The strain rate in evolutions of (elliptical) vortices in inviscid two-dimensional flows

Vosbeek, Pwc Pauline; Heijst, van Gjf Gert-Jan; Mogendorff, VP Veronique

doi:10.1063/1.1409536

Cited by 6 publications

(2 citation statements)

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“…29 An identical seed of half that value was observed by other workers to saturate without causing fission. 30 These results are consistent with ours if one infers that the m =2 seeds also contained a m = −4 component whose nonlinear instability was responsible for the subsequent fission and near fission.…”

Section: Nonlinear Fission Boundary Of M =−4supporting

confidence: 91%

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The evolution of Kirchhoff elliptic vortices

Mitchell¹,

Rossi

2008

Physics of Fluids

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A Kirchhoff elliptic vortex is a two-dimensional elliptical region of uniform vorticity embedded in an inviscid, incompressible, and irrotational fluid. By using analytic theory and contour dynamics simulations, we describe the evolution of perturbed Kirchhoff vortices by decomposing solutions into constituent linear eigenmodes. With small amplitude perturbations, we find excellent agreement between the short time dynamics and the predictions of linear analytic theory. Elliptical vortices must have aspect ratios less than a∕b=3 to be completely stable. At late times, unstable perturbations evolve to states consisting of filaments surrounding and connecting one or more separate vortex core regions. Even modes have two different evolution paths accessible to them, dependent on the initial phase. Ellipses can first fission into more than one separate region when a∕b=6.046, from the negative branch m=4 mode. Increasing the perturbation amplitude can result in nonlinear instability, while the perturbation is still small relative to any vortex dimension. For the lowest m modes, we quantify the transition from linear to nonlinear behavior.

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Section: Nonlinear Fission Boundary Of M =−4supporting

confidence: 91%

“…We are able to make limited comparisons with earlier studies where large perturbations were also used. 29,30 In Sec. V, we state our conclusions and discuss their possible relevance to fluid vortices with more realistic characteristics.…”

Section: Organization Of This Papermentioning

confidence: 99%