Abernathey, R., Marshall, J., Mazloff, M., and Shuckburgh, E.: Enhancement of
mesoscale eddy stirring at steering levels in the Southern Ocean, J.
Phys. Oceanogr., 40, 170–184, 2010. a

Aref, H.: Stirring by chaotic advection, J. Fluid Mech., 143,
1–21, 1984. a

Branicki, M. and Kirwan Jr., A.: Stirring: the Eckart paradigm revisited,
Int. J. Eng. Sci., 48, 1027–1042, 2010. a

Brett, G.: 3D rotating cylinder eddy codes,
https://doi.org/10.5281/zenodo.1560663, 2018. a

Brett, G. and Wang, P.: 3D rotating cylinder eddy data,
https://doi.org/10.5281/zenodo.1560204, 2018. a

Casati, G. and Ford, J.: Stochastic behavior in classical and quantum
hamiltonian systems, in: Stochastic Behavior in Classical and Quantum
Hamiltonian Systems, 93, Springer-Verlag, Berlin Heidelberg, 1979. a

Chirikov, B. V.: Research concerning the theory of non-linear resonance and
stochasticity, Tech. rep., CM-P00100691, original report for the Nuclear Physics Institute of
the Siberian section of the USSR Academy of Sciences, 1969, location Novosibirsk, translation by: Sanders, A. T., CERN Translation 71-40, 1971, Geneva, 1971. a

Chirikov, B. V.: A universal instability of many-dimensional oscillator
systems, Phys. Rep., 52, 263–379, 1979. a

Coulliette, C. and Wiggins, S.: Intergyre transport in a wind-driven, quasigeostrophic
double gyre: An application of lobe dynamics, Nonlin. Processes Geophys., 8, 69–94, https://doi.org/10.5194/npg-8-69-2001, 2001. a

D'Asaro, E.: Surface wave measurements from subsurface floats, J. Atmos. Ocean. Tech., 32, 816–827, 2015. a

D'Asaro, E. A., Farmer, D. M., Osse, J. T., and Dairiki, G. T.: A Lagrangian
float, J. Atmos. Ocean. Tech., 13, 1230–1246, 1996. a

Deese, H. E., Pratt, L. J., and Helfrich, K. R.: A laboratory model of exchange
and mixing between western boundary layers and subbasin recirculation gyres,
J. Phys. Oceanogr., 32, 1870–1889, 2002. a

Dombre, T., Frisch, U., Greene, J. M., Hénon, M., Mehr, A., and Soward,
A. M.: Chaotic streamlines in the ABC flows, J. Fluid Mech., 167,
353–391, 1986. a

Fereday, D. and Haynes, P.: Scalar decay in two-dimensional chaotic advection
and Batchelor-regime turbulence, Phys. Fluids, 16, 4359–4370, 2004. a

Fischer, P. F.: An overlapping Schwarz method for spectral element solution of
the incompressible Navier–Stokes equations, J. Comput. Phys., 133, 84–101, 1997. a

Flierl, G. R. and Woods, N. W.: Copepod aggregations: influences of physics and
collective behavior, J. Stat. Phys., 158, 665–698, 2015. a, b

Fountain, G., Khakhar, D., Mezić, I., and Ottino, J.: Chaotic mixing in a
bounded three-dimensional flow, J. Fluid Mech., 417, 265–301,
2000. a, b, c

Froyland, G., Padberg, K., England, M. H., and Treguier, A. M.: Detection of
coherent oceanic structures via transfer operators, Phys. Rev. Lett.,
98, 224503, https://doi.org/10.1103/PhysRevLett.98.224503, 2007. a

Froyland, G., Horenkamp, C., Rossi, V., Santitissadeekorn, N., and Gupta,
A. S.: Three-dimensional characterization and tracking of an Agulhas Ring,
Ocean Model., 52, 69–75, 2012. a

Greenspan, H. P.: The theory of rotating fluids, CUP Archive, Cambridge, UK, 1968. a, b

Griffies, S. M., Winton, M., Anderson, W. G., Benson, R., Delworth, T. L.,
Dufour, C. O., Dunne, J. P., Goddard, P., Morrison, A. K., Rosati, A.,
Wittenberg, A. T., Yin, J., and Zhang, R.: Impacts on ocean heat from transient mesoscale eddies in a hierarchy
of climate models, J. Climate, 28, 952–977, 2015. a

Gromeka, I.: Some cases of incompressible fluids motion, Scientific notes of
the Kazan University, Kazan, Russia, pp. 76–148, 1881. a

Hadjighasem, A., Farazmand, M., Blazevski, D., Froyland, G., and Haller, G.: A
critical comparison of Lagrangian methods for coherent structure detection,
Chaos: An Interdisciplinary Journal of Nonlinear Science, 27, 053104, https://doi.org/10.1063/1.4982720, 2017. a

Hallberg, R.: Using a resolution function to regulate parameterizations of
oceanic mesoscale eddy effects, Ocean Model., 72, 92–103, 2013. a

Haller, G.: Lagrangian coherent structures from approximate velocity data,
Phys. Fluids, 14, 1851–1861, 2002. a

Haller, G.: Lagrangian coherent structures, Annu. Rev. Fluid Mech.,
47, 137–162, 2015. a

Haller, G. and Beron-Vera, F. J.: Geodesic theory of transport barriers in
two-dimensional flows, Physica D, 241, 1680–1702, 2012. a

Haller, G. and Beron-Vera, F. J.: Coherent Lagrangian vortices: The black holes
of turbulence, J. Fluid Mech., 731, R4, https://doi.org/10.1017/jfm.2013.391, 2013. a

Haller, G., Karrasch, D., and Kogelbauer, F.: Material barriers to diffusive
and stochastic transport, P. Natl. Acad. Sci. USA,
115, 9074–9079, 2018. a

Haynes, P. and Shuckburgh, E.: Effective diffusivity as a diagnostic of
atmospheric transport: 2. Troposphere and lower stratosphere, J.
Geophys. Res.-Atmos., 105, 22795–22810, 2000. a

Ledwell, J. R., Watson, A. J., and Law, C. S.: Evidence for slow mixing across
the pycnocline from an open-ocean tracer-release experiment, Nature, 364,
701–703, 1993. a, b

Ledwell, J. R., Watson, A. J., and Law, C. S.: Mixing of a tracer in the
pycnocline, J. Geophys. Res.-Oceans, 103, 21499–21529,
1998. a, b

Lenn, Y.-D. and Chereskin, T. K.: Observations of Ekman currents in the
Southern Ocean, J. Phys. Oceanogr., 39, 768–779, 2009. a

Lopez, J. M. and Marques, F.: Sidewall boundary layer instabilities in a
rapidly rotating cylinder driven by a differentially corotating lid, Phys. Fluids, 22, 114109, https://doi.org/10.1063/1.3517292, 2010. a

Mahadevan, A.: The impact of submesoscale physics on primary productivity of
plankton, Annu. Rev. Mar. Sci., 8, 161–184, 2016. a

Malhotra, N., Mezić, I., and Wiggins, S.: Patchiness: A new diagnostic for
Lagrangian trajectory analysis in time-dependent fluid flows, Int.
J. Bifurcat. Chaos, 8, 1053–1093, 1998. a

Miller, P. D., Pratt, L. J., Helfrich, K. R., and Jones, C. K.: Chaotic
transport of mass and potential vorticity for an island recirculation,
J. Phys. Oceanogr., 32, 80–102, 2002. a

Nakamura, N.: Two-dimensional mixing, edge formation, and permeability
diagnosed in an area coordinate, J. Atmos. Sci., 53,
1524–1537, 1996. a, b

Nakamura, N. and Ma, J.: Modified Lagrangian-mean diagnostics of the
stratospheric polar vortices: 2. Nitrous oxide and seasonal barrier migration
in the cryogenic limb array etalon spectrometer and SKYHI general circulation
model, J. Geophys. Res.-Atmos., 102, 25721–25735,
1997. a

Ngan, K. and Shepherd, T. G.: Chaotic mixing and transport in Rossby-wave
critical layers, J. Fluid Mech., 334, 315–351, 1997. a

Okubo, A.: Oceanic diffusion diagrams, in: Deep Sea Research and Oceanographic
Abstracts, Elsevier, Amsterdam, the Netherlands, 18, 789–802, 1971. a

Olascoaga, M. J. and Haller, G.: Forecasting sudden changes in environmental
pollution patterns, P. Natl. Acad. Sci. USA, 13, 4738–4743, https://doi.org/10.1073/pnas.1118574109, 2012. a

Ottino, J.: Mixing, chaotic advection, and turbulence, Annu. Rev. Fluid Mech., 22, 207–254, 1990. a

Pattanayak, A. K.: Characterizing the metastable balance between chaos and
diffusion, Physica D, 148, 1–19, 2001. a

Pierrehumbert, R.: Tracer microstructure in the large-eddy dominated regime,
Chaos Soliton. Fract., 4, 1091–1110, 1994. a

Poje, A. and Haller, G.: Geometry of cross-stream mixing in a double-gyre ocean
model, J. Phys. Oceanogr., 29, 1649–1665, 1999. a

Polvani, L. M., Waugh, D., and Plumb, R. A.: On the subtropical edge of the
stratospheric surf zone, J. Atmos. Sci., 52, 1288–1309,
1995. a

Pratt, L. J., Rypina, I. I., Özgökmen, T., Wang, P., Childs, H., and
Bebieva, Y.: Chaotic advection in a steady, three-dimensional, Ekman-driven
eddy, J. Fluid Mech., 738, 143–183, 2014. a, b

Rogerson, A. M., Miller, P. D., Pratt, L. J., and Jones, C. K. R. T.:
Lagrangian motion and fluid exchange in a barotropic meandering jet, J. Phys. Oceanogr., 29, 2635–2655, 1999. a

Rom-Kedar, V., Leonard, A., and Wiggins, S.: An analytical study of transport,
mixing and chaos in an unsteady vortical flow, J. Fluid Mech.,
214, 347–394, 1990. a

Rypina, I., Brown, M., Beron-Vera, F., Kocak, H., Olascoaga, M., and
Udovydchenkov, I.: On the Lagrangian dynamics of atmospheric zonal jets and
the permeability of the stratospheric polar vortex, J.
Atmos. Sci., 64, 3595–3610, 2007. a

Rypina, I., Pratt, L., Wang, P., Özgökmen, T., and Mezic, I.: Resonance
phenomena in a time-dependent, three-dimensional model of an idealized eddy,
Chaos: An Interdisciplinary Journal of Nonlinear Science, 25, 087401, https://doi.org/10.1063/1.4916086, 2015. a, b, c, d

Rypina, I. I. and Pratt, L. J.: Trajectory encounter volume as a diagnostic of mixing
potential in fluid flows, Nonlin. Processes Geophys., 24, 189–202, https://doi.org/10.5194/npg-24-189-2017, 2017. a

Rypina, I. I., Brown, M. G., and Koçak, H.: Transport in an idealized
three-gyre system with application to the Adriatic Sea, J. Phys.
Oceanogr., 39, 675–690, 2009. a

Rypina, I. I., Pratt, L. J., Pullen, J., Levin, J., and Gordon, A. L.: Chaotic
advection in an archipelago, J. Phys. Oceanogr., 40,
1988–2006, 2010. a, b

Rypina, I. I., Pratt, L. J., and Lozier, M. S.: Near-surface transport pathways
in the North Atlantic Ocean: Looking for throughput from the subtropical to
the subpolar gyre, J. Phys. Oceanogr., 41, 911–925,
2011a. a

Rypina, I. I., Scott, S. E., Pratt, L. J., and Brown, M. G.: Investigating the connection
between complexity of isolated trajectories and Lagrangian coherent
structures, Nonlin. Processes Geophys., 18, 977–987, https://doi.org/10.5194/npg-18-977-2011, 2011b. a

Rypina, I. I., Kamenkovich, I., Berloff, P., and Pratt, L. J.: Eddy-induced
particle dispersion in the near-surface North Atlantic, J. Phys.
Oceanogr., 42, 2206–2228, 2012. a

Rypina, I. I., Llewellyn Smith, S. G., and Pratt, L. J.: Connection between encounter volume and diffusivity
in geophysical flows, Nonlin. Processes Geophys., 25, 267–278, https://doi.org/10.5194/npg-25-267-2018, 2018. a

Samelson, R.: Fluid exchange across a meandering jet, J. Phys.
Oceanogr., 22, 431–444, 1992. a

Samelson, R. M. and Wiggins, S.: Lagrangian transport in geophysical jets and
waves: The dynamical systems approach, vol. 31, Springer Science & Business
Media, Berlin, Germany, 2006. a

Sayol, J.-M., Orfila, A., Simarro, G., López, C., Renault, L., Galán,
A., and Conti, D.: Sea surface transport in the Western Mediterranean Sea: A
Lagrangian perspective, J. Geophys. Res.-Oceans, 118,
6371–6384, 2013. a

Shadden, S. C., Lekien, F., and Marsden, J. E.: Definition and properties of
Lagrangian coherent structures from finite-time Lyapunov exponents in
two-dimensional aperiodic flows, Physica D, 212,
271–304, 2005. a

Shepherd, T. G., Koshyk, J. N., and Ngan, K.: On the nature of large-scale
mixing in the stratosphere and mesosphere, J. Geophys. Res.-Atmos., 105, 12433–12446, 2000. a

Shuckburgh, E. and Haynes, P.: Diagnosing transport and mixing using a
tracer-based coordinate system, Phys. Fluids, 15, 3342–3357, 2003. a

Solomon, T. and Mezić, I.: Uniform resonant chaotic mixing in fluid flows,
Nature, 425, 376–380, 2003. a

Son, D.: Turbulent decay of a passive scalar in the Batchelor limit: Exact
results from a quantum-mechanical approach, Phys. Rev. E, 59, R3811, https://doi.org/10.1103/PhysRevE.59.R3811,
1999. a

Thiffeault, J.-L.: Stretching and curvature of material lines in chaotic flows,
Physica D, 198, 169–181, 2004.
a

Yuan, G. C., Pratt, L., and Jones, C.: Cross-jet Lagrangian transport and
mixing in a 2 1∕2-layer model, J. Phys. Oceanogr., 34,
1991–2005, 2004. a

Zambianchi, E. and Griffa, A.: Effects of finite scales of turbulence on
dispersion estimates, J. Marine Res., 52, 129–148, 1994. a