Image-Charge Method for Contour Dynamics in Systems with Cylindrical Boundaries

Coppa, Gianni; Peano, F.; Peinetti, F.

doi:10.1006/jcph.2002.7174

Cited by 12 publications

(8 citation statements)

References 17 publications

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“…This calculation implies the use of the Green function G(x, y; x 0 , y 0 ), which can be interpreted as the stream function of a flow induced by a unit point vortex located at a point (x 0 , y 0 ) on the (x, y)-plane, and computation of contour integrals over the patch boundaries. The construction of the Green function in complex domains is often facilitated by the use of image vortices (Coppa, Peano & Peinetti 2002;Johnson & McDonald 2004;Elcrat, Fornberg & Miller 2005;Crowdy & Surana 2007). For a plane with a circular cutout of unit radius centred at the origin of the frame of reference, a Green function can be written as Makarov, L. Kamp and G. van Heijst (e.g.…”

Section: Numerical Simulationssupporting

confidence: 40%

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

Kizner

Makarov²,

Kamp

et al. 2013

J. Fluid Mech.

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Instabilities and long-term evolution of two-dimensional circular flows around a rigid circular cylinder (island) are studied analytically and numerically. For that we consider a base flow consisting of two concentric neighbouring rings of uniform but different vorticity, with the inner ring touching the cylinder. We first study the inviscid linear stability of such flows to perturbations of the free edges of the rings. For a given ratio of the vorticity in the rings, the governing parameters of the problem are the radii of the inner and outer rings scaled on the cylinder radius. In this two-dimensional parameter space, we determine analytically the regions of linear stability/instability of each azimuthal mode m = 1, 2, . . . . In the physically most meaningful case of zero net circulation, for each mode m > 1, two regions are identified: a regular instability region where mode m is unstable along with some other modes, and a unique instability region where only mode m is unstable. After the conditions of linear instability are established, inviscid contour-dynamics and high-Reynolds-number finite-element simulations are conducted. In the regular instability regions, simulations of both kinds typically result in the formation of vortical dipoles or multipoles. In the unique instability regions, where the inner vorticity ring is much thinner than the outer ring, the inviscid contour-dynamics simulations do not reveal dipole emission. In the viscous simulation, because viscosity has time to widen the inner ring, the instability develops in the same manner as in the regular instability regions.

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Section: Numerical Simulationssupporting

confidence: 40%

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

Kizner

Makarov²,

Kamp

et al. 2013

J. Fluid Mech.

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“…Our method can perform numerical simulations of electron clouds, modelled as patches with sharp edges, in traps of various cross-sections. Backhaus et al (1988) and Coppa et al (2002) have also been concerned with a formulation of contour dynamics in a trap of circular cross-section. Figure 8 shows the evolution of an elliptical vortex patch with aspect ratio a/b = 9 computed using the new technique (note that the conformal map here is just the identity map).…”

Section: Electron Vortices In Plasma Trapsmentioning

confidence: 99%

“…The equations of motion for such plasmas are isomorphic to the Euler equations for an ideal incompressible fluid. Backhaus, Fajans & Wurtele (1988) and Coppa, Peano & Peinetti (2002) have considered a formulation of contour dynamics in a circular cylinder. Their approach, which relies on ideas from the method of images (which they call an 'image-charge' method), has many features in common with those devised by Johnson & McDonald (2005b, c).…”

Section: Introductionmentioning

confidence: 99%

Contour dynamics in complex domains

Crowdy

Surana

2007

J. Fluid Mech.

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This paper demonstrates that there is a contour dynamics formulation for the evolution of uniform vortex patches in any finitely connected planar domain bounded by impenetrable walls. A general numerical scheme is presented based on this formulation. The algorithm makes use of conformal mappings and follows the evolution of a conformal pre-image of a given vortex patch in a canonical multiply connected circular pre-image region. The evolution of vortex patches can be computed given just the conformal map from this pre-image region to the physical fluid region. The efficacy of the scheme is demonstrated by illustrative examples.

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“…2014), Poisson–Vlasov (Romé et al. 2000) and contour dynamics (Coppa, Peano & Peinetti 2002) methods.…”

Section: Introductionmentioning

confidence: 99%

Effect of initial conditions on electron–plasma turbulence: a multiresolution analysis

2015

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The transverse dynamics of a pure electron plasma confined in a Penning–Malmberg trap is investigated, taking advantage of two-dimensional particle-in-cell numerical simulations. The evolution of the electron plasma turbulence is studied by means of a wavelet-based multiresolution analysis. In particular, a modified recursive denoising algorithm is developed to separate coherent and incoherent (not necessarily homogeneous) components of the flow. A set of simulations have been carried out changing systematically the radii of an initial annular density distribution of the electrons. The results of the multiresolution analysis indicate that the initial density configuration may have a considerable effect on the evolution of turbulence. Even very small initial density fluctuations can lead to quite different final states, especially in the presence of multiple active diocotron modes characterized by similar growth rates.

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Image-Charge Method for Contour Dynamics in Systems with Cylindrical Boundaries

Cited by 12 publications

References 17 publications

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

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

Contour dynamics in complex domains

Effect of initial conditions on electron–plasma turbulence: a multiresolution analysis

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