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Published May 20, 2009 | public
Journal Article

Lagrangian coherent structures in low Reynolds number swimming


This work explores the utility of the finite-time Lyapunov exponent (FTLE) field for revealing flow structures in low Reynolds number biological locomotion. Previous studies of high Reynolds number unsteady flows have demonstrated that ridges of the FTLE field coincide with transport barriers within the flow, which are not shown by a more classical quantity such as vorticity. In low Reynolds number locomotion (O(1)–O(100)), in which viscous diffusion rapidly smears the vorticity in the wake, the FTLE field has the potential to add new insight to locomotion mechanics. The target of study is an articulated two-dimensional model for jellyfish-like locomotion, with swimming Reynolds number of order 1. The self-propulsion of the model is numerically simulated with a viscous vortex particle method, using kinematics adapted from previous experimental measurements on a live medusan swimmer. The roles of the ridges of the computed forward- and backward-time FTLE fields are clarified by tracking clusters of particles both backward and forward in time. It is shown that a series of ridges in front of the jellyfish in the forward-time FTLE field transport slender fingers of fluid toward the lip of the bell orifice, which are pulled once per contraction cycle into the wake of the jellyfish, where the fluid remains partitioned. A strong ridge in the backward-time FTLE field reveals a persistent barrier between fluid inside and outside the subumbrellar cavity. The system is also analyzed in a body-fixed frame subject to a steady free stream, and the FTLE field is used to highlight differences in these frames of reference.

Additional Information

© Institute of Physics and IOP Publishing Limited 2009. Received 2 September 2008, in final form 16 December 2008. Published 21 April 2009. Print publication: Issue 20 (20 May 2009). MMW acknowledges the support of a GAANN Fellowship from the US Department of Education. JDE was supported by the National Science Foundation under award CBET-0645228. The authors also acknowledge funding from the NSF Biological Oceanography Program (OCE-0623475 to JOD).

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