Lagrangian coherent structures
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Lagrangian coherent structures are structures which separate dynamically distinct regions in time-varying systems such as turbulent flows in fluid mechanics. They can be defined in terms of finite-time Lyapunov exponents based on a frame-independent description of the system in terms of Lagrangian mechanics. Finite-time Lyapunov exponents can be used to find separatrices in time-dependent systems, which are often analogous to stable and unstable manifolds of time-independent systems. These separatrices are Lagrangian Coherent Structures. These structures divide dynamically distinct regions in the flow and reveal geometry which is often hidden when viewing the vector field or even trajectories of the system. Therefore these structures often provide a nice tool in analyzing systems with general time-dependence, especially for understanding transport.
Software packages have been developed to perform Lagrangian coherent structures computations:
- Dabiri, John O. "LCS MATLAB Kit". (source code)
- Shadden, Shawn C. "FlowVC". (source code)
- Haller, George. "LCS Tool".
- Jimenez, Raymond; Vankerschaver, Joris. "cuda_ftle". (source code)
- Mills, Peter. "CTRAJ".
- Du Toit, Philip C. "Newman". Archived from the original on 2010-06-13. (source code)
- Salman, H.; Hesthaven, J. S.; Warburton, T.; Haller, G. (2006). "Predicting transport by Lagrangian coherent structures with a high-order method". Theoretical and Computational Fluid Dynamics 21: 39. Bibcode:2007ThCFD..21...39S. doi:10.1007/s00162-006-0031-0.
- Haller, George. "Lagrangian Coherent Structures in 2D Turbulence". Archived from the original on 2007-10-09.
- Green, M. A.; Rowley, C. W.; Haller, G. (2007). "Detection of Lagrangian coherent structures in three-dimensional turbulence". Journal of Fluid Mechanics 572: 111. doi:10.1017/S0022112006003648.
- Kasten, J.; Hotz, I.; Hege, H. C. (2012). "On the Elusive Concept of Lagrangian Coherent Structures". Topological Methods in Data Analysis and Visualization II. Mathematics and Visualization. p. 207. doi:10.1007/978-3-642-23175-9_14. ISBN 978-3-642-23174-2.
- Shadden, S. C.; Lekien, F.; Marsden, J. E. (2005). "Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows". Physica D: Nonlinear Phenomena 212 (3–4): 271–304. Bibcode:2005PhyD..212..271S. doi:10.1016/j.physd.2005.10.007.
- Mathur, M.; Haller, G.; Peacock, T.; Ruppert-Felsot, J.; Swinney, H. (2007). "Uncovering the Lagrangian Skeleton of Turbulence". Physical Review Letters 98 (14). Bibcode:2007PhRvL..98n4502M. doi:10.1103/PhysRevLett.98.144502.
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