Quantifying transport in numerically generated velocity fields

Miller, Patrick D.; Jones, Christopher K. R. T.; Rogerson, A. M.; Pratt, Lawrence J.

doi:10.1016/s0167-2789(97)00115-2

Cited by 101 publications

(98 citation statements)

References 20 publications

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“…In such cases the advection dynamics is not chaotic, and hence beyond the scope of the present article; however, concepts of dynamical systems can usefully be applied to characterize such advection. 44 The motion of individual particles in random maps is as ''random looking'' as that of diffusive particles. By considering however ensembles of particles which are in this case subjected to the same realization of the random flow, one can uniquely define chaos characteristics ͑like , , and K 0 ), which are to be treated as averages over all realizations ͑or over sufficiently long times͒.…”

Section: ͑12͒mentioning

confidence: 99%

Chaotic advection, diffusion, and reactions in open flows

Tél

Károlyi

Péntek

et al. 2000

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity.

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Section: ͑12͒mentioning

confidence: 99%

Chaotic advection, diffusion, and reactions in open flows

Tél

Károlyi

Péntek

et al. 2000

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…This observation inspires us to understand and predict different evolution patterns of a fluid parcel, depending on its initial location and time of release. Such patterns are known to be delineated by repelling material lines or finite-time stable manifolds [16,17,18,19,20,21]. Here we shall use a recently developed nonlinear technique, Direct Lyapunov Exponent [6] (DLE) analysis, which identifies repelling or attracting material lines in velocity data as local maximizing curves of material stretching.…”

Section: Numerical Experimentsmentioning

confidence: 99%

Lagrangian Structures in Very High-Frequency Radar Data and Optimal Pollution Timing

Lekien¹

2003

AIP Conference Proceedings

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Abstract. Very High-frequency (VHF) radar technology produces detailed surface velocity maps near the surface of coastal waters. The use of measured velocity data in environmental prediction, however, has remained unexplored. In this paper, we uncover a striking flow structure in coastal radar observations along the coast of Florida. This structure governs the spread of organic contaminants or passive drifters released in the area. We compute the Lyapunov exponents of the VHF radar data to determine optimal release windows in which contaminants are advected efficiently away from the coast and we show that a VHF radar-based pollution release scheme using the hidden flow structure reduces the effect of industrial pollution in the coastal environment.

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“…The dynamics are then governed by an advection-diffusion equation for the scalar potential vorticity. Such eddy diffusivity has significant consequences in the advection of passive scalars, in general, fluids, and has been addressed in statistical , numerical (Miller et al, 1997; and theoretical (Fannjiang and Papanicolaou, 1994) senses. Bounds on the eddy diffusivity (Fannjiang and Papanicolaou, 1994;Biferale et al, 1995;Mezić et al, 1996), and descriptions of chaotic motion (Rom-Kedar and Poje, 1999;Klapper, 1992;Jones, 1994), are several features of interest.…”

Section: Eddies and Their Stabilitymentioning

confidence: 99%

mentioning

confidence: 99%

Diffusive draining and growth of eddies

Balasuriya

Jones

2001

Nonlin. Processes Geophys.

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Abstract. The diffusive effect on barotropic models of mesoscale eddies is addressed, using the Melnikov method from dynamical systems. Simple geometric criteria are obtained, which identify whether a given eddy grows or drains out, under a diffusive (and forcing) perturbation on a potential vorticity conserving flow. Qualitatively, the following are shown to be features conducive to eddy growth (and, thereby, stability in a specific sense): (i) large radius of curvature of the eddy boundary, (ii) potential vorticity contours more tightly packed within the eddy than outside, (iii) acute eddy pinchangle, (iv) small potential vorticity gradient across the eddy boundary, and (v) meridional wind forcing, which increases in the northward direction. The Melnikov approach also suggests how tendrils (filaments) could be formed through the breaking of the eddy boundary, as a diffusion-driven advective process. Eddies and their stabilityRings (or eddies) are significant oceanographic features which contribute considerably to fluid transport in the ocean. In particular, mesoscale (of the order of 100 km) rings formed near the Gulf Stream sometimes survive as coherent structures for periods of up to one year (Richardson, 1983). Submesoscale (of the order of 10 km ) eddies may also be long-lived, and we address both mesoscale and submesoscale eddies in the present work. The observational persistence of such eddies has led to theoretical (Flierl, 1988;Helfrich and Send, 1988;Dewar and Gailliard, 1994;Dewar and Killworth, 1995;Paldor, 1999), numerical (Helfrich and Send, 1988;Dewar and Gailliard, 1994;Dewar and Killworth, 1995;Dewar et al., 1999;Paldor, 1999;McWilliams et al., 1986) and experimental (Voropayev et al., 1999) analyses of stability. Since many results indicate that eddies would tend to be unstable, explaining their persistence remains anCorrespondence to: S. Balasuriya (sanjeeva.balasuriya@oberlin.edu) active area of research. In this paper, we address a particular aspect of stability of such eddies, which reflects the effect of small diffusivity on the eddy boundary.Though characterised by swirling fluid motions, eddies are often identified experimentally through Eulerian contour plots of temperature, height, salinity, or potential vorticity fields, usually obtained from two-dimensional satellite imaging data (for a review and pictures of contours, see Richardson, 1983), or from numerical schemes. Since fluid motion in the upper ocean tends to remain on surfaces of constant temperature (resp. salinity, potential vorticity, etc), rotational motion results around maxima/minima points of the appropriate scalar field, thereby forming a 'ring' (or vortical motion) in the expected sense. Often, tendrils (or filaments) are seen to emanate from these eddies, which appear to wrap around the eddy (see Fig. 4 in the experimental paper by Voropayev et al., 1999, for example).The dynamics governing the behaviour of such eddies is assumed to be close to a two-dimensional incompressible flow in which potential vorticity is con...

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Quantifying transport in numerically generated velocity fields

Cited by 101 publications

References 20 publications

Chaotic advection, diffusion, and reactions in open flows

Chaotic advection, diffusion, and reactions in open flows

Lagrangian Structures in Very High-Frequency Radar Data and Optimal Pollution Timing

Diffusive draining and growth of eddies

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