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Lagrangian coherent structures in n-dimensional systems

Lekien, Francois and Shadden, Shawn C. and Marsden, Jerrold E. (2007) Lagrangian coherent structures in n-dimensional systems. Journal of Mathematical Physics, 48 (6). Art. No. 065404. ISSN 0022-2488. doi:10.1063/1.2740025.

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Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring is to identify the dynamic boundaries between these almost-invariant regions. Recently, ridges in finite-time Lyapunov exponent fields have been used to define such hyperbolic, almost material, Lagrangian coherent structures in two-dimensional systems. The objective of this paper is to develop and apply a similar theory in higher dimensional spaces. While the separatrix nature of these structures is their most important property, a necessary condition is their almost material nature. This property is addressed in this paper. These results are applied to a model of Rayleigh-Bénard convection based on a three-dimensional extension of the model of Solomon and Gollub.

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Additional Information:© 2007 American Institute of Physics (Received 7 September 2006; accepted 23 April 2007; published online 13 June 2007) This work was partially supported by Office of Naval Research Grant No. N00014-04-1-0534 and has profited from the motivation and support of the entire Adaptive Sampling and Prediction (ASAP) team. The authors are grateful to Naomi Leonard for her valuable support and thank Chad Coulliette, George Haller, Manuel Fiadeiro, and Thomas Curtin for helpful remarks and enlightening discussions.
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Office of Naval Research (ONR)N00014-04-1-0534
Subject Keywords:flow simulation; Benard convection; Rayleigh-Benard instability; Lyapunov methods
Issue or Number:6
Record Number:CaltechAUTHORS:LEKjmp07
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8500
Deposited By: Archive Administrator
Deposited On:16 Aug 2007
Last Modified:08 Nov 2021 20:50

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