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First published online May 18, 2006
Journal of Experimental Biology 209, 2025-2033 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02242
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Fast-swimming hydromedusae exploit velar kinematics to form an optimal vortex wake

John O. Dabiri1,*, Sean P. Colin2 and John H. Costello3

1 Graduate Aeronautical Laboratories and Bioengineering, California Institute of Technology, Mail Code 138-78, Pasadena, CA 91125, USA
2 Biology and Marine Biology, Roger Williams University, MNS 241, Bristol, RI 02809, USA
3 Biology, Providence College, Providence, RI 02918, USA


Figure 1
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  		Fig. 1. Morphological analysis of N. bachei. (A,B) Images of N. bachei (A) at rest, and (B) during jet ejection. Image height is 7.2 mm. V, velum; DV, velar diameter; T, tentacles; OC, oral cavity; MW, mesogleal wall; A, animal apex. Out-pocketing of velum into funnel shape is discernable in B. (C) Sample of image analysis. Image from B superimposed with reconstructions of the oral cavity boundary (broken black line) and velum (solid black line), based on control points (white circles).

 

Figure 2
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  		Fig. 2. Measurements of N. bachei body kinematics during fast swimming. Two sets of measurements from distinct swimming cycles from two different animals (black and grey circles) are presented to indicate the repeatability of the swimming motions. Maximum measurement uncertainty is ±6%. A curve fit to the data (solid black line) is used in subsequent analyses. (A) Velar diameter versus time during the swimming cycle. (B) Oral cavity volume versus time during the swimming cycle.

 

Figure 3
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  		Fig. 3. Plot of vortex formation time (T*) during the jet ejection phase (t/Tejection) of the swimming cycle (solid black line). At the end of the ejection phase (black star), the vortex formation time coincides with the range of values producing maximum vortex growth in mechanically generated jet flows with similar aperture kinematics (grey band) (Dabiri and Gharib, 2005bGo), where the aperture diameter contraction rate ranges between 15% and 30% of the average jet velocity. For comparison, the measured velar aperture contraction rate in N. bachei is approximately 20% of the average jet velocity. Broken lines indicate measurement uncertainty of ±10% associated with calculation of vortex formation time (see Materials and methods). Note that the local plateau in the vortex formation time near t/Tejection=0.7 is within the error of the measurement trend.

 

Figure 4
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  		Fig. 4. Optimal vortex formation during fast-swimming of N. bachei. Image from dye flow visualization showing vortex formation in the wake of the animal. Image height is 7.2 mm. No trailing flow exists directly behind the vortex (see also movie in supplementary material), supporting the conclusion that the animal generates a single vortex (shown schematically in inset) per swimming cycle, despite the fact that T*max{approx}8.

 

Figure 5
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  		Fig. 5. Measurement and models of N. bachei swimming trajectory. The ratio of instantaneous forward motion (relative to its position at the start of the measured swimming cycle) to the maximum forward motion, x/Xmax, is plotted versus the current point in the full swimming cycle (i.e. ejection and relaxation). Both the real animal (solid black line) and the model that includes transient velar kinematics (broken black line) achieve continuous forward motion, whereas the model that assumes a constant velar aperture (dotted grey line) swims backward during the latter portion of the swimming cycle. Measurement uncertainty is ±3%.

 




© The Company of Biologists Ltd 2006