independent of the number of sources but the detailed structure depends on the energy input scale. Second, the effects of rotation about a vertical axis are investigated. It is found that when the Rossby deformation radius exceeds the size of the flow domain, the inverse energy cascade still occurs. However, for smaller values of the deformation scale, which in these experiments are comparable to or smaller than the forcing scale, the inverse cascade is altered by baroclinic instability. When flow structures develop on a scale larger than the deformation scale, usually by the merging of vortices of like sign, these structures are observed to split into smaller vortices of a scale comparable to the deformation scale. The flow appears to evolve with a balance between an anticascade produced by the two-dimensionality of the flow and a cascade due to baroclinic instability. For Rossby radii much smaller than the domain size the flow evolves into finite clumps of vorticity and an asymmetry between anticyclones and cyclones develops. A predominance of coherent anticyclones is observed, and the cyclonic vorticity is contained in more diffuse structures.