Quasi-steady monopole and tripole attractors for relaxing vortices

Rossi, Louis F.; Lingevitch, Joseph F.; Bernoff, Andrew J.

doi:10.1063/1.869353

Cited by 53 publications

(81 citation statements)

References 19 publications

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“…Using the Lamb-Oseen vortex with a superposed m = 2 perturbation of moderate amplitude, a numerical study is performed spanning the parameter space given by ␦ and Re, the amplitude of perturbation and the Reynolds number, respectively. Rossi et al 9 gave results for ␦ = 0.25 and Re= 10 3 , 5ϫ 10 3 , 10 4 , which we have reproduced. In addition, we present calculations with varying perturbation amplitudes, and attempt to determine whether there is in fact a threshold amplitude that separates two asymptotic states ͑axisymmetric and tripolar͒.…”

Section: Introductionsupporting

confidence: 68%

“…The main case discussed in Rossi et al 9 corresponds to ␦ = 0.25 and Re= 10 4 , with Re= ⌫ / ͑total circulation divided by the viscosity͒. Figure 1 shows the evolution of the total vorticity for this case.…”

Section: Emergence Of a Tripole From Perturbed Vorticesmentioning

confidence: 99%

“…20 An inviscid vortex method was used in the work of Koumoutsakos 12 on elliptical vortices, whereas Rossi et al 9 used a viscous method based on core spreading, de-scribed by Rossi. 21 The method used herein also utilizes the core spreading approach to viscosity, but applies a new concept of meshless spatial adaption; the method was fully tested and presented by Barba 22 and Barba et al…”

Section: Methodsmentioning

confidence: 99%

“…Instead, one observes the appearance of a quasisteady, rotating tripole which seems to evolve in the viscous time scale. Rossi et al 9 suggest that there is a threshold amplitude below which the flow evolves toward axisymmetry. Above the threshold, they argue, the negative portion of the m = 2 perturbation does not become mixed, due to the creation of a separatrix of the streamlines in a frame rotating with the structure.…”

Section: Introductionmentioning

confidence: 99%

“…9 It was found that, if the amplitude of the perturbation is large enough, the flow does not relax to axisymmetry. Instead, one observes the appearance of a quasisteady, rotating tripole which seems to evolve in the viscous time scale.…”

Section: Introductionmentioning

confidence: 99%

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Emergence and evolution of tripole vortices from net-circulation initial conditions

Barba

Leonard

2007

Physics of Fluids

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The emergence of coherent vortical structures is a hallmark of the evolution of two-dimensional turbulence. Two fundamental processes of this evolution have been identified in vortex merging and vortex axisymmetrization. The question of whether axisymmetrization is a universal process has recently been answered in the negative. In the linear approximation, vortices indeed become axisymmetric, due to shear-enhanced diffusion. In the case of nonlinear interactions, other outcomes are possible; in the present work, we discuss a situation in which the flow reorganizes into a tripolar vortex. By performing an extensive numerical study, spanning the parameter space, we pursue the questions of what dictates if the flow will become axisymmetric or will develop into a quasisteady tripolar vortex, and what are the stages and the time scales of the flow evolution. The initial condition in this study consists of a Gaussian monopole with a quadrupolar perturbation. The amplitude of the perturbation and the Reynolds number determine the evolution. A tripole emerges for sufficiently large amplitude of the perturbation, and we seek to find a critical amplitude that varies with Reynolds number. We make several physical observations derived from visualizing and postprocessing numerous flow simulations: looking at the decay of the perturbation with respect to viscous or shear diffusion time scales; applying mixing theory; obtaining the first few azimuthal modes of the vorticity field; and describing the long-time evolution.

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Section: Introductionsupporting

confidence: 68%

Section: Emergence Of a Tripole From Perturbed Vorticesmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Emergence and evolution of tripole vortices from net-circulation initial conditions

Barba

Leonard

2007

Physics of Fluids

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A Lagrangian vortex method for unbounded flows

Moussa¹,

Carley²

2008

Numerical Methods in Fluids

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SUMMARYA technique is presented for velocity calculations on the highly distorted node distributions typical of those found in Lagrangian vortex methods. The method solves the partial differential equation for streamfunction directly on the nodes, via a sparse, symmetric system of equations that can be solved using standard iterative solvers. When implemented in a triangulated vortex method, the technique gives computation times which scale as N 1.23 , where N is the number of nodes. The computation scheme is derived for two-dimensional problems and applied to the prediction of the evolution of perturbed multipolar vortices. Due to the numerical performance of the method, it has been possible to examine such evolution at higher and lower Reynolds numbers than have been considered in published numerical studies.

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Advances in viscous vortex methods?meshless spatial adaption based on radial basis function interpolation

Barba

Leonard

Allen

2005

Int. J. Numer. Meth. Fluids

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SUMMARYVortex methods have a history as old as ÿnite di erences. They have since faced di culties stemming from the numerical complexity of the Biot-Savart law, the inconvenience of adding viscous e ects in a Lagrangian formulation, and the loss of accuracy due to Lagrangian distortion of the computational elements. The ÿrst two issues have been successfully addressed, respectively, by the application of the fast multipole method, and by a variety of viscous schemes which will be brie y reviewed in this article. The standard method to deal with the third problem is the use of remeshing schemes consisting of tensor product interpolation with high-order kernels. In this work, a numerical study of the errors due to remeshing has been performed, as well as of the errors implied in the discretization itself using vortex blobs. In addition, an alternative method of controlling Lagrangian distortion is proposed, based on ideas of radial basis function (RBF) interpolation (brie y reviewed here). This alternative is formulated grid-free, and is shown to be more accurate than standard remeshing. In addition to high-accuracy, RBF interpolation allows core size control, either for correcting the core spreading viscous scheme or for providing a variable resolution in the physical domain. This formulation will allow in theory the application of error estimates to produce a truly adaptive spatial reÿnement technique. Proof-of-concept is provided by calculations of the relaxation of a perturbed monopole to a tripole attractor.

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Quasi-steady monopole and tripole attractors for relaxing vortices

Cited by 53 publications

References 19 publications

Emergence and evolution of tripole vortices from net-circulation initial conditions

Emergence and evolution of tripole vortices from net-circulation initial conditions

A Lagrangian vortex method for unbounded flows

Advances in viscous vortex methods?meshless spatial adaption based on radial basis function interpolation

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