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

Barba, L. A. and Leonard, A. (2007) Emergence and evolution of tripole vortices from net-circulation initial conditions. Physics of Fluids, 19 (1). Art. No. 017101. ISSN 1070-6631.

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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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Additional Information:©2007 American Institute of Physics (Received 13 April 2006; accepted 16 November 2006; published online 3 January 2007) Computing time provided by the Laboratory for Advanced Computation in the Mathematical Sciences (LCMS) of the University of Bristol ( Thanks to the PETSc team for prompt and always helpful tech support. L.A.B. thanks S. Le Dizès and E. Villermaux for discussions and correspondence. L.A.B.’s travel was possible thanks to a Nuffield Foundation Award.
Subject Keywords:vortices; turbulent diffusion; shear turbulence; flow simulation; mixing; numerical analysis
Issue or Number:1
Record Number:CaltechAUTHORS:BARpof07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7015
Deposited By: Archive Administrator
Deposited On:05 Jan 2007
Last Modified:02 Oct 2019 23:38

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