Stability of point-vortex multipoles revisited

Kizner, Ziv

doi:10.1063/1.3596270

Cited by 19 publications

(13 citation statements)

References 35 publications

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“…For large-scale, slowly varying flows in a rotating system, the Coriolis term is the dominant acceleration, as measured by the smallness of the Rossby number. Rotation and horizontal convergence/divergence add an intrinsic length scale, the radius of deformation L d , which changes the falloff of velocity to the modified Bessel function K 1 (16,17). The equations are known as the equivalent barotropic system.…”

Section: Significancementioning

confidence: 99%

“…Single shielded vortices, i.e., vortices with v = 0 outside a certain radius, have various modes of instability (26), and they often break into tripoles (27), consisting of a central vortex of one sign and two satellite vortices of the opposite sign orbiting 180°apart. Tripoles are stable both in the barotropic and equivalent barotropic system (17,28). Vortex crystals, in which many small vortices in random patterns spontaneously merge into geometric patterns of much larger vortices, are seen in laboratory experiments (14) and numerical simulations using the 2D Euler equations (29,30).…”

Section: Significancementioning

confidence: 99%

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Modeling the stability of polygonal patterns of vortices at the poles of Jupiter as revealed by the Juno spacecraft

Ingersoll

Klipfel

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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From its pole-to-pole orbit, the Juno spacecraft discovered arrays of cyclonic vortices in polygonal patterns around the poles of Jupiter. In the north, there are eight vortices around a central vortex, and in the south there are five. The patterns and the individual vortices that define them have been stable since August 2016. The azimuthal velocity profile vs. radius has been measured, but vertical structure is unknown. Here, we ask, what repulsive mechanism prevents the vortices from merging, given that cyclones drift poleward in atmospheres of rotating planets like Earth? What atmospheric properties distinguish Jupiter from Saturn, which has only one cyclone at each pole? We model the vortices using the shallow water equations, which describe a single layer of fluid that moves horizontally and has a free surface that moves up and down in response to fluid convergence and divergence. We find that the stability of the pattern depends mostly on shielding—an anticyclonic ring around each cyclone, but also on the depth. Too little shielding and small depth lead to merging and loss of the polygonal pattern. Too much shielding causes the cyclonic and anticyclonic parts of the vortices to fly apart. The stable polygons exist in between. Why Jupiter’s vortices occupy this middle range is unknown. The budget—how the vortices appear and disappear—is also unknown, since no changes, except for an intruder that visited the south pole briefly, have occurred at either pole since Juno arrived at Jupiter in 2016.

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Section: Significancementioning

confidence: 99%

Section: Significancementioning

confidence: 99%

Modeling the stability of polygonal patterns of vortices at the poles of Jupiter as revealed by the Juno spacecraft

Ingersoll

Klipfel

et al. 2020

Proc. Natl. Acad. Sci. U.S.A.

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“…The stability of a two-layer point-vortex tripole is known to be dependent on the total PV of the tripole, and on the separation between the core and the satellite vortices; 15,16 in the case of zero total circulation, all two-layer point-vortex tripoles are stable. The situation with tripoles comprised by finite-size patches of uniform PV is different.…”

Section: Introductionmentioning

confidence: 98%

Two-layer geostrophic tripoles comprised by patches of uniform potential vorticity

et al. 2015

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International audienceThe so-called carousel tripoles are constructed and characterized in the framework of two-layer quasi-geostrophic contour dynamics, and their stability is examined. Such a tripole is a steadily rotating doubly symmetric ensemble of three collinear vortices, or more specifically, uniform-potential-vorticity patches, with the central, core vortex, located in the upper layer, and the two remaining, satellite vortices, in the lower layer, or vice versa. The carousel tripole solutions are obtained with the use of a numerical iterative procedure. A tripole with zero total potential vorticity can be generally identified by a point in the plane spanned by two parameters, namely, the typical size of the patches relative to the Rossby deformation radius, and some shape parameter. We consider two kinds of the parameter plane by taking as the second parameter either the distance d between the centroids of the core and one of the satellites (termed also separation) or, alternatively, the minimal distance h between the core centroid and the satellite contour, measured along the symmetry axis that passes through the centroids of the core and satellites. Accordingly, to capture the stationary tripoles, we use two alternative numerical procedures, which are based on fixing the first or the second pair of parameters. This is done because the areas of convergence of the two procedures differ somewhat from each other. The areas of convergence are plotted in the parameter planes, and in each of the planes, two branches of solutions are found bifurcating from some segments of the lines bounding the convergence areas. Stability is tested in numerical simulations with the numerical noise taken as a perturbation factor. Stability/instability of a tripole is determined by examining the oscillations in the perimeter of one of the vortex satellites. For each tripole size, both stable and unstable solutions exist. The stability bounds coincide with the bifurcation lines, so that one branch of the solutions is stable while the other is not. As a whole, tripoles with considerable separation behave stably

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“…Considering two-layer quasi-geostrophic flows, Kizner (2006) introduced the concept of a hetonic quartet, a collinear ensemble of two point-vortex hetons, and studied their nonlinear stability. Nonlinear stability of point-vortex multipoles in the barotropic and two-layer fluid was investigated by Kizner (2011, 2014), who based his analysis on two invariants of motion which depend on intervortical distances only.…”

Section: Introductionmentioning

confidence: 99%