Stable and unstable monopolar vortices in a stratified fluid

Abstract

This paper presents experiments on planar monopolar vortex structures generated in a non-rotating, stratifi ed fluid. In order to study the dynamics of such planar vortices in the laboratory, angular momentum was generated in a specifi c horizontal layer of the stratifi ed fl uid, by using three different generation mechanisms. The lens-shaped monopolar vortices thus created were in some cases stable and conserved their circular symmetry, while in other cases they appeared to be unstable, leading to the formation of a multipoled vortex with a different topology. Characteristics such as cross-sectional profiles (angular velocity and vorticity) and vorticity-stream function scatter plots have been measured experimentally by using digital image processing techniques. The characteristics of the monopolar vortices are compared with analytical vortex models known from literature. Simple models, based on vertical diffusion of vorticity, are proposed to describe the monopolar vortex decay ; they show reasonable agreement with the experimental results. From the multipolar structures, the tripolar vortex and a specific case of a triangular vortex, neither having been observed before in a stratified fluid, are studied in detail. A comparison with point-vortex models yields good agreement. Although these multipolar vortices appear to persist for a long while, they are found eventually to be unstable and to transform into a monopolar vortex.

On the interaction between two oppositely signed, shielded, monopolar vortices

“…The purpose of the experiments is to investigate the interaction behavior of two flat pancakelike shielded monopolar vortices of opposite vorticity. The monopolar vortices described in this paper are generated by the so-called tangential injection method, 13 in which an amount of fluid of matching density is injected horizontally along the inner wall of a small cylinder at the height of the density interface. After the injection of the fluid is stopped, the flow inside the cylinder is allowed to adjust to a purely circular motion ͑during a time ͒, after which the cylinder is carefully lifted and removed from the tank.…”

“…The decay of the vortices is caused by diffusion of momentum in the direction perpendicular to the flow field. [12][13][14] It can be seen that the positive vortex ͑repre-sented by the squares͒ is only initially slightly stronger than the negative vortex ͑circles͒, and therefore the dipole moves in a straight path after it has been formed ͑i.e., after t Ϸ150 s͒. To obtain more detailed information on the dipole, we focus on a smaller region of the domain moving with the dipole.…”

“…An equivalent formation of tripoles in the interaction of like-signed shielded monopoles has been found in numerical simulations of shielded vortex merger by Carton 23 and Carton and Bertrand. 24 It is unclear whether the instability of both experimental vortices is caused by the mutual influence of the vortices, because it was shown by Flór and van Heijst 13 that also a single monopole, generated by the tangential injection method, could become unstable and form a tripole. It is, however, reasonable to assume that each monopole perturbs the other, thereby perhaps triggering the instability.…”

“…Furthermore, the interaction of vortices in a stratified fluid can, as described in the present work, be compared with results from purely 2D numerical simulations. Previous studies, numerical as well as experimental, 13,[15][16][17] have shown that shielded monopolar ͑i.e., axisymmetric͒ vortices can be unstable, both in purely twodimensional flows and in laboratory experiments with rotating homogeneous fluids and nonrotating stratified fluids. In this paper we not only investigate in detail the interaction of two oppositely signed shielded monopolar vortices and their re-organization into two dipoles, but we also show that the presence of the other vortex can perturb a shielded monopolar vortex, resulting in the formation of a tripole.…”

“…In laboratory experiments it was found that monopolar vortices in a nonrotating stratified fluid are always characterized by a shielded vorticity structure. [12][13][14] Therefore, the interaction between two oppositely signed monopolar vortices in a stratified fluid provides a way to study the formation process of a compact dipole as described by C&B in detail. Furthermore, the interaction of vortices in a stratified fluid can, as described in the present work, be compared with results from purely 2D numerical simulations.…”