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First published online April 8, 2004
Journal of Experimental Biology 207, 1633-1642 (2004)
Published by The Company of Biologists 2004
doi: 10.1242/jeb.00948
Strouhal numbers and optimization of swimming by odontocete cetaceans
1 SSC San Diego, 53560 Hull Street, 211, San Diego, CA 92152, USA
2 Department of Biology, West Chester University, West Chester, PA 19383,
USA
* Author for correspondence (e-mail: rohr{at}spawar.navy.mil)
Accepted 17 February 2004
Swimming efficiencies of fish and cetaceans have been related to a certain
synchrony between stroke cycle frequency, peak-to-peak tail/fluke amplitude
and mean swimming speed. These kinematic parameters form a non-dimensional
wake parameter, referred to as a Strouhal number, which for the range between
0.20 and 0.40 has been associated with enhanced swimming efficiency for fish
and cetaceans. Yet to date there has been no direct experimental
substantiation of what Strouhal numbers are preferred by swimming cetaceans.
To address this lack of data, a total of 248 Strouhal numbers were calculated
for the captive odontocete cetaceans Tursiops truncatus,
Pseudorca crassidens, Orcinus orca, Globicephala
melaena, Lagenorhynchus obliquidens and Stenella
frontalis. Although the average Strouhal number calculated for each
species is within the accepted range, considerable scatter is found in the
data both within species and among individuals. A greater proportion of
Strouhal values occur between 0.20 and 0.30 (74%) than the 0.25–0.35
(55%) range predicted for maximum swimming efficiency. Within 0.05 Strouhal
increments, the greatest number of Strouhal values was found between 0.225 and
0.275 (44%). Where propulsive efficiency data were available (Tursiops
truncatus, Pseudorca crassidens, Orcinus orca), peak
swimming efficiency corresponded to this same Strouhal range. The odontocete
cetacean data show that, besides being generally limited to a range of
Strouhal numbers between 0.20 and 0.40, the kinematic parameters comprising
the Strouhal number provide additional constraints. Fluke-beat frequency
normalized by the ratio of swimming speed to body length was generally
restricted from 1 to 2, whereas peak-to-peak fluke amplitude normalized by
body length occurred predominantly between 0.15 and 0.25. The results indicate
that the kinematics of the propulsive flukes of odontocete cetaceans are not
solely dependent on Strouhal number, and the Strouhal number range for
odontocete cetaceans occurs at slightly (
20%) lower values than
previously predicted for maximum swimming efficiency.
Key words: Strouhal number, swimming, dolphin, cetacean, odontocete, Tursiops, Pseudorca, Orcinus, Lagenorhynchus, Globicephala, Stenella, Delphinapterus
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