Horseshoes in hurricanes

Aurell E., Boffetta G., Crisanti A., Paladin G., Vulpiani A.: Predictability in the large: An extension of the concept of Lyapunov exponent. J. Phys. A 30, 1–26 (1997)

Beigie D., Leonard A., Wiggins S.: Chaotic transport in the homoclinic and heteroclinic tangle regions of quasiperiodically forced two-dimensional dynamical systems. Nonlinearity 4, 775–819 (1991)

F. O. Bryan, Introduction: Ocean modeling—eddy or not. In: Ocean Modeling in an Eddying Regime, M. Hecht and H. Hasumi (eds.), American Geophysical Union, 2008, 1–3.

Campbell D.K., Rosenau P., Zaslavsky G.M.: Introduction: The Fermi–Pasta–Ulam problem—The first fifty years. Chaos 15, 015101 (2005)

Chelton D.B., Schlax M.G., Samelson R.M., de Szoeke R.A.: Global observations of large oceanic eddies. Geophys. Res. Lett. 34, L15606 (2007)

Chen S.S., Zhao W., Donelan M.A., Price J.F., Walsh E.J.: The CBLAST-Hurricane Program and the next-generation fully coupled atmosphere-wave-ocean models for hurricane research and prediction. Bull. Amer. Meteor. Soc 88, 311–317 (2007)

d’Ovidio F., Fernández V., Hernández-Garca E., López C.: Mixing structures in the Mediterranean Sea from finite-size Lyapunov exponents. Geophys. Res. Lett. 31, L17203 (2004)

Dellnitz M., Junge O., Koon W.S., Lekien F., Lo M.W., Marsden J.E., Padberg K., Preis R., Ross S., Thiere B.: Transport in dynamical astronomy and multibody problems. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 15, 699–727 (2005)

Drvillon M.: The GODAE/Mercator-Ocean global ocean forecasting system: Results, applications and prospects. J. Operational Oceanogr. 1, 51–57 (2008)

Emanuel K.: Contribution of tropical cyclones to meridional heat transport by the oceans. J. Geophys. Res. 106, 14771–14781 (2001)

Emanuel K.: Environmental factors affecting tropical cyclone power dissipation. J. Climate 20, 5497–5509 (2007)

B. Fox-Kemper and D. Menemenlis, Can large eddy simluation techniques improve mesoscale rich ocean models? In: Ocean Modeling in an Eddying Regime, M. Hecht and H. Hasumi (eds.), American Geophysical Union, 2008, 319–337.

Franco E., Pekarek D., Peng J., Dabiri J.: Geometry of unsteady fluid transport during fluid-structure interactions. J. Fluid Mech. 589, 125–145 (2007)

Froyland G., Padberg K., England M.H., Treguier A.M.: Detection of coherent oceanic structures via transfer operators. Phys. Rev. Lett. 98, 224503 (2007)

Froyland G., Padberg K.: Almost invariant sets and invariant manifold—connecting probabilistic and geometric descriptions of coherent structures in flows. Phys. D 238, 1507–1523 (2009)

Gawlik E., Marsden J., Du Toit P., Campagnola S.: Lagrangian coherent structures in the planar elliptic restricted three-body problem. Celestial Mech. Dynam. Astronom. 103, 227–249 (2009)

Gent P.R., Mcwilliams J.C.: Isopycnal mixing in ocean circulation models. J. Phys. Oceanogr. 20, 150–155 (1990)

Haller G., Yuan G.: Lagrangian coherent structures and mixing in two-dimensional turbulence. Phys. D 147, 352–370 (2000)

Haller G.: Distinguished material surfaces and coherent structures in three-dimensional fluid flows. Phys. D 149, 248–277 (2001)

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

Hecht M.W., Holm D.D., Petersen M.R., Wingate B.A.: The LANS-α and Leray turbulence parameterizations in primitive equation ocean modeling. J. Phys. A 41, 344009 (2008)

Hecht M.W., Holm D.D., Petersen M.R., Wingate B.A.: Implementation of the LANS-α turbulence model in a primitive equation ocean model. J. Comput. Phys. 227, 5691–5716 (2008)

Houze J., Robert A., Chen S.S., Smull B.F., Lee W., Bell M.M.: Hurricane intensity and eyewall replacement. Science 315, 1235–1239 (2007)

Ide K., Small D., Wiggins S.: Distinguished hyperbolic trajectories in time-dependent fluid flows: Analytical and computational approach for velocity fields defined as data sets. Nonlinear Process. Geophys. 9, 237–263 (2002)

O. Junge, J. E. Marsden, and I. Mezic, Uncertainty in the dynamics of conservative maps. In: Proceedings of the 43rd IEEE Connference on Decision and Control, 2004, 2225–2230.

B. Kuo, et al., Hurricane Isabel Data Produced by the Weather Research and Forecast (WRF) Model, Courtesy of NCAR, and the U.S. National Science Foundation.

F. Lekien, Time-dependent dynamical systems and geophysical flows. PhD thesis, California Institute of Technology, 2003.

Lekien F., Coulliette C., Mariano A.J., Ryan E.H., Shay L.K., Haller G., Marsden J.: Pollution release tied to invariant manifolds: A case study for the coast of Florida. Phys. D 210, 1–20 (2005)

Lekien F., Shadden S.C., Marsden J.E.: Lagrangian coherent structures in n-dimensional systems. J. Math. Phys. 48, 065404 (2007)

Li Z., Chao Y., McWilliams J.C., Ide K.: A three-dimensional variational data assimilation scheme for the Regional Ocean Modeling System: Implementation and basic experiments. J. Geophys. Res. 113, C05002 (2008)

Lipinski D., Mohseni K.: A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures. Chaos 20, 017504 (2010)

Lorenz E.N.: Deterministic non-periodic flow. J. Atmos. Sci. 20, 130–141 (1963)

MacKay R.S., Meiss J.D., Percival I.C.: Transport in Hamiltonian systems. Phys. D 13, 55–81 (1984)

Mathur M., Haller G., Peacock T., Ruppert-Felsot J.E., Swinney H.L.: Uncovering the Lagrangian skeleton of turbulence. Phys. Rev. Lett. 98, 144502 (2007)

P. Odier, Characterization of turbulent mixing in an Oceanic Overflow Facility. Abstract submitted to DFD07 Meeting of the American Physical Society, 2007.

Peacock T., Dabiri J.: Introduction to Focus Issue: Lagrangian coherent structures. Chaos 20, 017501 (2010)

Peng J., Dabiri J.O.: Transport of inertial particles by Lagrangian coherent structures: Application to predator-prey interaction in jellyfish feeding. J. Fluid Mech. 623, 75–84 (2009)

H. Poincaré, New Methods of Celestial Mechanics. Springer, 1899.

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

Rom-Kedar V., Wiggins S.: Transport in two-dimensional maps: Concepts, examples, and a comparison of the theory of Rom-Kedar and Wiggins with the Markov model of MacKay, Meiss, Ott, and Percival. Phys. D 51, 248–266 (1991)

Sadlo F., Peikert R.: Efficient visualization of Lagrangian coherent structures by filtered AMR ridge extraction. IEEE Trans. Vis. Comput. Graph. 13, 1456–1463 (2007)

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

Schiermeier Q.: Oceanography: Churn, churn, churn. Nature 447, 522–524 (2007)

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

Shadden S.C., Katija K., Rosenfeld M., Marsden J.E., Dabiri J.O.: Transport and stirring induced by vortex formation. J. Fluid Mech. 593, 315–331 (2007)

Shadden S., Taylor C.: Characterization of coherent structures in the cardiovascular system. Ann. Biomed. Eng. 36, 1152–1162 (2008)

Smale S.: Differentiable dynamical systems. Bull. Amer. Math. Soc. 73, 747–817 (1967)

Smale S.: Finding a horseshoe on the beaches of Rio. Math. Intelligencer 20, 39–44 (1998)

S. Solomon, D. Qin, M. Manning, Z. Chen, M. Marquis, K. B. Averyt, M. Tignor, and H. L. Miller (eds.), Climate Change 2007: The Physical Science Basis. Contribution of Working Group I to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge University Press, 2007.

Sundermeyer M.A., Terray E.A., Ledwell J.R., Cunningham A.G., LaRocque P.E., Banic J., Lillycrop W.J.: Threedimensional mapping of fluorescent dye using a scanning, depth-resolving airborne lidar. J. Atmos. Oceanic Technol. 24, 1050–1065 (2007)

Tallapragada P., Ross S.D.: Particle segregation by Stokes number for small neutrally buoyant spheres in a fluid. Phys. Rev. E 78, 036308 (2008)

Tanaka M., Ross S.: Separatrices and basins of stability from time series data: An application to biodynamics. Nonlinear Dynam. 58, 1–21 (2009)

Vellinga M., Wood R.A.: Global climatic impacts of a collapse of the Atlantic thermohaline circulation. Climatic Change 54, 251–267 (2002)

Weinkauf T., Sahner J., Sahner J., Theisel H., Theisel H., Hege H.C.: Cores of swirling particle motion in unsteady flows. IEEE Trans. Vis. Comput. Graph. 13, 1759–1766 (2007)