Instabilities of the flow around a cylinder and emission of vortex dipoles

Kizner, Ziv; Makarov, Viatcheslav Georgievich; Kamp, Leon Lpj; Heijst, Gert Jan van

doi:10.1017/jfm.2013.345

Cited by 7 publications

(12 citation statements)

References 22 publications

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“…Until about , the deformation of the vorticity rings is similar to that in the flat-bottom case (see Kizner et al. 2013) as well as in the weak-slope case (figures 2 and 4). However, at , the closed flow does not emit any dipoles, and remains organized in a two-ring pattern.…”

Section: Beta Effect At Steep Slopes Formation Of Quasi-steady Patternssupporting

confidence: 72%

“…The integration in time is performed with an implicit second-order backward-difference scheme whose absolute tolerance is and employing fourth-order integration for the rectangular Lagrangian elements used (for details see Kizner et al. 2013).…”

Section: Problem Statement and Methodsmentioning

confidence: 99%

“…As is known, in the flat-bottom case, the -mode instability of a barotropic flow around an island may lead to the emission of dipoles for (Kizner et al. 2013). At weak slopes, namely at of order 0.01, the instability is expected to evolve basically in the same way, as long as the topographic background vorticity appearing in (2.2) is negligible compared to the vorticity .…”

Section: Beta Effect At Weak Slopes Trajectories Of Emitted Dipolesmentioning

confidence: 99%

“…The instability of two-dimensional flat-bottom circular flows with stepwise vorticity profiles around a rigid cylinder (island) was investigated by Kizner et al. (2013). It was shown that the instability of azimuthal mode may lead to the emission of vortex dipoles.…”

Section: Introductionmentioning

confidence: 99%

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Barotropic annular flows, vortices and waves on a beta cone

2019

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We consider two-dimensional quasi-geostrophic annular flows around a circular island with a radial offshore bottom slope. Since the conical bottom topography causes a certain beta effect, by analogy with the conventional beta plane we term our model a beta cone. Our focus is on the flows with zero total circulation, which are composed of two concentric rings of uniform potential vorticity (PV) attached to the island. The linear stability of such flows on a beta cone was investigated in a previous publication of ours. In the present paper, we study numerically the nonlinear evolution of weakly viscous flows, whose parameters are fitted so as to guarantee the highest instability of the azimuthal mode $m=1,\ldots ,6$. We study the production of vortices and Rossby waves due to the instability, consider the effect of waves on the emerging vortices and the interaction between the vortices. As in the flat-bottom case, at $m\geqslant 2$, the instability at weak bottom slopes normally leads to the emission of $m$ dipoles. However, a fundamental difference between the flat-bottom and beta-cone cases is observed in the trajectories of the dipoles as the latter recede from the island. When the flow is initially counterclockwise, the conical beta effect may force the dipoles to make a complete turn, come back to the island and rearrange in new couples that again leave the island and return. This quasi-periodic process gradually fades due to filamentation, wave radiation and viscous dissipation. Another possible outcome is symmetrical settling of $m$ dipoles in a circular orbit around the island, in which they move counterclockwise. This behaviour is reminiscent of the adaptation of strongly tilted beta-plane modons (dipoles) to the eastward movement. If the initial flow is clockwise, the emerged dipoles usually disintegrate, but sometimes, the orbital arrangement is possible. At a moderate slope, the evolution of an unstable flow, which is initially clockwise, may end up in the formation of a counterclockwise flow. At steeper slopes, a clockwise flow may transform into a quasi-stationary vortex multipole. When the slope is sufficiently steep, the topographic Rossby waves developing outside of the PV rings can smooth away the instability crests and troughs at the outer edge of the main flow, thus preventing the vortex production but allowing the formation of a new quasi-stationary pattern, a doubly connected coherent PV structure possessing $m$-fold symmetry. Such an $m$-fold pattern can be steady only if it rotates counterclockwise, otherwise it radiates Rossby waves and transforms eventually into a circularly symmetric flow.

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Section: Beta Effect At Steep Slopes Formation Of Quasi-steady Patternssupporting

confidence: 72%

Section: Problem Statement and Methodsmentioning

confidence: 99%

Section: Beta Effect At Weak Slopes Trajectories Of Emitted Dipolesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Barotropic annular flows, vortices and waves on a beta cone

2019

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“…This again requires y 0 and h to be of opposite sign: a seamount destabilizes anticyclones while a depression destabilizes cyclones. Kizner et al (2013) and Rabinovich et al (2018) showed a similar m 5 1 instability for flow around an island. We can understand the mode-1 dynamics better by noting that they represent the set of PV patches wobbling around the origin while remaining circular.…”

Section: Two-step Isolated Barotropic Vortexmentioning

confidence: 70%

Influence of Bottom Topography on Vortex Stability

Zhao

Chieusse-Gérard

Flierl

2019

Journal of Physical Oceanography

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The effects of topography on the linear stability of both barotropic vortices and two-layer, baroclinic vortices are examined by considering cylindrical topography and vortices with stepwise relative vorticity profiles in the quasigeostrophic approximation. Four vortex configurations are considered, classified by the number of relative vorticity steps in the horizontal and the number of layers in the vertical: barotropic one-step vortex (Rankine vortex), barotropic two-step vortex, and their two-layer, baroclinic counterparts with the vorticity steps in the upper layer. In the barotropic calculation, the vortex is destabilized by topography having an oppositely signed potential vorticity jump while stabilized by topography of same-signed jump, that is, anticyclones are destabilized by seamounts while stabilized by depressions. Further, topography of appropriate sign and magnitude can excite a mode-1 instability for a two-step vortex, especially relevant for topographic encounters of an otherwise stable vortex. The baroclinic calculation is in general consistent with the barotropic calculation except that the growth rate weakens and, for a two-step vortex, becomes less sensitive to topography (sign and magnitude) as baroclinicity increases. The smaller growth rate for a baroclinic vortex is consistent with previous findings that vortices with sufficient baroclinic structure could cross the topography relatively easily. Nonlinear contour dynamics simulations are conducted to confirm the linear stability analysis and to describe the subsequent evolution.

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Vortex collision against static and spinning round cylinders: A lattice Boltzmann study

Rosis

2023

Computers & Fluids

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Instabilities of the flow around a cylinder and emission of vortex dipoles

Cited by 7 publications

References 22 publications

Barotropic annular flows, vortices and waves on a beta cone

Barotropic annular flows, vortices and waves on a beta cone

Influence of Bottom Topography on Vortex Stability

Vortex collision against static and spinning round cylinders: A lattice Boltzmann study

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