Abstract
In linear stratifications, vortices have a typical flat shape that appears to be not only a compromise between the rotation and the stratification of the background flow through their Coriolis parameter f and buoyancy frequency , but also involves the buoyancy frequency N c within the vortices and their Rossby number R o . We derive an analytical solution for the self-similar ellipsoidal shape of the vortices and the law for their aspect ratio. From this law, we show that long-lived vortices must necessary be either weakly stratified anticyclones or superstratified cyclones (which is less likely to occur). These predictions are experimentally and numerically verified and agree with published measurements for Jovian vortices and ocean meddies. This approach can be applied to a gaussian stratification to give good insights of the shape of vortices in protoplanetary disks and their sustainability.
Highlights
The scenario of planetesimal formation in protoplanetary disks proposed by Barge & Sommeria (1995) [1] is based on the trapping of solid dust particles in persistent anticyclonic vortices
A vertical laser sheet seen from a side camera allows to extract the contour of the vortex in the vertical plane and its vertical aspect ratio
Following the approach described in the previous section, we started to look at the shape and aspect ratio of vortices in a Gaussian stratification
Summary
The scenario of planetesimal formation in protoplanetary disks proposed by Barge & Sommeria (1995) [1] is based on the trapping of solid dust particles in persistent anticyclonic vortices. There is extensive numerical proof that anticyclonic long-lived coherent structures effectively trap particles in rotating flows, and numerical scenarios that take into account the stratification of the disk [2]. These structures are of main importance for the understanding of planet formation. Environments such as the vortices in the Jovian atmosphere or the Meddies in the Atlantic Ocean and could be of great interest to predict the shape of vortices in proto-planetary disks
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