Lagrangian Methods in Oceanography

LCS Web Sites

Francois Lekien
Lagrangian Coherent Structures in 2D Turbulence

LCS Papers and Tutorials

Lagrangian Coherent Structures: Analysis of Time-Dependent Dynamical Systems Using Finite-Time Lyapunov Exponents

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

LCS Toolbox

Matlab toolbox for LCS.

CAPD Library

A library for investigating the numerics of dynamic systems.

CHomP

Quantification of topological properties of an image or pattern.

cmgraphs

For the computation of Conley-Morse graphs.

FlowVC

A research code for computing FTLE and extracting LCS.

LCS Matlab

A Matlab toolkit for working with LCS.

cuda_ftle

Computing FTLE fields and LCS by parallel processing using nVida CUDA.

Mangen

Computation of invariant manifolds, LCS and hyperbolic properties for velocity fields defined by 2D+1 datasets.