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Published June 2007 | Published
Journal Article Open

Lagrangian coherent structures in n-dimensional systems

Abstract

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.

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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