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First published online March 31, 2005
Journal of Experimental Biology 208, 1445-1451 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01530

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Propulsive force calculations in swimming frogs II. Application of a vortex ring model to DPIV data

Eize J. Stamhuis^1,* and Sandra Nauwelaerts²

¹ Department of Marine Biology, University of Groningen, Biological Centre, PO Box 14, 9750 AA Haren, The Netherlands
² Department of Biology, University of Antwerp, campus 3 eiken, Universiteitsplein 1, B-2610 Wilrijk (Antwerpen), Belgium

View larger version (36K): [in a new window]   Fig. 1. Diagram of a vortex ring in cross section with the X' and Y' axes indicated, velocity components and velocity profiles. (A) Cross section of vortex ring left behind by the frog foot just disappearing on the left. Red, clockwise vorticity; blue, anti-clockwise vorticity; Y'-axis is normal to the vortex ring; X'-axis is perpendicular to the normal axis, parallel to the ring plane. (B) Predicted v velocity profile along the Y'-axis. (C) Predicted u velocity profile through vortex core along the Y'-axis. (D) Predicted v velocity profile along the X'-axis through both vortex cores.

View larger version (65K): [in a new window]   Fig. 2. Top views of a swimming frog during two successive stages of the kick cycle, illustrating the absence of assumed propulsion enhancement mechanisms. (A) Leg extension phase, showing rearward-directed flow around the webbed feet without mutual interference, indicated by the forward-directed flow inbetween (colour indicates flow magnitude, red=vmax 0.66 m s–1; blue 0 m s–1). (B) Just after completion of the extension phase showing two separate vortex rings, one from each leg (colour indicates vorticity ranging from –0.15 s–1=blue to 0.15 s–1=red).

View larger version (15K): [in a new window]   Fig. 3. Example graphs from vortex ring velocity profiles. (A) The velocity profile v(Y') of the jet along the normal axis of the vortex ring. (B) Velocity profile u(Y') through one of the vortex cores. (C) The velocity distribution v along the X' axis through the central jet and both vortex cores.