ICCE 2012 Cover Image


waves and currents
lyapunov exponents

How to Cite

Orfila, A., Galan, A., Simarro, G., & Sayol, J. M. (2012). MIXING IN COASTAL AREAS INFERRED FROM LYAPUNOV EXPONENTS: IMPLICATIONS FOR TRANSPORT. Coastal Engineering Proceedings, 1(33), waves.8. https://doi.org/10.9753/icce.v33.waves.8


We study the horizontal surface mixing and the transport induced by waves, using local Lyapunov exponents and high resolution data from numerical simulations of waves and currents. By choosing the proper spatial (temporal) parameters we compute the Finite Size and Finite Time Lyapunov exponents (FSLE and FTLE) focussing on the local stirring and diffusion inferred from the Lagrangian Coherent Structures (LCS). The methodology is tested by deploying a set of eight lagrangian drifters and studying the path followed against LCS derived under current field and waves and currents.


Antonov, J. I., R. A. Locarnini, T. P. Boyer, A. V. Mishonov, and H. E. Garcia (2006), World Ocean Atlas 2005, Volume 2: Salinity. S. Levitus, Ed. NOAA Atlas NESDIS 62, U.S. Government Printing Oce, Washington, D.C., 182 pp.

d'Ovidio, F., V. Fernandez, E. Hernandez-Garcia and C. Lopez (2004), Mixing structures in the Mediterranean sea from Finite-Size Lyapunov Exponents, Geophys. Res. Lett, 31, L17203, doi:10.1029/2004GL020328.http://dx.doi.org/10.1029/2004GL020328

Galan, A., Orï¬la, A., Simarro, G., Hernandez-Carrasco, I. and Lopez, C. (2012), Wave mixing rise inferred from Lyapunov exponents, Env. Fluid Mech., 12 (3), 291-300, doi: 0.1007/s10652-012-9238-3.

Grell, G. A., J. Dudhia, and D. R. Stauer (1995), A description of the ï¬fth-generation penn state/NCAR mesoscale model (MM5), NCAR/TN-398+STR, National Center for Atmospheric Research, Boulder, CO, 122 pp.

Haller, G. and G. Yuan (2000), Lagrangian coherent structures and mixing in two-dimensional turbulence,Physica D, 147, 352-370. How reliable are Finite-Size Lyapunov Exponents for the assessment of ocean dynamics.

Hernandez-Carrasco, I., C. Lopez, E. Hernandez-Garcia and A. Turiel (2011), Ocean Modelling,36, 208- 218.

Joseph, B. and B. Legras (2002), Relation between kinematic boundaries, stirring, and barriers for the Antartic Polar vortex, Journal of the Atmospheric Sciences, 59, 1198-1212.

Komen, G.J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann and P.A.E.M. Janssen (1994), Dynamics and Modelling of Ocean Waves, Cambridge University Press.

Lapeyre, G. (2002), Characterization of ï¬nite-time Lyapunov exponents and vectors in two-dimensional turbulence, Chaos, 12 (3), 688-698, doi:10.1063/1.1499395.http://dx.doi.org/10.1063/1.1499395

Locarnini, R. A., A. V. Mishonov, J. I. Antonov, T. P. Boyer, and H. E. Garcia (2006), World Ocean Atlas 2005, Volume 1: Temperature. S. Levitus, Ed. NOAA Atlas NESDIS 61, U.S. Government Printing Oce, Washington, D.C., 182 pp.

Longuet-Higgins, M.S. and R.W. Stewart (1964), Radiation stresses in water waves: a physical discussion with applications, Deep Sea Res., 11, 529"¸Î c 562

Mancho, M., E. Hernandez-Garcia, D. Small, S. Wiggins and V. Fernandez (2008), Lagrangian Transport through an Ocean Front in the Northwestern Mediterranean Sea, J. of Phys. Ocean., 38, 1222-1237.

Molcard, A.,A.C. Poje, and T.M. Özgökmen, (2006), Directed drifter launch strategies for Lagrangian data assimilation using hyperbolic trajectories, Ocean Modelling, 12, 268-289.

Özgökmen, T.M., A. Gria, A.J. Mariano and L.I. Piterbarg (2000), On the predictability of Lagrangian trajectories in the ocean, J. Atmos. Ocean. Tech., 17 (3), 366-383.

Shadden,S. C., F. Lekien and J. E. Marsden (2005), Deï¬nition and properties of Lagrangian coherent structures from ï¬nite-time Lyapunov exponents in two-dimensional aperiodic floows, Physica D, 212, (3-4), 271-304.

Song, Y. and D. B. Haidvogel (1994), A semi-implicit ocean circulation model using a generalized topography-following coordinate system, J. Comp. Phys., 115 (1), 228-244.

Wiggins, S. (1992), Chaotic transport in Dynamical Systems, Springer Verlag, New York.

Authors retain copyright and grant the Proceedings right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this Proceedings.