Experimental investigations of quasi-two-dimensional vortices in a stratified fluid with source–sink forcing

Abstract

This paper describes laboratory experiments on the self-organizing character of geophysical turbulence. The experiments were carried out in a linearly stratified fluid, forced horizontally with sources and sinks around a horizontal ring. The flow was visualized with small particles illuminated by a horizontal light sheet, recorded with a camera and analysed with an advanced particle tracking system. Qualitative and quantitative data, such as flow patterns, velocity and vorticity fields, were obtained. In the experiments, the inverse energy cascade was clearly observed: the flow organized into a single quasi-steady, coherent vortex structure of the largest available scale. This vortex is maintained against diffusion of momentum by entrainment of vorticity from its exterior. In this process, patches of vorticity of the same sign as the core of this large structure intermittently cross the vorticity barrier around the vortex. Patches of opposite vorticity were observed to be effectively blocked by the barrier. The direction of rotation of the vortex was set by a slight bias in the experimental apparatus and could be changed by imposing a small initial circulation in the opposite sense, the magnitude of which suggested a measure for the bias. A detailed study of the effects of changing forcing parameters was carried out. The number of sinks (which play only a passive role) does not affect the flow, whereas the number of sources sets the lengthscale of the forcing and thereby determines the size of the vortices that are created close to the ring, as well as that of the large central vortex that emerges. However, after longer times of forcing, the vortex size also depends on the strength of the forcing. The velocities in the large vortex structure scale with the mean velocity from the sources, and with the square root of their number. Measurements were also taken of the decay of the vortex. After switching off the forcing it quickly becomes axisymmetric and a linear functional relationship is established between the vorticity and streamfunction. The spin-down time was observed to be much shorter than can be accounted for by vertical viscous diffusion alone: initially the short horizontal scale of the vorticity barrier causes a relatively fast decay, whereas at later times the size of the vortex as a whole is important.