Skip to main content

Advertisement

SpringerLink
Log in

Nonlinear dynamics of inertial particles in the ocean: from drifters and floats to marine debris and Sargassum

  • Feature Article
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Buoyant, finite-size, or inertial particle motion is fundamentally unlike neutrally buoyant, infinitesimally small, or Lagrangian particle motion. The de-jure fluid mechanics framework for the description of inertial particle dynamics is provided by the Maxey–Riley equation. Derived from first principles—a result of over a century of research since the pioneering work by Sir George Stokes—the Maxey–Riley equation is a Newton-type law with several forces including (mainly) flow, added mass, shear-induced lift, and drag forces. In this paper, we present an overview of recent efforts to transfer the Maxey–Riley framework to oceanography. These involved: (1) including the Coriolis force, which was found to explain behavior of submerged floats near mesoscale eddies; (2) accounting for the combined effects of ocean current and wind drag on inertial particles floating at the air–sea interface, which helped understand the formation of great garbage patches and the role of anticyclonic eddies as plastic debris traps; and (3) incorporating elastic forces, which are needed to simulate the drift of pelagic Sargassum. Insight into the nonlinear dynamics of inertial particles in every case was possible to be achieved by investigating long-time asymptotic behavior in the various Maxey–Riley equation forms, which represent singular perturbation problems involving slow and fast variables.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Adapted from [12]

Fig. 4

Adapted from [14]

Fig. 5
Fig. 6

Adapted from [14]

Fig. 7

Adapted from [13]

Fig. 8

Adapted from [65]

Fig. 9

Adapted from [57]

Fig. 10

Similar content being viewed by others

Notes

  1. If \(t\in [t_1,t_2]\subset {\mathbb {R}}\), as in applications involving measurements, \(M_0\) will not form, strictly speaking, a manifold since it will necessary include corners. Yet \(M_0\!\setminus \!\partial M_0\) represents a well-defined manifold.

References

  1. Aksamit, N., Sapsis, T., Haller, G.: Machine-learning mesoscale and submesoscale surface dynamics from Lagrangian ocean drifter trajectories. J. Phys. Oceanogr. 50, 1179–1196 (2020)

    Google Scholar 

  2. Allshouse, M.R., Ivey, G.N., Lowe, R.J., Jones, N.L., Beegle-krause, C., Xu, J., Peacock, T.: Impact of windage on ocean surface Lagrangian coherent structures. Environ. Fluid Mech. 17, 473–483 (2017)

    Google Scholar 

  3. Arnold, V.I.: Mathematical Methods of Classical Mechanics, 2nd edn. Springer, Berlin (1989)

    Google Scholar 

  4. Auton, T.R.: The lift force on a spherical body in a rotational flow. J. Fluid Mech. 183, 199–218 (1987)

    MATH  Google Scholar 

  5. Auton, T.R., Hunt, F.C.R., Prud’homme, M.: The force exerted on a body in inviscid unsteady non-uniform rotational flow. J. Fluid Mech. 197, 241–257 (1988)

    MathSciNet  MATH  Google Scholar 

  6. Babiano, A., Cartwright, J.H., Piro, O., Provenzale, A.: Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems. Phys. Rev. Lett. 84, 5,764–5,767 (2000)

    Google Scholar 

  7. Basset, A.B.: Treatise on Hydrodynamics, vol. 2, pp. 285–297. Deighton Bell, London (1888)

    Google Scholar 

  8. Beron-Vera, F.J., Miron, P.: A minimal Maxey-Riley model for the drift of Sargassum rafts. J. Fluid Mech. 98, A8 (2020)

    MathSciNet  MATH  Google Scholar 

  9. Beron-Vera, F.J.: Constrained-Hamiltonian shallow-water dynamics on the sphere. In: Velasco-Fuentes, O.U., Sheinbuam, J., Ochoa, J. (eds.) Nonlinear Processes in Geophysical Fluid Dynamics: A Tribute to the Scientific Work of Pedro Ripa, pp. 29–51. Kluwer, London (2003)

    Google Scholar 

  10. Beron-Vera, F.J., Olascoaga, M.J., Goni, G.J.: Oceanic mesoscale vortices as revealed by Lagrangian coherent structures. Geophys. Res. Lett. 35, L12603 (2008)

    Google Scholar 

  11. Beron-Vera, F.J., Wang, Y., Olascoaga, M.J., Goni, G.J., Haller, G.: Objective detection of oceanic eddies and the Agulhas leakage. J. Phys. Oceanogr. 43, 1426–1438 (2013)

    Google Scholar 

  12. Beron-Vera, F.J., Olascoaga, M.J., Haller, G., Farazmand, M., Triñanes, J., Wang, Y.: Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean. Chaos 25, 087412 (2015)

    MathSciNet  Google Scholar 

  13. Beron-Vera, F.J., Olascoaga, M.J., Lumpkin, R.: Inertia-induced accumulation of flotsam in the subtropical gyres. Geophys. Res. Lett. 43, 12228–12233 (2016)

    Google Scholar 

  14. Beron-Vera, F.J., Olascoaga, M.J., Miron, P.: Building a Maxey–Riley framework for surface ocean inertial particle dynamics. Phys. Fluids 31, 096602 (2019)

    Google Scholar 

  15. Boussinesq, J.V.: Sur la résistance quóppose un fluide indéfini au repos, sans pesanteur, au mouvement varié dúne sphére solide qu’il mouille sur toute sa surface, quand les vitesses restent bien continues et assez faibles pour que leurs carrés et produits soient négligeables. Compt. Rendu l’Acad. Sci. 100, 935–937 (1885)

    MATH  Google Scholar 

  16. Brach, L., Deixonne, P., Bernard, M.F., Durand, E., Desjean, M.C., Perez, E., van Sebille, E., ter Halle, A.: Anticyclonic eddies increase accumulation of microplastic in the north atlantic subtropical gyre. Mar. Pollut. Bull. 126, 191–196 (2018)

    Google Scholar 

  17. Breivik, O., Allen, A.A., Maisondieu, C., Olagnon, M.: Advances in search and rescue at sea. Ocean Dyn. 63, 83–88 (2013)

    Google Scholar 

  18. Cartwright, J.H.E., Feudel, U., Károlyi, G., de Moura, A., Piro, O., Tél, T.: Dynamics of finite-size particles in chaotic fluid flows. In: Thiel, M., et al. (eds.) Nonlinear Dynamics and Chaos: Advances and Perspectives, pp. 51–87. Springer, Berlin (2010)

    MATH  Google Scholar 

  19. Corrsin, S., Lumely, J.: On the equation of motion for a particle in turbulent fluid. Appl. Sci. Res. A 6, 114 (1956)

    MathSciNet  MATH  Google Scholar 

  20. Cozar, A., Echevarria, F., Gonzalez-Gordillo, J.I., Irigoien, X., Ubeda, B., Hernandez-Leon, S., Palma, A.T., Navarro, S., Garcia-de Lomas, J., andrea R, Fernandez-de Puelles ML, Duarte CM, : Plastic debris in the open ocean. Proc. Natl. Acad. Sci. USA 111, 10239–10244 (2014)

  21. Cushman-Roisin, B., Chassignet, E.P., Tang, B.: Westward motion of mesoscale eddies. J. Phys. Oceanogr. 20, 758–768 (1990)

    Google Scholar 

  22. Daitche, A., Tél, T.: Memory effects are relevant for chaotic advection of inertial particles. Phys. Rev. Lett. 107, 244501 (2011)

    Google Scholar 

  23. Daitche, A., Tél, T.: Memory effects in chaotic advection of inertial particles. New J. Phys. 16, 073008 (2014)

    Google Scholar 

  24. Dee, D.P., Uppala, S.M., Simmons, A.J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M.A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A.C.M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A.J., Haimberger, L., Healy, S.B., Hersbach, H., Holm, E.V., Isaksen, L., Kallberg, P., Kohler, M., Matricardi, M., McNally, A.P., Monge-Sanz, B.M., Morcrette, J.J., Park, B.K., Peubey, C., de Rosnay, P., Tavolato, C., Thepaut, J.N., Vitart, F.: The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q. J. R. Meteorol. Soc. 137, 553–597 (2011)

    Google Scholar 

  25. Dvorkin, Y., Paldor, N., Basdevant, C.: Reconstructing balloon trajectories in the tropical stratosphere with a hybrid model using analysed fields. Q. J. R. Meteorol. Soc. 127, 975–988 (2001)

    Google Scholar 

  26. Fenichel, N.: Persistence and smoothness of invariant manifolds for flows. Indiana Univ. Math. J. 21, 193–226 (1972)

    MathSciNet  MATH  Google Scholar 

  27. Fenichel, N.: Geometric singular perturbation theory for ordinary differential equations. J. Differ. Equ. 31, 51–98 (1979)

    MathSciNet  MATH  Google Scholar 

  28. Ganser, G.H.: A rational approach to drag prediction of spherical and nonspherical particles. Powder Technol. 77, 143–152 (1993)

    Google Scholar 

  29. Garfield, N., Collins, C.A., Paquette, R.G., Carter, E.: Lagrangian exploration of the California Undercurrent, 1992–95. J. Phys. Oceanogr. 29, 560–583 (1999)

    Google Scholar 

  30. Gatignol, R.: The faxen formulae for a rigid particle in an unsteady non-uniform stokes flow. J. Mech. Theor. Appl. 1, 143–160 (1983)

    MATH  Google Scholar 

  31. Goldstein, H.: Classical Mechanics, p. 672. Addison-Wesley, Boston (1981)

    Google Scholar 

  32. Haidvogel, D.B., Bryan, F.: Climate System Modeling, pp. 371–412. Oxford Press, Oxford (1992)

    Google Scholar 

  33. Haller, G.: An objective definition of a vortex. J. Fluid Mech. 525, 1–26 (2005)

    MathSciNet  MATH  Google Scholar 

  34. Haller, G.: Solving the inertial particle equation with memory. J. Fluid Mech. 874, 1–4 (2014)

    MathSciNet  MATH  Google Scholar 

  35. Haller, G., Beron-Vera, F.J.: Coherent Lagrangian vortices: the black holes of turbulence. J. Fluid Mech. 731, R4 (2013)

    MATH  Google Scholar 

  36. Haller, G., Beron-Vera, F.J.: Addendum to ‘Coherent Lagrangian vortices: the black holes of turbulence’. J. Fluid Mech. 755, R3 (2014)

    Google Scholar 

  37. Haller, G., Sapsis, T.: Where do inertial particles go in fluid flows? Phys. D 237, 573–583 (2008)

    MathSciNet  MATH  Google Scholar 

  38. Haller, G., Sapsis, T.: Localized instability and attraction along invariant manifolds. SIAM J. Appl. Dyn. Syst. 9, 611–633 (2010)

    MathSciNet  MATH  Google Scholar 

  39. Haller, G., Hadjighasem, A., Farazmand, M., Huhn, F.: Defining coherent vortices objectively from the vorticity. J. Fluid Mech. 795, 136–173 (2016)

    MathSciNet  MATH  Google Scholar 

  40. Haller, G., Karrasch, D., Kogelbauer, F.: Material barriers to diffusive and stochastic transport. Proc. Natl. Acad. Sci. 115, 9074–9079 (2018)

    MathSciNet  MATH  Google Scholar 

  41. Haszpra, T., Tél, T.: Volcanic ash in the free atmosphere: a dynamical systems approach. J. Phys. Conf. Ser. 333, 012008 (2011)

    Google Scholar 

  42. Henderson, K.L., Gwynllyw, D.R., Barenghi, C.F.: Particle tracking in Taylor–Couette flow. Eur. J. Mech. B. Fluids 26, 738–748 (2007)

    MathSciNet  MATH  Google Scholar 

  43. 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., Werner, F.E.: 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 (2020)

    Google Scholar 

  44. Jones, C.K.R.T.: Dynamical Systems. Lecture Notes in Mathematics. In: Geometric Singular Perturbation Theory, vol. 1609. Springer, Berlin, pp. 44–118 (1995)

  45. Kundu, P.K., Cohen, I.M., Dowling, D.R.: Fluid Mechanics, 5th edn. Academic Press, London (2012)

    MATH  Google Scholar 

  46. Langin, K.: Mysterious masses of seaweed assault Caribbean islands. Sci. Mag. (2018)

  47. Langlois, G.P., Farazmand, M., Haller, G.: Asymptotic dynamics of inertial particles with memory. J. Nonlinear Sci. 25, 1225–1255 (2015)

    MathSciNet  MATH  Google Scholar 

  48. Le Traon, P.Y., Nadal, F., Ducet, N.: An improved mapping method of multisatellite altimeter data. J. Atmos. Ocean. Technol. 15, 522–534 (1998)

    Google Scholar 

  49. Le Blond, P.H., Mysak, L.A.: Waves in the Ocean. Elsevier Oceanography Series, vol. 20. Elsevier Science, Amsterdam (1978)

  50. Lebreton, L., Slat, B., Ferrari, F., Sainte-Rose, B., Aitken, J., Marthouse, R., Hajbane, S., Cunsolo, S., Schwarz, A., Levivier, A., Noble, K., Debeljak, P., Maral, H., Schoeneich-Argent, R., Brambini, R., Reisser, J.: Evidence that the great pacific garbage patch is rapidly accumulating plastic. Sci. Rep. 8, 4666 (2018)

    Google Scholar 

  51. Lumpkin, R., Pazos, M.: Measuring surface currents with Surface Velocity Program drifters: the instrument, its data and some recent results. In: Griffa, A., Kirwan, A.D., Mariano, A., Özgökmen, T., Rossby, T. (eds.) Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics, pp. 39–67. Cambridge University Press, Cambridge (2007). chap 2

    MATH  Google Scholar 

  52. Lumpkin, R., Grodsky, S.A., Centurioni, L., Rio, M.H., Carton, J.A., Lee, D.: Removing spurious low-frequency variability in drifter velocities. J. Atmos. Ocean. Technol. 30, 353–360 (2012)

    Google Scholar 

  53. Maxey, M.R., Riley, J.J.: Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26, 883 (1983)

    MATH  Google Scholar 

  54. Medina, S.: The quantification of inertial effects on floating objects in a laboratory setting. Undergraduate Thesis, University of Miami (2020)

  55. Michaelides, E.E.: Review—The transient equation of motion for particles, bubbles and droplets. ASME J. Fluids Eng. 119, 233–247 (1997)

    Google Scholar 

  56. Miron, P., Beron-Vera, F.J., Olascoaga, M.J., Koltai, P.: Markov-chain-inspired search for MH370. Chaos Interdiscipl. J. Nonlinear Sci. 29, 041105 (2019)

    Google Scholar 

  57. Miron, P., Medina, S., Olascaoaga, M.J., Beron-Vera, F.J.: Laboratory verification of a Maxey–Riley theory for inertial ocean dynamics. Phys. Fluids 32, 071703 (2020)

    Google Scholar 

  58. Miron, P., Olascoaga, M.J., Beron-Vera, F.J., Triñanes, J., Putman, N.F., Lumpkin, R., Goni, G.J.: Clustering of marine-debris-and Sargassum-like drifters explained by inertial particle dynamics. Geophys. Res. Lett. 47, e2020GL089874 (2020)

    Google Scholar 

  59. Montabone, L.: Vortex dynamics and particle transport in barotropic turbulence. Ph.D. thesis, University of Genoa, Italy (2002)

  60. Morrow, R., Birol, F., Griffin, D.: Divergent pathways of cyclonic and anti-cyclonic ocean eddies. Geophys. Res. Lett. 31, L24311 (2004)

    Google Scholar 

  61. Nesterov, O.: Consideration of various aspects in a drift study of MH370 debris. Ocean Sci. 14, 387–402 (2018)

    Google Scholar 

  62. Niiler, P.P., Davis, R.E., White, H.J.: Water-following characteristics of a mixed layer drifter. Deep-Sea Res. 34, 1867–1881 (1987)

    Google Scholar 

  63. Nof, D.: Modeling the drift of objects floating in the sea. Abstract [PO43D-07] presented at Ocean Sciences Meeting 216, New Orleans, LA (2016)

  64. Novelli, G., Guigand, C., Cousin, C., Ryan, E.H., Laxague, N.J., Dai, H., Haus, B.K., Özgökmen, T.M.: A biodegradable surface drifter for ocean sampling on a massive scale. J. Atmos. Ocean. Technol. 34(11), 2509–2532 (2017)

    Google Scholar 

  65. Olascoaga, M.J., Beron-Vera, F.J., Miron, P., Triñanes, J., Putman, N.F., Lumpkin, R., Goni, G.J.: Observation and quantification of inertial effects on the drift of floating objects at the ocean surface. Phys. Fluids 32, 026601 (2020)

    Google Scholar 

  66. Olivieri, S., Picano, F., Sardina, G., Iudicone, D., Brandt, L.: The effect of the Basset history force on particle clustering in homogeneous and isotropic turbulence. Phys. Fluids 26, 041704 (2014)

    Google Scholar 

  67. Oseen, C.W.: Hydrodynamik. Akademische Verlagsgesellschaft, Leipzig (1927)

    MATH  Google Scholar 

  68. Pedlosky, J.: Geophysical Fluid Dynamics, 2nd edn. Springer, Berlin (1987)

    MATH  Google Scholar 

  69. Phillips, O.M.: Dynamics of the Upper Ocean. Cambridge University Press, Cambridge (1997)

    Google Scholar 

  70. Prasath, S.G., Vasa, N., Govindarajan, R.: Accurate solution method for the Maxey–Riley equation, and the effects of Basset history. J. Fluid Mech. 868, 428–460 (2019)

    MathSciNet  MATH  Google Scholar 

  71. Provenzale, A.: Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech. 31, 55–93 (1999)

    MathSciNet  Google Scholar 

  72. Provenzale, A., Babiano, A., Zanella, A.: Dynamics of Lagrangian tracers in barotropic turbulence. In: Chaté, H., Villermaux, E., Chomaz, J.M. (eds.) Mixing and Dispersion in Geophysical Contexts. NATO ASI Series (Series B: Physics), vol. 373. Springer, Boston (1998)

    Google Scholar 

  73. Riley, J.J.: Ph.D. thesis, The John Hopkins University, Baltimore, Maryland (1971)

  74. Ripa, P.: La increíble historia de la malentendida fuerza de Coriolis (The Incredible Story of the Misunderstood Coriolis Force). Fondo de Cultura Económica (1997)

  75. Ripa, P.: Caída libre y la figura de la Tierra. Rev, Mex, Fís. 41, 106–127 (1995)

    Google Scholar 

  76. Ripa, P.: Inertial oscillations and the \(\beta \)-plane approximation(s). J. Phys. Oceanogr. 27, 633–647 (1997)

    Google Scholar 

  77. Röhrs, J., Christensen, K.H., Hole, L.R., Broström, G., Drivdal, M., Sundby, S.: Observation-based evaluation of surface wave effects on currents and trajectory forecasts. Ocean Dyn. 62, 1519–1533 (2012)

    Google Scholar 

  78. Rubin, J., Jones, C.K.R.T., Maxey, M.: Settling and asymptotic motion of aerosol particles in a cellular flow field. J. Nonlinear Sci. 5, 337–358 (1995)

    MathSciNet  MATH  Google Scholar 

  79. Sapsis, T., Haller, G.: Instabilities in the dynamics of neutrally buoyant particles. Phys. Fluids 20(1), 017102 (2008)

    MATH  Google Scholar 

  80. Sapsis, T., Haller, G.: Inertial particle dynamics in a hurricane. J. Atmos. Sci. 66, 2481–2492 (2009)

    Google Scholar 

  81. Sapsis, T.P., Ouellette, N.T., Gollub, J.P., Haller, G.: Neutrally buoyant particle dynamics in fluid flows: comparison of experiments with lagrangian stochastic models. Phys. Fluids 23, 093304 (2011)

    Google Scholar 

  82. Squires, K.D., Yamazaki, H.: Preferential concentration of marine particles in isotropic turbulence. Deep-Sea Res. I 42, 1989–2004 (1995)

    Google Scholar 

  83. Steinberg, J.M., Pelland, N.A., Eriksen, C.C.: Observed evolution of a California undercurrent eddy. J. Phys. Oceanogr. 49, 649–674 (2019)

    Google Scholar 

  84. Stokes, G.G.: On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Philos. Soc. 9, 8 (1851)

    Google Scholar 

  85. Stommel, H.: The westward intensification of wind-driven ocean currents. Trans. AGU 29, 202–206 (1948)

    Google Scholar 

  86. Sudharsan, M., Brunton, S.L., Riley, J.J.: Lagrangian coherent structures and inertial particle dynamics. Phys. Rev. E 93, 033108 (2016)

    Google Scholar 

  87. Tanga, P., Provenzale, A.: Dynamics of advected tracers with varying buoyancy. Phys. D 76, 202–215 (1994)

    Google Scholar 

  88. Tanga, P., Babiano, A., Dubrulle, B., Provenzale, A.: Forming planetesimals in vortices. Icarus 121, 158–170 (1996)

    Google Scholar 

  89. Tchen, C.M.: PhD thesis, Delft, Martinus Nijhoff, The Hage (1947)

  90. Temam, R.: Inertial manifolds. Math. Intell. 12, 68–74 (1990)

    MathSciNet  MATH  Google Scholar 

  91. Trinanes, J.A., Olascoaga, M.J., Goni, G.J., Maximenko, N.A., Griffin, D.A., Hafner, J.: Analysis of flight MH370 potential debris trajectories using ocean observations and numerical model results. J. Oper. Oceanogr. 9, 126–138 (2016)

    Google Scholar 

  92. van Sebille, E., Griffies, S.M., Abernathey, R., Adams, T.P., Berloff, P., Biastoch, A., Blanke, B., Chassignet, E.P., Cheng, Y., Cotter, C.J., Deleersnijder, E., Döös, K., Drake, H.F., Drijfhout, S., Gary, S.F., Heemink, A.W., Kjellsson, J., Koszalka, I.M., Lange, M., Lique, C., MacGilchrist, G.A., Marsh, R., Adame, C.G.M., McAdam, R., Nencioli, F., Paris, C.B., Piggott, M.D., Polton, J.A., Rühs, S., Shah, S.H., Thomas, M.D., Wang, J., Wolfram, P.J., Zanna, L., Zika, J.D.: Lagrangian ocean analysis: fundamentals and practices. Ocean Modell. 121, 49–75 (2018)

  93. Wang, M., Hu, C., Barnes, B., Mitchum, G., Lapointe, B., Montoya, J.P.: The great Atlantic Sargassum belt. Science 365, 83–87 (2019)

    Google Scholar 

  94. Wooding, C.M., Furey, H.H., Pacheco, M.A.: RAFOS float processing at the Woods Hole Oceanographic Institution. Technical report, Woods Hole Oceanographic Institution (2015)

  95. Woodward, J.R., Pitchford, J.W., Bees, M.A.: Physical flow effects can dictate plankton population dynamics. J. R. Soc. Interface 16, 20190247 (2019)

    Google Scholar 

  96. Zeugin, T., Krol, Q., Fouxon, I., Holzner, M.: Sedimentation of snow particles in still air in Stokes regime. Geophys. Res. Lett. 47, e2020GL087832 (2020)

    Google Scholar 

Download references

Acknowledgements

The constructive criticism of two anonymous reviewers led to improvements to this paper. I want to acknowledge the influence exerted by Gustavo Goñi on my career for triggering my interest in nonlinear dynamics while I was an undergraduate student of oceanography, and by Paco Villaverde, Roberto Delellis, the late Pedro Ripa, and Mike Brown for conveying subsequent sustain to it. Doron Nof’s presentation at the 2016 Ocean Science Meeting [63] provided inspiration for the work that led to the derivation of the BOM equation in collaboration with Maria Olascoaga and Philippe Miron, with whom I am in debt for the benefit of many discussions on inertial ocean dynamics. I thank George Haller and Chris Jones for clarifying comments on geometric singular perturbation theory. Remark 14 is due to Mohammad Farazmand. Remark 27 was brought to my attention by Tamás Tél. This work builds on lectures I imparted at the CISM–ECCOMAS International Summer School on “Coherent Structures in Unsteady Flows: Mathematical and Computational Methods,” Udine, Italy, June 3–7, 2019, organized by George Haller. Support for the work overviewed here was provided by CONACyT–SENER (Mexico) grant 201441, the Gulf of Mexico Research Initiative, and the University of Miami’s Cooperative Institute for Marine and Atmospheric Science.

Author information

Authors and Affiliations

  1. Department of Atmospheric Sciences, Rosenstiel School of Marine and Atmospheric Science, University of Miami, Miami, FL, 3349, USA

    Francisco J. Beron-Vera

Authors
  1. Francisco J. Beron-Vera
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francisco J. Beron-Vera.

Ethics declarations

Conflict of interest

The author declares that he has no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Beron-Vera, F.J. Nonlinear dynamics of inertial particles in the ocean: from drifters and floats to marine debris and Sargassum. Nonlinear Dyn 103, 1–26 (2021). https://doi.org/10.1007/s11071-020-06053-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-06053-z

Keywords

Search

Navigation