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First published online May 18, 2006
Journal of Experimental Biology 209, 2170-2181 (2006)
Published by The Company of Biologists 2006
doi: 10.1242/jeb.02254

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Hydrodynamic consequences of flexural stiffness and buoyancy for seaweeds: a study using physical models

Hannah Louise Stewart

Department of Integrative Biology, University of California, Berkeley, CA 94720, USA

View larger version (87K): [in a new window]   Fig. 1. Top: forereef (top row) and backreef (bottom row) models. From left to right: buoyant stiff, extra-buoyant moderately stiff, buoyant flexible and buoyant very flexible. Non-buoyant models were created by adding small lead shot to the flexible models. Rigid models were created by tying stiff models to the thin stainless steel rod at the far left of top row. Markings on ruler are in cm. Bottom: forereef models in `upright' positions in air to demonstrate differences in stiffness. EI decreases from left to right: 1, rigid; 2, stiff; 3, moderately stiff; 4, flexible; 5, very flexible.

View larger version (13K): [in a new window]   Fig. 2. Flexural stiffness (EI) and buoyancy of backreef and forereef models. Values are means ± s.d., N=3. EI of real backreef algae = 1.45x10-3, and of forereef algae = 4.51x10-3. Buoyancy of real backreef algae = 0.023 N, while forereef algae are negatively buoyant (-0.011 N) (Stewart 2004).

View larger version (15K): [in a new window]   Fig. 3. Unidirectional water velocity to a height of 25 cm above the floor of the flume at five motor settings (indicated by different symbols and fit with logarithmic best-fit lines highlighting the velocity profile in the flume at each flow speed). The height of the upright models (14 cm) is marked by a dotted line.

View larger version (11K): [in a new window]   Fig. 4. Velocity profile of flow in wave tank at 14 cm (the height of the models) over time.

View larger version (11K): [in a new window]   Fig. 5. Drag force experienced by forereef (filled symbols) and backreef (open symbols) shapes of (A) very flexible models, (B) flexible models, (C) stiff models and (D) extra-buoyant models at increasing unidirectional flow speed. Data are not shown for non-buoyant or rigid models as these comparisons were made by adding lead shot to stiff models, and attaching a steel rod to stiff models, altering their buoyancy and flexural stiffness but not their shape.

View larger version (17K): [in a new window]   Fig. 6. (A) Drag force experienced by models as a function of EI at the highest unidirectional flow speed (0.73 m s-1) for all models (excluding rigid models). Values are means ± s.d., N=6. Values for extra-buoyant and non-buoyant models fall above and below the best-fit logarithmic trend lines fit to data from buoyant models, respectively. (B) The maximum force experienced by models in waves for all models excluding rigid models (means ± s.d., N=6). Values for extra-buoyant and non-buoyant models fall above the best-fit logarithmic trend lines fit to data from buoyant models.

View larger version (14K): [in a new window]   Fig. 7. Angle of deflection of models of increasing EI at the highest unidirectional flow speed. Values are means ± s.d., N=3. Upright posture is 90°. Non-buoyant models deflect more than buoyant models of the same EI as determined by Kruskall-Wallis non-parametric analysis (H=33.56, d.f.=11, P<0.05). Extra buoyant models deflect less than predicted by best-fit trend lines fit to data from models that vary in EI.

View larger version (13K): [in a new window]   Fig. 8. The index of compaction of all models at the highest unidirectional flow speed (73 cm s-1). Values are means ± s.d., N=6. Only the most flexible models were significantly compacted, and backreef models more so than forereef models, as determined by Kruskall-Wallis non-parametric analysis (H=30.23, d.f.=11, P<0.05) and Nemenyi post-hoc multiple comparisons (Zar, 1999). Letters that are different indicate significant differences between groups as determined by Nemenyi post-hoc multiple comparisons (Zar, 1999).

View larger version (9K): [in a new window]   Fig. 9. Tracings of the motion of models of each type in waves. Arrows indicate the distance the tip of the model moved from its upright position (dotted line) in one direction per wave (not to scale). a, very flexible, buoyant; b, flexible, buoyant; c, flexible, non-buoyant; d, stiff, extra-buoyant; e, stiff, buoyant; f, rigid buoyant.

View larger version (35K): [in a new window]   Fig. 10. (A) Water velocity and model position during the passage of a wave. For water velocity, positive numbers indicate the water is moving in one direction in the wave tank, and negative numbers indicate that the water is moving in the other direction. In each direction the water speed increases to a maximum velocity and then slows down before reversing and going in the other direction. Position indicates the distance deflected by the model at a particular water velocity. (B) Position of stiff and flexible models during the passage of a wave. Stiff models are deflected the maximum distance during high velocities, and begin to right themselves as the flow slows. Flexible models are deflected the maximum distance just before the flow begins to move in the opposite direction. (C) Position of models of various levels of buoyancy during the passage of a wave. Extra-buoyant and non-buoyant models are deflected less during each wave than are moderately buoyant models, and are extended in the direction of flow during higher velocities than are moderately buoyant models.

View larger version (18K): [in a new window]   Fig. 11. Force and position of points 1 and 2 on a very flexible model during waves. Models of the lowest flexural stiffness experienced whiplashing (see text for explanation) where the tip of the model lagged behind the middle portion. Maximum force is experienced when point 2 is displaced the furthest (highlighted by dotted line). Maximum displacement of point 1 occurs after the model experiences peak force. x axis is time in arbitrary units.

View larger version (13K): [in a new window]   Fig. 12. Relative velocity of models at time of peak force in waves as a function of EI. Values are means ± s.d., N=6.