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First published online October 10, 2003

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The ontogenetic scaling of hydrodynamics and swimming performance in jellyfish (Aurelia aurita)

Matthew J. McHenry^1,* and Jason Jed²

¹ The Museum of Comparative Zoology, Harvard University, 26 Oxford St, Cambridge, MA 02138, USA
² The Department of Integrative Biology, University of California, Berkeley, CA 94720, USA

View larger version (24K): [in a new window]   Fig. 1. Morphometrics and hydrodynamic modeling. (A) The filled dots show the landmarks used to reconstruct the shape of the body and provide measurements for the parameters noted. (B,C) The two hydrodynamic models used in the present study are illustrated with the drag, D, and thrust, T, vectors predicted to be generated as the bell contracts and the bell margin adducts. (B) The jet model assumes thrust to be generated by a jet, Tjet. (C) The paddle model assumes thrust is generated by paddling, Tpaddle.

View larger version (51K): [in a new window]   Fig. 2. Representative kinematics of swimming in Aurelia aurita. (A) Video frames for one propulsive cycle. (B) The positions of landmarks (filled dots) were used to reconstruct the outer surface of the bell (thick line) and the inner surface of the bell cavity (thin line). (C) Measurements for the bell height (blue line) and diameter (red line) are shown during the pulse (gray band) and recovery (white band) phases of the propulsive cycle. (D) The margin angle and (E) the swimming speed are shown over time.

View larger version (35K): [in a new window]   Fig. 3. A computational simulation of jellyfish swimming. (A) A schematic of the body illustrates its shape at the beginning and immediately following the pulse phase (gray bar) for each propulsive cycle. (B) The jet model calculated thrust production from changes in bell height (blue line) and diameter (red line) and (C) the paddle model calculated thrust from changes in margin angle. (D) The force predicted by jet thrust (Tjet; green line), and drag (D; violet line) during a simulation of the jet model. The paddle thrust (Tpaddle; orange line) was generated in a separate simulation of the paddle model, and the drag generated during this simulation is not shown. (E) The changes in swimming speed predicted by paddle and jet models.

View larger version (21K): [in a new window]   Fig. 4. An experimental test of paddle and jetting models for the hydrodynamics of swimming in Aurelia aurita. The relationship between the measured and predicted mean swimming is shown for the paddle model (A) and the jet model (B). The black line has a slope of 1, which represents a perfectly accurate prediction of measured speed (N=18). The diameter of points is proportional to the bell diameter of jellyfish (see legend for scale). Representative large (J1; bell diameter, 8.5 cm) and small (J2; bell diameter, 1.8 cm) jellyfish are highlighted in black. The speed predictions for each model are compared with measurements of speed for J1 (C) and J2 (D).

View larger version (15K): [in a new window]   Fig. 5. The scaling of bell morphology with body mass. Linear regressions found by reduced major axis (black line; b) were significantly different (see Table 1 for statistics) from the null hypothesis (green line; bo), which predicts geometric similarity in bell height (A), bell diameter (B) and the ratio of height to diameter (C). The gray silhouettes in C approximate the bell shape of small and large medusae.

View larger version (14K): [in a new window]   Fig. 6. The scaling of bell kinematics with body mass. The null hypothesis (green line; bo), of kinematic similarity predicted constant values in duty factor and pulse frequency. (A) Duty factor was independent of body mass, as predicted by kinematic similarity. (B) The reduced major axis regression (black line; b) shows a decrease in pulse frequency with increasing body mass (see Table 1 for statistics).

View larger version (16K): [in a new window]   Fig. 7. The scaling of hydrodynamic forces predicted by the jet model. Maximum acceleration reaction (A) and thrust (B) scaled as predicted by kinematic similarity (green line; bo), but drag (C) increased with a lower exponent (black line; b) than the null hypothesis (see Table 1 for statistics).

View larger version (14K): [in a new window]   Fig. 8. The scaling of swimming performance. (A) The null hypothesis (green line; bo) was significantly different from the reduced major axis regression for measurements of swimming speed (black line; b). The measured scaling factor was not significantly different from predictions for the jet model (blue line; bjet), but was significantly different for the paddle model (orange line; bpaddle; see Table 2 for statistics). (B) There was no null hypothesis predicted for the hydrodynamic cost of transport (see Table 1 for statistics).

View larger version (64K): [in a new window]   Fig. 9. Parameter maps show how the scaling of the height-to-diameter ratio and pulse frequency with body mass is predicted to affect swimming speed and the hydrodynamic cost of transport. Gray lines follow patterns of ontogenetic change, and the performance values to the right of these lines are the mean performance predicted over ontogeny. (A,B) Gray silhouettes show the shape of the bell at high (prolate) and low (oblate) height to diameter values. The thin, broken, horizontal line shows isometric scaling where the jellyfish maintain a prolate morphology at all sizes, the solid line follows the allometric scaling that we measured (Fig. 5), and the thick, broken, horizontal line shows the isometric scaling where jellyfish maintain an oblate morphology at all sizes. (C,D) The thin, broken, horizontal line follows a constant high value of pulse frequency at all body sizes, the solid line tracks the change in frequency that we measured (Fig. 6), and the thick, broken, horizontal line maintains a constant low value for pulse frequency at all body sizes. (D) Notice that we have coded values for the hydrodynamic cost of transport (THCOT) exceeding 0.40 J kg-1 m-2 as light green in order to maintain a scale that results in visible typography for the rest of this parameter map.

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