Relaxation of 2D Turbulence to Vortex Crystals

Fine, K. S.; Cass, A. C.; Flynn, W.G.; Driscoll, C. F.

doi:10.1103/physrevlett.75.3277

Cited by 247 publications

(197 citation statements)

References 30 publications

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“…Patch/line-vortex systems are also studied because of their relevance in modelling the relaxation of 2D turbulence in which an initially turbulent vorticity distribution coalesces into a number of distinct vorticity maxima effectively superposed on the region of ambient vorticity. 8 Durkin and Fajans 9,10 have performed experiments in a Malmberg-Penning trap in an attempt to under the dynamics of ''vortex-within-a-vortex'' phenomena. Jin and Dubin 11 later performed an analysis on such a system.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of a class of two-dimensional multipolar vortex equilibria

Crowdy

Cloke

2002

Physics of Fluids

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The stability properties of a class of explicit multipolar vortex solutions of the two-dimensional Euler equations found in Crowdy ͓Phys. Fluids. 11, 2556 ͑1999͔͒ are studied. While the tripole solutions are linearly unstable in all configurations, it is found that the exact quadrupolar vortices have distinguished linear stability properties revealing them to be neutrally stable in all configurations. This result is consistent with observations by previous investigators on the general robustness of quadrupolar vortex structures. Higher-order multipolar structures are linearly unstable when the satellites are too close together, but become neutrally stable when the satellites are far enough apart and the ambient vortex patch sufficiently distorted. The nonlinear evolution of perturbed solutions is investigated numerically using contour dynamics methods. Some new results concerning limiting states involving cusp singularities in the vortex patch boundaries are also presented.

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Section: Introductionmentioning

confidence: 99%

Stability analysis of a class of two-dimensional multipolar vortex equilibria

Crowdy

Cloke

2002

Physics of Fluids

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“…Coherent structures have been recently observed in laboratories [1][2][3][4][5][6] and are subjects of theoretical analysis for understanding underlying physics [7]. In both ECR plasmas [4] and gun-produced plasmas [5], two-arms spirals are commonly observed, and in particular the spiral structure observed in the ECR plasmas have interesting features: (1) the stationary structure is observed in a certain range of the background pressure, (2) the direction of the arm stretching is reversed when the magnetic field is reversed, and (3) the arm winding is identified as an Archimedes spiral, that is the curve spiraling into the origin which in polar coordinates is given by the equation…”

mentioning

confidence: 96%

Spiral Structures in Magnetized Rotating Plasmas

Kono

Tanaka

2000

Phys. Rev. Lett.

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“…This clearly shows, and this is one of the main conclusions of the present work, that the coherent structures naturally formed during the system's long term evolution, are in fact local thermodynamical equilibrium states. It would be interesting to test these theoretical results by experiment, using for instance, a device similar to the one used by the Driscoll group [13]. In order to obtain the effects related to the potential vorticity, the particles in the device should have a non negligible Larmor radius.…”

Section: Discussionmentioning

confidence: 99%

“…The system freely evolved by successive merging of vortices, in such a way that the mean size of vortices grew with time. The long time behavior of almost inviscid of two-dimensional turbulent flow was investigated by Fine et al [13], using an electron plasma column. They obtained a final stationary state consisting in a few vortices forming a quasi-crystal structure.…”

Section: Numerical Simulations Of Decaying Turbulence and Relaxationmentioning

confidence: 99%

Relaxation towards localized vorticity states in drift plasma and geostrophic flows

Agullo¹,

Verga

2004

Phys. Rev. E

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The drift of ions in a magnetized plasma or the height fluctuations of a rotating fluid layer are described by the conservation equation of a potential vorticity. This potential vorticity contains an intrinsic length scale, the hybrid Larmor radius in plasma, and the Rossby length in the quasigeostrophic flow. The influence of this scale in the evolution of a random initial vorticity field is investigated using a thermodynamic approach. In contrast to the perfect fluid case, where the vorticity tends to a well defined stationary state, complete relaxation towards an equilibrium state is not observed in numerical simulations of quasi-geostrophic decaying turbulence. The absence of global thermodynamic equilibrium is explained by the relaxation towards states of local equilibrium where the vorticity is concentrated. Interaction between these separated regions is extremely weak. Explicit, axisymmetric, localized solutions of the mean field integro-differential equation of extremal entropy states are obtained using asymptotic methods. Comparison of the computed solutions with the observed coherent structures, shows that they effectively correspond to states in local thermodynamic equilibrium.

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Relaxation of 2D Turbulence to Vortex Crystals

Cited by 247 publications

References 30 publications

Stability analysis of a class of two-dimensional multipolar vortex equilibria

Stability analysis of a class of two-dimensional multipolar vortex equilibria

Spiral Structures in Magnetized Rotating Plasmas

Relaxation towards localized vorticity states in drift plasma and geostrophic flows

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