We present results from an experiment designed to better understand the mechanism by which ocean currents and winds control flotsam drift. The experiment consisted of deploying in the Florida Current and subsequent satellite tracking of specially designed drifting buoys of various sizes, buoyancies, and shapes. We explain the differences in the trajectories described by the special drifters as a result of their inertia, primarily buoyancy, which constrains the ability of the drifters to adapt their velocities to instantaneous changes in the ocean current and wind that define the carrying flow field. Our explanation of the observed behavior follows from the application of a recently proposed Maxey–Riley theory for the motion of finite-sized particles floating on the ocean surface. The nature of the carrying flow and the domain of validity of the theory are clarified, and a closure proposal is made to fully determine its parameters in terms of the carrying fluid system properties and inertial particle characteristics.
REFERENCES
1.
Ø.
Breivik
, A. A.
Allen
, C.
Maisondieu
, and M.
Olagnon
, “Advances in search and rescue at sea
,” Ocean Dyn.
63
, 83
–88
(2013
).2.
L.
Bellomo
, A.
Griffa
, S.
Cosoli
, P.
Falco
, R.
Gerin
, I.
Iermano
, A.
Kalampokis
, Z.
Kokkini
, A.
Lana
, M.
Magaldi
, I.
Mamoutos
, C.
Mantovani
, J.
Marmain
, E.
Potiris
, J.
Sayol
, Y.
Barbin
, M.
Berta
, M.
Borghini
, A.
Bussani
, L.
Corgnati
, Q.
Dagneaux
, J.
Gaggelli
, P.
Guterman
, D.
Mallarino
, A.
Mazzoldi
, A.
Molcard
, A.
Orfila
, P.-M.
Poulain
, C.
Quentin
, J.
Tintoré
, M.
Uttieri
, A.
Vetrano
, E.
Zambianchi
, and V.
Zervakis
, “Toward an integrated HF radar network in the Mediterranean Sea to improve search and rescue and oil spill response: The TOSCA project experience
,” J. Oper. Oceanogr.
8
, 95
–107
(2015
).3.
M. T.
Brooks
, V. J.
Coles
, and W. C.
Coles
, “Inertia influences pelagic Sargassum advection and distribution
,” Geophys. Res. Lett.
46
, 2610
–2618
, (2019
).4.
M.
Wang
, C.
Hu
, B.
Barnes
, G.
Mitchum
, B.
Lapointe
, and J. P.
Montoya
, “The great Atlantic Sargassum belt
,” Science
365
, 83
–87
(2019
).5.
K. L.
Law
, S.
Morét-Ferguson
, N. A.
Maximenko
, G.
Proskurowski
, E. E.
Peacock
, J.
Hafner
, and C. M.
Reddy
, “Plastic accumulation in the North Atlantic subtropical gyre
,” Science
329
, 1185
–1188
(2010
).6.
A.
Cozar
, F.
Echevarria
, J. I.
Gonzalez-Gordillo
, X.
Irigoien
, B.
Ubeda
, S.
Hernandez-Leon
, A. T.
Palma
, S.
Navarro
, J.
Garcia-de Lomas
, A.
Ruiz
, M. L.
Fernandez-de Puelles
, and C. M.
Duarte
, “Plastic debris in the open ocean
,” Proc. Natl. Acad. Sci. U. S. A.
111
, 10239
–10244
(2014
).7.
J. A.
Trinanes
, M. J.
Olascoaga
, G. J.
Goni
, N. A.
Maximenko
, D. A.
Griffin
, and J.
Hafner
, “Analysis of flight MH370 potential debris trajectories using ocean observations and numerical model results
,” J. Oper. Oceanogr.
9
, 126
–138
(2016
).8.
P.
Miron
, F. J.
Beron-Vera
, M. J.
Olascoaga
, and P.
Koltai
, “Markov-chain-inspired search for MH370
,” Chaos
29
, 041105
(2019
).9.
I.
Rypina
, S. R.
Jayne
, S.
Yoshida
, A. M.
Macdonald
, E.
Douglas
, and K.
Buesseler
, “Short-term dispersal of Fukushima-derived radionuclides off Japan: Modeling efforts and model-data intercomparison
,” Biogeosciences
10
, 4973
–4990
(2013
).10.
J. P.
Matthews
, L.
Ostrovsky
, Y.
Yoshikawa
, S.
Komori
, and H.
Tamura
, “Dynamics and early post-tsunami evolution of floating marine debris near Fukushima Daiichi
,” Nat. Geosci.
10
, 598
–603
(2017
).11.
S.
Szanyi
, J. V.
Lukovich
, and D. G.
Barber
, “Lagrangian analysis of sea-ice dynamics in the Arctic Ocean
,” Polar Res.
35
, 30778
(2016
).12.
C. B.
Paris
, S. A.
Murawski
, M. J.
Olascoaga
, A. C.
Vaz
, I.
Berenshtein
, P.
Miron
, and F. J.
Beron-Vera
, “Connectivity of the Gulf of Mexico continental shelf fish populations and implications of simulated oil spills
,” in Scenarios and Responses to Future Deep Oil Spills: Fighting the Next War
, edited by S. A.
Murawski
, C. H.
Ainsworth
, S.
Gilbert
, D. J.
Hollander
, C. B.
Paris
, M.
Schlüter
, and D. L.
Wetzel
(Springer Nature
, Switzerland
, 2020
), pp. 369
–389
.13.
N.
Putman
, R.
Lumpkin
, A.
Sacco
, and K.
Mansfield
, “Passive drift or active swimming in marine organisms?
,” Proc. R. Soc. B
283
, 20161689
(2016
).14.
M. J.
Olascoaga
and G.
Haller
, “Forecasting sudden changes in environmental pollution patterns
,” Proc. Natl. Acad. Sci. U. S. A.
109
, 4738
–4743
(2012
).15.
M. K.
Gough
, F. J.
Beron-Vera
, M. J.
Olascoaga
, J.
Sheinbaum
, J.
Juoanno
, and R.
Duran
, “Persistent transport pathways in the Northwestern Gulf of Mexico
,” J. Phys. Oceanogr.
49
, 353
–367
(2019
).16.
R.
Lumpkin
and M.
Pazos
, “Measuring surface currents with surface velocity program drifters: The instrument, its data and some recent results
,” in Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics
, edited by A.
Griffa
, A. D.
Kirwan
, A.
Mariano
, T.
Özgökmen
, and T.
Rossby
(Cambridge University Press
, 2007
), Chap. 2, pp. 39
–67
.17.
F. J.
Beron-Vera
, M. J.
Olascoaga
, and R.
Lumpkin
, “Inertia-induced accumulation of flotsam in the subtropical gyres
,” Geophys. Res. Lett.
43
, 12228
–12233
, (2016
).18.
F. J.
Beron-Vera
, M. J.
Olascoaga
, and P.
Miron
, “Building a Maxey–Riley framework for surface ocean inertial particle dynamics
,” Phys. Fluids
31
, 096602
(2019
).19.
M. R.
Maxey
and J. J.
Riley
, “Equation of motion for a small rigid sphere in a nonuniform flow
,” Phys. Fluids
26
, 883
(1983
).20.
E. E.
Michaelides
, “Review—The transient equation of motion for particles, bubbles and droplets
,” J. Fluids Eng.
119
, 233
–247
(1997
).21.
A.
Provenzale
, “Transport by coherent barotropic vortices
,” Annu. Rev. Fluid Mech.
31
, 55
–93
(1999
).22.
J. H. E.
Cartwright
, U.
Feudel
, G.
Károlyi
, A.
de Moura
, O.
Piro
, and T.
Tél
, “Dynamics of finite-size particles in chaotic fluid flows
,” in Nonlinear Dynamics and Chaos: Advances and Perspectives
, edited by M.
Thiel
, et al (Springer-Verlag Berlin Heidelberg
, 2010
), pp. 51
–87
.23.
A.
Babiano
, J. H.
Cartwright
, O.
Piro
, and A.
Provenzale
, “Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems
,” Phys. Rev. Lett.
84
, 5764
–5767
(2000
).24.
R. D.
Vilela
, A. P. S.
de Moura
, and C.
Grebogi
, “Finite-size effects on open chaotic advection
,” Phys. Rev. E
73
, 026302
(2006
).25.
T.
Sapsis
and G.
Haller
, “Instabilities in the dynamics of neutrally buoyant particles
,” Phys. Fluids
20
, 017102
(2008
).26.
F. J.
Beron-Vera
, M. J.
Olascoaga
, G.
Haller
, M.
Farazmand
, J.
Triñanes
, and Y.
Wang
, “Dissipative inertial transport patterns near coherent Lagrangian eddies in the ocean
,” Chaos
25
, 087412
(2015
).27.
G.
Haller
, A.
Hadjighasem
, M.
Farazmand
, and F.
Huhn
, “Defining coherent vortices objectively from the vorticity
,” J. Fluid Mech.
795
, 136
–173
(2016
).28.
Ø.
Breivik
and A.
Allen
, “An operational search and rescue model for the Norwegian Sea and the North Sea
,” J. Mar. Syst.
69
, 99
–113
(2008
).29.
A. V.
Duhec
, R. F.
Jeanne
, N.
Maximenko
, and J.
Hafner
, “Composition and potential origin of marine debris stranded in the Western Indian Ocean on remote Alphonse Island, Seychelles
,” Mar. Pollut. Bull.
96
, 76
–86
(2015
).30.
M. R.
Allshouse
, G. N.
Ivey
, R. J.
Lowe
, N. L.
Jones
, C.
Beegle-krause
, J.
Xu
, and T.
Peacock
, “Impact of windage on ocean surface Lagrangian coherent structures
,” Environ. Fluid Mech.
17
, 473
–483
(2017
).31.
P. Y.
Le Traon
, F.
Nadal
, and N.
Ducet
, “An improved mapping method of multisatellite altimeter data
,” J. Atmos. Oceanic Technol.
15
, 522
–534
(1998
).32.
D. P.
Dee
, S. M.
Uppala
, A. J.
Simmons
, P.
Berrisford
, P.
Poli
, S.
Kobayashi
, U.
Andrae
, M. A.
Balmaseda
, G.
Balsamo
, P.
Bauer
, P.
Bechtold
, A. C. M.
Beljaars
, L.
van de Berg
, J.
Bidlot
, N.
Bormann
, C.
Delsol
, R.
Dragani
, M.
Fuentes
, A. J.
Geer
, L.
Haimberger
, S. B.
Healy
, H.
Hersbach
, E. V.
Holm
, L.
Isaksen
, P.
Kallberg
, M.
Kohler
, M.
Matricardi
, A. P.
McNally
, B. M.
Monge-Sanz
, J.-J.
Morcrette
, B.-K.
Park
, C.
Peubey
, P.
de Rosnay
, C.
Tavolato
, J.-N.
Thepaut
, and F.
Vitart
, “The ERA-interim reanalysis: Configuration and performance of the data assimilation system
,” Q. J. R. Meteorol. Soc.
137
, 553
–597
(2011
).33.
On the sphere, with local coordinates x1 = (λ − λ0) · a⊙ cos ϑ0 and x2 = (ϑ − ϑ0)·a⊙, where a⊙ is the planet’s mean radius and λ (respectively, ϑ) is longitude (respectively, latitude), the Maxey–Riley set takes the form (5) with f = 2Ω sin ϑ + τ⊙1, where Ω is the planet’s rotation rate and , , where γ⊙ ≔ sec ϑ⊙ cos ϑ and . In turn, the reduced Maxey–Riley set takes the form (12) with , with γ⊙, f, and ω as above.
34.
P. H.
Le Blond
and L. A.
Mysak
, Waves in the Ocean
, Elsevier Oceanography Series Vol. 20 (Elsevier Science
, Amsterdam
, 1978
), p. 602
.35.
36.
R.
Gatignol
, “The Faxen formulae for a rigid particle in an unsteady non-uniform Stokes flow
,” J. Mec. Theor. Appl.
2
, 143
–160
(1983
).37.
T. R.
Auton
, F. C. R.
Hunt
, and M.
Prud’Homme
, “The force exerted on a body in inviscid unsteady non-uniform rotational flow
,” J. Fluid Mech.
197
, 241
(1988
).38.
L.
Montabone
, “Vortex dynamics and particle transport in barotropic turbulence
,” Ph.D. thesis, University of Genoa
, Italy
, 2002
.39.
T. R.
Auton
, “The lift force on a spherical body in a rotational flow
,” J. Fluid Mech.
183
, 199
–218
(1987
).40.
41.
G. H.
Ganser
, “A rational approach to drag prediction of spherical and nonspherical particles
,” Powder Technol.
77
, 143
–152
(1993
).42.
N.
Fenichel
, “Geometric singular perturbation theory for ordinary differential equations
,” J. Differ. Equations
31
, 53
–98
(1979
).43.
C. K. R. T.
Jones
, “Geometric singular perturbation theory
,” in Dynamical Systems
, Lecture Notes in Mathematics (Springer-Verlag
, Berlin
, 1995
), pp. 44
–118
.44.
G.
Haller
and T.
Sapsis
, “Where do inertial particles go in fluid flows?
,” Physica D
237
, 573
–583
(2008
).45.
J.
Röhrs
, K. H.
Christensen
, L. R.
Hole
, G.
Broström
, M.
Drivdal
, and S.
Sundby
, “Observation-based evaluation of surface wave effects on currents and trajectory forecasts
,” Ocean Dyn.
62
, 1519
–1533
(2012
).46.
O.
Nesterov
, “Consideration of various aspects in a drift study of MH370 debris
,” Ocean Sci.
14
, 387
–402
(2018
).47.
F. J.
Beron-Vera
, Y.
Wang
, M. J.
Olascoaga
, G. J.
Goni
, and G.
Haller
, “Objective detection of oceanic eddies and the Agulhas leakage
,” J. Phys. Oceanogr.
43
, 1426
–1438
(2013
).48.
G.
Haller
and F. J.
Beron-Vera
, “Coherent Lagrangian vortices: The black holes of turbulence
,” J. Fluid Mech.
731
, R4
(2013
).49.
F. J.
Beron-Vera
, M. J.
Olascaoaga
, Y.
Wang
, J.
Triñanes
, and P.
Pérez-Brunius
, “Enduring Lagrangian coherence of a Loop Current ring assessed using independent observations
,” Sci. Rep.
8
, 11275
(2018
).50.
F. J.
Beron-Vera
, A.
Hadjighasem
, Q.
Xia
, M. J.
Olascoaga
, and G.
Haller
, “Coherent Lagrangian swirls among submesoscale motions
,” Proc. Natl. Acad. Sci. U. S. A.
116
, 18251
–18256
(2018
).51.
M.
van der Mheen
, C.
Pattiaratchi
, and E.
van Sebille
, “Role of Indian Ocean dynamics on accumulation of buoyant debris
,” J. Geophys. Res.: Oceans
124
, 2571
–2590
, (2019
).52.
F. J.
Beron-Vera
, M. J.
Olascoaga
, and P.
Miron
, “Corrigendum and addendum to “building a Maxey–Riley framework for surface ocean inertial particle dynamics
,”” (unpublished).53.
P.
Ripa
, “Least squares data fitting
,” Cienc. Mar.
28
, 75
–105
(2002
).54.
J. R.
Dormand
and P. J.
Prince
, “A family of embedded Runge–Kutta formulae
,” J. Comput. Appl. Math.
6
, 19
–26
(1980
).55.
P. P.
Niiler
, R. E.
Davis
, and H. J.
White
, “Water-following characteristics of a mixed layer drifter
,” Deep-Sea Res., Part A
34
, 1867
–1881
(1987
).56.
G.
Haller
, “Lagrangian coherent structures from approximate velocity data
,” Phys. Fluids
14
, 1851
–1861
(2002
).57.
R. T.
Rockafellar
and R. J.
Wets
, Variational Analysis
(Springer-Verlag
, 2005
), p. 117
.58.
P.
Miron
, M. J.
Olascoaga
, F. J.
Beron-Vera
, J. T.
Triñanes
, N. F.
Putman
, R.
Lumpkin
, and G. J.
Goni
, “Assessing inertial effects in the ocean using custom drifters
,” (unpublished).© 2020 Author(s).
2020
Author(s)
You do not currently have access to this content.