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Dynamics of passive scalars and tracers advected by a two-dimensional tripolar vortex

  • PAULO J. S. A. FERREIRA de SOUSA (a1) (a2) and JOSÉ C. F. PEREIRA (a2)
Abstract

The dynamics of passive scalars and tracers during the formation and subsequent persistence of a laminar tripolar vortex, obtained through an unstable monopolar vortex seeded with a k = 2 azimuthal perturbation, is investigated. Two-dimensional direct numerical simulations of passive scalars with Schmidt numbers Sc = 0.1, 1, 10 and 100 are performed. The scalar variance for the four cases is analysed, as well as the different dispersion patterns up to 10 times greater than the time for formation of the tripolar vortex. During the formation of the tripole, an accelerated scalar dissipation is observed. That dissipation is connected to the advection-dominated processes associated with the growth of the perturbation mode. During that process, the patterns of mixing of the different passive scalars are very much the same as for vorticity. This stage of accelerated dissipation is preceded and followed by stages of diffusion-dominated scalar dissipation. Passive Lagrangian tracers are used to explore the transport of fluid elements during the evolution, and to provide a detailed view of the tripolar vortex formation and behaviour for longer times. Chaotic mixing was studied by examining patterns of spatial variation of finite-time Lyapunov exponents. As the perturbation grows and the tripolar vortex is formed, two large regions of regular flow, divided by a region of chaotic flow, form for each satellite. When the tripole is fully formed, it is composed of three distinct regular regions, corresponding to the core of negative vorticity and the two satellites of positive vorticity. The comparison between the evolution for vorticity, concentration, randomly distributed particles and Lyapunov exponents shows that transport occurs mainly in the regions of chaotic flow that surround the tripolar vortex after its formation. For longer times, both the chaotic/regular flow interfaces and the vorticity gradients are responsible for the integrity of the tripolar system.

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Email address for correspondence: ferreiradesousa@gmail.com
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E. R. Abraham & M. M. Bowen 2002 Chaotic stirring by a mesoscale surface-ocean flow. Chaos 12, 373381.

X. Carton , G. R. Flierl & L. Polvani 1989 The generation of tripoles from unstable axisymmetric isolated vortex structures. Europhys. Lett. 9, 339344.

P. J. S. A. Ferreira de Sousa & J. C. F. Pereira 2005 Fourth and tenth order compact finite difference solutions of perturbed circular vortex flows. Intl J. Numer. Fluids 49, 603618.

G. J. F. van Heijst & R. C. Kloosterziel 1989 Tripolar vortices in a rotating fluid. Nature 338, 569571.

L. Kuznetsov & G. M. Zaslavsky 1998 Regular and chaotic advection in the flow field of a three-vortex system. Phys. Rev. E 58, 73307349.

B. Legras , P. Santangelo & R. Benzi 1988 High-resolution numerical experiments for forced two-dimensional turbulence. Europhys. Lett. 5, 3742.

C. E. Leith 1984 Minimum enstrophy vortices. Phys. Fluids 27, 13881395.

J. M. Ottino 1990 Mixing, chaotic advection, and turbulence. Annu. Rev. Fluid Mech. 22, 207254.

R. T. Pierrehumbert 1991 Large-scale horizontal mixing in planetary atmospheres. Phys. Fluids A 3, 12501260.

R. T. Pierrehumbert & H. Yang 1993 Global chaotic mixing on isentropic surfaces. J. Atmos. Sci. 50, 24622480.

R. D. Pingree & B. LeCann 1992 Anticyclonic eddy x91 in the southern bay of Biscay, May 1991 to February 1992. J. Geophys. Res. 97, 1435314367.

J. Vranjes , G. Maric & P. K. Shukla 1999 aTripolar vortices and vortex chains in dusty plasma Phys. Lett. A 258, 317322.

J. Vranjes , L. Stenflo & P. K. Shukla 1999 bTripolar vortices and vortex chains in a shallow atmosphere. Phys. Lett. A 267, 184187.

Z. Warhaft 2000 Passive scalars in turbulent flows. Annu. Rev. Fluid Mech. 32, 203240.

D. Waugh , E. R. Abraham & M. M. Bowen 2006 Spatial variations of stirring in the surface ocean: a case study of the Tasman sea. J. Phys. Oceanogr. 36, 526542.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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