Lagrangian Methods in Oceanography
LCS Web Sites
Francois Lekien
Lagrangian Coherent Structures in 2D Turbulence
LCS Papers and Tutorials
Allshouse, Michael R. and Jean-Luc Thiffeault,
Detecting coherent structures using braids,
Physica D, Vol. 241, 2012, 95-105
http://www.sciencedirect.com/science/article/pii/S0167278911002752
Beron-Vera, F. J. et al.,
Oceanic mesoscale eddies as revealed by Lagrangian coherent structures,
GRL, Vol. 35, 2008, L12603
Web
Coulliete, Chad et al.,
Optimal pollution mitigation in Monterey Bay based on coastal radar data and
nonlinear dynamics,
Environmental Science and Technology, Vol. 41, 2007, 6562-6572
http://pubs.acs.org/doi/abs/10.1021/es0630691
de Oliveira, Luis C. et al.,
Robust tori-like Lagrangian coherent structures,
Physica A: Statistical Mechanics and Its Applications, Vol. 391, 6611-6616
http://www.sciencedirect.com/science/article/pii/S0378437112007297
Doerner, R. et al.,
Stable manifolds and predictability of dynamical systems,
Chaos, Solitons and Fractals, Vol. 10, 1999, 1759-1782
Farazmand, Mohammed and George Haller,
Computing Lagrangian coherent structures from their variational theory,
Chaos, Vol. 22, 2012, 03128
http://chaos.aip.org/resource/1/chaoeh/v22/i1/p013128_s1
Farazmand, Mohammad and George Haller,
Attracting and repelling Lagrangian coherent structures from a single computation,
Chaos, Vol. 23, 2013, 023101
http://chaos.aip.org/resource/1/chaoeh/v23/i2/p023101_s1
Froyland, Gary and Kathrin Padberg,
Almost invariant sets and invariant manifolds: Connecting probabilistic and
geometric descriptions of coherent structures in flows,
Physica D, Vol. 238, 2009, 1507-1523
http://www.sciencedirect.com/science/article/pii/S0167278909000803
Haller, G.,
Distinguished material surfaces and coherent structures in 3-D flows,
Physica D, Vol. 149, 2001, 248-277
Haller, G.,
Lagrangian coherent structures from approximate velocity data,
Phys. Fluids A, Vol. 14, 2002, 1851-1861
Web
Haller, G.,
A variational theory of hyperbolic Lagrangian Coherent Structures,
Physica D, Vol. 240, 2011, 574-598
http://www.sciencedirect.com/science/article/pii/S0167278910003143
Haller, G. and Francisco J. Beron-Vera,
Geodesic theory of transport barriers in two-dimensional flows,
Physica D, Vol. 241, 2012, 1680-1702
http://www.sciencedirect.com/science/article/pii/S016727891200187X
Haller, G. and A. C. Poje,
Finite-time transport in aperiodic flows,
Physica D, Vol. 119, 1998, 352-380
Web
Haller, G. and G. Yuan,
Lagrangian coherent structures and mixing in 2-D turbulence,
Physica D, Vol. 147, 2000, 352-370
Web
Inanc, Tamer et al.,
Optimal trajectory generation in ocean flows,
American Control Conference, Portland, OR, June 8-10, 2005, 674-679
Lekien, F.,
Time-Dependent Dynamical Systems and Geophysical Flows,
PhD Thesis, Caltech, 2003
Lekien, F. et al.,
Pollution release tied to invariant manifolds: A case study for the coast of Florida,
Physica D., Vol. 210, 2005, 1-20
Web
Lermusiaux, P. F. J. and F. Lekien,
Dynamics and Lagrangian coherent structures in the ocean and their uncertainty,
in "Dynamic Systems Methods in Fluid Dynamics," J. E. Marsden and J. Scheurle, eds.,
2005, 19-20
Web
Mancho, A. M. et al.,
A tutorial on dynamical systems concepts applies to Lagrangian transport in oceanic flows
defined as finite time data sets: Theoretical and computational issues,
Physics Reports, Vol. 437, 2006, 55-124
Mezic, Igor and S. Loire and Vladimir A. Fonoberov and P. Hogan,
A new mixing diagnostic and Gulf oil spill movement,
Science, Vol. 330, 486-489
http://www.sciencemag.org/content/330/6003/486
Provenzale, A.,
Transport by coherent barotrophic vortices,
Ann. Rev. Fluid Mech., Vol. 31, 1999, 55-93
Sadlo, F. and R. Peikart,
Visualizing Lagrangian coherent structures and comparison to vector field topology,
Proc. TopoInVis, Leipzig, Germany, Mar. 4-6, 2007
Web
Sadlo, F. and R. Peikart,
Efficient visualization of Lagrangian coherent structures by filtered AMR ridge extraction,
IEEE Trans. Visual. Comp. Graph., Vol. 13, 2007, 1456-1463
Web
Shadden, S. C. et al.,
Definition and properties of Lagrangian coherent structures from finite-time Lyapunov
exponents in 2-D aperiodic flows,
Physica D, Vol. 212, 2005, 271-304
Web
Wiggins, S.,
The dynamical systems approach to Lagrangian transport in oceanic flows,
Ann. Rev. Fluid Mech., Vol. 37, 2005, 295-328
Software
Matlab toolbox for LCS.
A library for investigating the numerics of dynamic systems.
Quantification of topological properties of an image or pattern.
For the computation of Conley-Morse graphs.
A research code for computing FTLE and extracting LCS.
A Matlab toolkit for working with LCS.
Computing FTLE fields and LCS by parallel processing using nVida CUDA.
Computation of invariant manifolds, LCS and hyperbolic properties for velocity fields defined by 2D+1 datasets.