Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T12:34:47.634Z Has data issue: false hasContentIssue false
  • English
  • Français

A minimal Maxey–Riley model for the drift of Sargassum rafts

Published online by Cambridge University Press:  06 October 2020

F. J. Beron-Vera Open the ORCID record for F. J. Beron-Vera [Opens in a new window]  and
P. Miron Open the ORCID record for P. Miron [Opens in a new window]
F. J. Beron-Vera*
Affiliation:
Department of Atmospheric Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, USA
P. Miron
Affiliation:
Department of Atmospheric Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Inertial particles (i.e. with mass and of finite size) immersed in a fluid in motion are unable to adapt their velocities to the carrying flow and thus they have been the subject of much interest in fluid mechanics. In this paper we consider an ocean setting with inertial particles elastically connected forming a network that floats at the interface with the atmosphere. The network evolves according to a recently derived and validated Maxey–Riley equation for inertial particle motion in the ocean. We rigorously show that, under sufficiently calm wind conditions, rotationally coherent quasigeostrophic vortices (which have material boundaries that resist outward filamentation) always possess finite-time attractors for elastic networks if they are anticyclonic, while if they are cyclonic provided that the networks are sufficiently stiff. This result is supported numerically under more general wind conditions and, most importantly, is consistent with observations of rafts of pelagic Sargassum, for which the elastic inertial networks represent a minimal model. Furthermore, our finding provides an effective mechanism for the long range transport of Sargassum, and thus for its connectivity between accumulation regions and remote sources.

JFM classification

Mixing: Chaotic advection Geophysical and Geological Flows: Ocean processes
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 904 , 10 December 2020 , A8
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aksamit, N., Sapsis, T. & Haller, G. 2020 Machine-learning mesoscale and submesoscale surface dynamics from Lagrangian ocean drifter trajectories. J. Phys. Oceanogr. 50, 1179–1196.CrossRefGoogle Scholar
Arnold, V. I. 1989 Mathematical Methods of Classical Mechanics, 2nd edn. Springer.CrossRefGoogle Scholar
Auton, T. R. 1987 The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218.CrossRefGoogle Scholar
Auton, T. R., Hunt, F. C. R. & Prud'homme, M. 1988 The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257.CrossRefGoogle Scholar
Babiano, A., Cartwright, J. H., Piro, O. & Provenzale, A. 2000 Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems. Phys. Rev. Lett. 84, 5764–5767.CrossRefGoogle Scholar
Bahar, I., Atilgan, A. R. & Erman, B. 1997 Direct evaluation of thermal fluctuations in proteins using a single-parameter harmonic potential. Folding and Design 2 (3), 173–181.CrossRefGoogle ScholarPubMed
Beron-Vera, F. J., Hadjighasem, A., Xia, Q., Olascoaga, M. J. & Haller, G. 2019 a Coherent Lagrangian swirls among submesoscale motions. Proc. Natl Acad. Sci. USA 116, 18251–18256.CrossRefGoogle ScholarPubMed
Beron-Vera, F. J., Olascoaga, M. J. & Goni, G. J. 2008 Oceanic mesoscale vortices as revealed by Lagrangian coherent structures. Geophys. Res. Lett. 35, L12603.CrossRefGoogle Scholar
Beron-Vera, F. J., Olascoaga, M. J., Haller, G., Farazmand, M., Triñanes, J. & Wang, Y. 2015 Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean. Chaos 25, 087412.CrossRefGoogle ScholarPubMed
Beron-Vera, F. J., Olascoaga, M. J. & Lumpkin, R. 2016 Inertia-induced accumulation of flotsam in the subtropical gyres. Geophys. Res. Lett. 43, 12228–12233.CrossRefGoogle Scholar
Beron-Vera, F. J., Olascoaga, M. J. & Miron, P. 2019 b Building a Maxey–Riley framework for surface ocean inertial particle dynamics. Phys. Fluids 31, 096602.CrossRefGoogle Scholar
Beron-Vera, F. J., Olascaoaga, M. J., Wang, Y., Triñanes, J. & Pérez-Brunius, P. 2018 Enduring Lagrangian coherence of a loop current ring assessed using independent observations. Sci. Rep. 8, 11275.CrossRefGoogle ScholarPubMed
Bird, R. B., Curtiss, C. F., Armstrong, R. C. & Hassager, O. 1977 Dynamics of Polymeric Liquids, vol. 2. John Wiley and Sons.Google Scholar
Brach, L., Deixonne, P., Bernard, M.-F., Durand, E., Desjean, M.-C., Perez, E., van Sebille, E. & ter Halle, A. 2018 Anticyclonic eddies increase accumulation of microplastic in the north atlantic subtropical gyre. Mar. Pollut. Bull. 126, 191–196.CrossRefGoogle ScholarPubMed
Cartwright, J. H. E., Feudel, U., Károlyi, G., de Moura, A., Piro, O. & Tél, T. 2010 Dynamics of finite-size particles in chaotic fluid flows. In Nonlinear Dynamics and Chaos: Advances and Perspectives (eds. Thiel, M., et al. ), pp. 51–87. Springer-Verlag.CrossRefGoogle Scholar
Chelton, D. B., Schlax, M. G. & Samelson, R. M. 2011 Global observations of nonlinear mesoscale eddies. Prog. Oceanogr. 91, 167–216.CrossRefGoogle Scholar
Cushman-Roisin, B., Chassignet, E. P. & Tang, B. 1990 Westward motion of mesoscale eddies. J. Phys. Oceanogr. 20, 758–768.2.0.CO;2>CrossRefGoogle Scholar
D'Asaro, E. A., Shcherbina, A. Y., Klymak, J. M., Molemaker, J., Novelli, G., Guigand, C. M., Haza, A. C., Haus, B. K., Ryan, E. H., Jacobs, G. A., et al. 2018 Ocean convergence and the dispersion of flotsam. Proc. Natl Acad. Sci. 115, 1162–1167.CrossRefGoogle ScholarPubMed
Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., et al. 2011 The ERA-interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 137, 553–597.CrossRefGoogle Scholar
Farazmand, M. & Haller, G. 2016 Polar rotation angle identifies elliptic islands in unsteady dynamical systems. Physica D 315, 1–12.CrossRefGoogle Scholar
Fenichel, N. 1979 Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equ. 31, 51–98.CrossRefGoogle Scholar
Fu, L. L, Chelton, D. B., Le Traon, P.-Y. & Morrow, R. 2010 Eddy dynamics from satellite altimetry. Oceanography 23, 14–25.CrossRefGoogle Scholar
Goldstein, H. 1981 Classical Mechanics, p. 672, Addison-Wesley.Google Scholar
Gordon, A. 1986 Interocean exchange of thermocline water. J. Geophys. Res. 91, 5037–5046.CrossRefGoogle Scholar
Gower, J., King, S. & Goncalves, P. 2008 Global monitoring of plankton blooms using MERIS MCI. Intl J. Remote Sens. 29, 6209–6216.CrossRefGoogle Scholar
Gower, J., Young, E. & King, S. 2013 Satellite images suggest a new Sargassum source region in 2011. Remote Sens. Lett. 4, 764–773.CrossRefGoogle Scholar
Graef, F. 1998 On the westward translation of isolated eddies. J. Phys. Oceanogr. 28, 740–745.2.0.CO;2>CrossRefGoogle Scholar
Haller, G. 2016 Climate, black holes and vorticity: how on earth are they related? SIAM News 49, 1–2.Google Scholar
Haller, G. & Beron-Vera, F. J. 2013 Coherent Lagrangian vortices: the black holes of turbulence. J. Fluid Mech. 731, R4.CrossRefGoogle Scholar
Haller, G. & Beron-Vera, F. J. 2014 Addendum to ‘Coherent Lagrangian vortices: the black holes of turbulence’. J. Fluid Mech. 755, R3.CrossRefGoogle Scholar
Haller, G., Hadjighasem, A., Farazmand, M. & Huhn, F. 2016 Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136–173.CrossRefGoogle Scholar
Haller, G., Karrasch, D. & Kogelbauer, F. 2018 Material barriers to diffusive and stochastic transport. Proc. Natl Acad. Sci. 115, 9074–9079.CrossRefGoogle ScholarPubMed
Haller, G. & Sapsis, T. 2008 Where do inertial particles go in fluid flows? Physica D 237, 573–583.CrossRefGoogle Scholar
Haller, G. & Yuan, G. 2000 Lagrangian coherent structures and mixing in two-dimensional turbulence. Physica D 147, 352–370.CrossRefGoogle Scholar
Henderson, K. L., Gwynllyw, D. R. & Barenghi, C. F. 2007 Particle tracking in Taylor–Couette flow. Eur. J. Mech. (B/Fluids) 26, 738–748.CrossRefGoogle Scholar
Johns, E. M., Lumpkin, R., Putman, N. F., Smith, R. H., Muller-Karger, F. E., Rueda-Roa, D. T., Hu, C., Wang, M., Brooks, M. T., Gramer, L. J., et al. 2020 The establishment of a pelagic sargassum population in the tropical atlantic: biological consequences of a basin-scale long distance dispersal event. Prog. Oceanogr. 182, 102269.CrossRefGoogle Scholar
Jones, C. K. R. T. 1995 Geometric singular perturbation theory. In Dynamical Systems, Lecture Notes in Mathematics, vol. 1609, pp. 44–118. Springer-Verlag.CrossRefGoogle Scholar
Langin, K. 2018 Mysterious masses of seaweed assault Caribbean islands. Sci. Mag. 360 (6394), 1157–1158.Google Scholar
Maxey, M. R. & Riley, J. J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883.CrossRefGoogle Scholar
McWilliams, J. C. 2016 Submesoscale currents in the ocean. Proc. R. Soc. Lond. A 472, 20160117.Google ScholarPubMed
Michaelides, E. E. 1997 Review – the transient equation of motion for particles, bubbles and droplets. Trans. ASME: J. Fluids Engng 119, 233–247.Google Scholar
Miron, P., Medina, S., Olascaoaga, M. J. & Beron-Vera, F. J. 2020 Laboratory verification of a Maxey–Riley theory for inertial ocean dynamics. Phys. Fluids 32, 071703.CrossRefGoogle Scholar
Montabone, L. 2002 Vortex dynamics and particle transport in barotropic turbulence. PhD thesis, University of Genoa, Italy.Google Scholar
Morrow, R., Birol, F. & Griffin, D. 2004 Divergent pathways of cyclonic and anti-cyclonic ocean eddies. Geophys. Res. Lett. 31, L24311.CrossRefGoogle Scholar
Nof, D. 1981 On the $\beta$-induced movement of isolated baroclinic eddies. J. Phys. Oceanogr. 11, 1662–1672.2.0.CO;2>CrossRefGoogle Scholar
Ody, A., Thibaut, T., Berline, L., Changeux, T., Andre, J.-M., Chevalier, C., Blanfune, A., Blanchot, J., Ruitton, S., Stiger-Pouvreau, V., et al. 2019 From In Situ to satellite observations of pelagic Sargassum distribution and aggregation in the Tropical North Atlantic Ocean. PLoS ONE 14, 1–29.CrossRefGoogle ScholarPubMed
Olascoaga, M. J., Beron-Vera, F. J., Miron, P., Triñanes, J., Putman, N. F., Lumpkin, R. & Goni, G. J. 2020 Observation and quantification of inertial effects on the drift of floating objects at the ocean surface. Phys. Fluids 32, 026601.CrossRefGoogle Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics, 2nd edn. Springer.CrossRefGoogle Scholar
Picardo, J. R., Vincenzi, D., Pal, N. & Ray, S. S. 2018 Preferential sampling of elastic chains in turbulent flows. Phys. Rev. Lett. 121, 244501.CrossRefGoogle ScholarPubMed
Provenzale, A. 1999 Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech. 31, 55–93.CrossRefGoogle Scholar
Putman, N. F., Goni, G. J., Gramer, L. J., Hu, C., Johns, E. M., Trinanes, J. & Wang, M. 2018 Simulating transport pathways of pelagic Sargassum from the Equatorial Atlantic into the Caribbean Sea. Prog. Oceanogr. 165, 205–214.CrossRefGoogle Scholar
Ripa, P. 2000 Effects of the Earth's curvature on the dynamics of isolated objects. Part II: the uniformly translating vortex. J. Phys. Oceanogr. 30, 2504–2514.2.0.CO;2>CrossRefGoogle Scholar
Sapsis, T. & Haller, G. 2010 Clustering criterion for inertial particles in two-dimensional time-periodic and three-dimensional steady flows. Chaos 20, 017515.CrossRefGoogle ScholarPubMed
Sapsis, T. P., Ouellette, N. T., Gollub, J. P. & Haller, G. 2011 Neutrally buoyant particle dynamics in fluid flows: comparison of experiments with Lagrangian stochastic models. Phys. Fluids 23, 093304.CrossRefGoogle Scholar
Talley, L. D., Pickard, G. L., Emery, W. J. & Swift, J. H. 2011 Introduction to Descriptive Physical Oceanography, 6th edn. Academic Press.CrossRefGoogle Scholar
Tanga, P. & Provenzale, A. 1994 Dynamics of advected tracers with varying buoyancy. Physica D 76, 202–215.CrossRefGoogle Scholar
Tel, T., Kadi, L., Janosi, I. M. & Vincze, M. 2018 Experimental demonstration of the water-holding property of three-dimensional vortices. EPL 123, 44001.CrossRefGoogle Scholar
Tel, T., Vincze, M. & Janosi, I. M. 2020 Vortices capturing matter: a classroom demonstration. Phys. Educ. 55, 015007.CrossRefGoogle Scholar
Wang, M., Hu, C., Barnes, B. B., Mitchum, G., Lapointe, B. & Montoya, J. P. 2019 The great Atlantic Sargassum belt. Science 365, 83–87.CrossRefGoogle ScholarPubMed
Wang, Y., Olascoaga, M. J. & Beron-Vera, F. J. 2015 Coherent water transport across the South Atlantic. Geophys. Res. Lett. 42, 4072–4079.CrossRefGoogle Scholar
Wang, Y., Olascoaga, M. J. & Beron-Vera, F. J. 2016 The life cycle of a coherent Lagrangian Agulhas ring. J. Geophys. Res. 121, 3944–3954.CrossRefGoogle Scholar