Algebraic instability of hollow electron columns and cylindrical vortices

Smith, R. C.; Rosenbluth, M. N.

doi:10.1103/physrevlett.64.649

Cited by 98 publications

(62 citation statements)

References 10 publications

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“…This can be considered as a coupling to a mode with angular wavenumber n = 1, and this mode includes infinitesimal translations of the vortex (Smith & Rosenbluth 1990;Ting & Klein 1991;Lingevitch & Bernoff 1995;Llewellyn Smith 1995). In this paper we consider flows confined to the plane, and the case where the coherent vortex is immersed in a weak background gradient of vorticity; an example is that of a point vortex introduced at the midline of a weak plane Poiseuille shear flow.…”

Section: Introductionmentioning

confidence: 99%

Vortex motion in a weak background shear flow

2004

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A point vortex is introduced into a weak background vorticity gradient at finite Reynolds number. As the vortex spreads viscously so the background vorticity becomes wrapped around it, leading to enhanced diffusion of vorticity, but also giving a feedback on the vortex and causing it to move. This is investigated in the linear approximation, using a similarity solution for the advection of weak vorticity around the vortex, at finite and infinite Reynolds number. A logarithmic divergence in the far field requires the introduction of an outer length scale L and asymptotic matching. In this way results are obtained for the motion of a vortex in a weak vorticity field modulated on the large scale L and these are confirmed by means of numerical simulations.

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Section: Introductionmentioning

confidence: 99%

Vortex motion in a weak background shear flow

2004

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“…This is essentially the solution presented in RD94, although the derivation has followed Smith & Rosenbluth (1990). However, the far field behaviour of (5.6) is quite different here.…”

Section: First-order Solutionmentioning

confidence: 81%

The motion of a non-isolated vortex on the beta-plane

Smith

1997

J. Fluid Mech.

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The trajectory of a non-isolated monopole on the beta-plane is calculated as an asymptotic expansion in the ratio of the strength of the vortex to the beta-effect. The method of matched asymptotic expansions is used to solve the equations of motion in two regions of the flow: a near field where the beta-effect enters as a first-order forcing in relative vorticity, and a wave field in which the dominant balance is a linear one between the beta-effect and the rate of change of relative vorticity. The resulting trajectory is computed for Gaussian and Rankine vortices.

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“…According to the classical theory, the m0 = 1 diocotron spectrum does not present discrete unstable modes (regardless of the equilibrium density profile) [1], while the continuum spectrum can only produce an algebraic growth proportional to t 1/ 2 [2]. On the contrary, experiments show that the linear growth of the mode is exponential [3,4].…”

Section: Introductionmentioning

confidence: 99%

Rigorous fluid model for 3D analysis of the diocotron instability

Coppa¹,

D’Angola²,

Delzanno³

et al. 2002

AIP Conference Proceedings

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Abstract. A refinement to the theory published by Finn et al. is presented here. Compression effects are taken into account by a rigorous definition of the plasma length and by modifying the expression of the velocity field. The perturbation of the plasma length is calculated exactly by a suitable Green function. Growth rates and real frequencies of the unstable m0 = I mode are compared with the experimental values, showing a good agreement when compression effects are strong (i.e., for short traps).

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Algebraic instability of hollow electron columns and cylindrical vortices

Cited by 98 publications

References 10 publications

Vortex motion in a weak background shear flow

Vortex motion in a weak background shear flow

The motion of a non-isolated vortex on the beta-plane

Rigorous fluid model for 3D analysis of the diocotron instability

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