Interactions and decay of vortices in stratified turbulence

BY FRANS DE ROOIJ, PAUL F. LINDEN & STUART B. DALZIEL
Department of Applied Mathematics and Theoretical Physics, University of Cambridge,
Silver Street, Cambridge CB3 9EW, UK
October 1996

On large scales, the flows in the atmosphere and oceans can be regarded as two-dimensional. The specific characteristics of two-dimensional flows are therefore important in the study of geophysical turbulence. The absence of vortex stretching and twisting will cause an inverse energy cascade: a turbulent flow will self-organise into coherent structures.

This paper describes laboratory experiments investigating the self-organising and dispersion characteristics of geophysical turbulence. They were carried out in a linearly stratified fluid, horizontally forced with sources and sinks around a ring. The flow was visualized with small particles illuminated in a horizontal plane, recorded with a camera and analysed with an advanced particle tracking system. Qualitative and quantitative data, such as velocity and vorticity values, were obtained.

In the experiments the inverse energy cascade was clearly observed: the flow organised into a single quasi-steady, coherent vortex structure of the largest available scale. This vortex is maintained against vertical diffusion of momentum by intermittent entrainment of vorticity from its exterior. Its sense of rotation was set by a slight bias in the experimental apparatus, but could be changed by a small opposing initial circulation. A detailed study of the effects of changing forcing parameters was carried out. The number of (passive) sinks does not affect the flow, whereas the number of (active) sources sets the length scale 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, its 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 taken as well of the decay of the vortex. After switching off the forcing it quickly becomes axisymmetric and the vorticity becomes a linear function of the streamfunction. The spin-down time was observed to be much shorter than calculated from viscous decay. 


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