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Published January 15, 2008 | Published
Journal Article Open

An overview of a Lagrangian method for analysis of animal wake dynamics


The fluid dynamic analysis of animal wakes is becoming increasingly popular in studies of animal swimming and flying, due in part to the development of quantitative flow visualization techniques such as digital particle imaging velocimetry (DPIV). In most studies, quasi-steady flow is assumed and the flow analysis is based on velocity and/or vorticity fields measured at a single time instant during the stroke cycle. The assumption of quasi-steady flow leads to neglect of unsteady (time-dependent) wake vortex added-mass effects, which can contribute significantly to the instantaneous locomotive forces. In this paper we review a Lagrangian approach recently introduced to determine unsteady wake vortex structure by tracking the trajectories of individual fluid particles in the flow, rather than by analyzing the velocity/vorticity fields at fixed locations and single instants in time as in the Eulerian perspective. Once the momentum of the wake vortex and its added mass are determined, the corresponding unsteady locomotive forces can be quantified. Unlike previous studies that estimated the time-averaged forces over the stroke cycle, this approach enables study of how instantaneous locomotive forces evolve over time. The utility of this method for analyses of DPIV velocity measurements is explored, with the goal of demonstrating its applicability to data that are typically available to investigators studying animal swimming and flying. The methods are equally applicable to computational fluid dynamics studies where velocity field calculations are available.

Additional Information

Published by The Company of Biologists 2008. Accepted 22 May 2007. First published online December 28, 2007. The authors thank C.P. Ellington and J.L. van Leeuwen for organizing the conference session in which this paper was originally presented in August 2006; M.S. Gordon for comments on the manuscript; and G.L. Brown, J.E. Marsden and P. Moin for enlightening discussions. The authors are also grateful to the anonymous referee for valuable suggestions that have led to several improvements in the manuscript. This research is funded by a grant from the Ocean Sciences Division, Biological Oceanography Program at NSF (OCE 0623475) to J.O.D.

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