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. 2024 Aug;21(217):20240063.
doi: 10.1098/rsif.2024.0063. Epub 2024 Aug 2.

Three-dimensional shape of natural riblets in the white shark: relationship between the denticle morphology and swimming speed of sharks

Affiliations

Three-dimensional shape of natural riblets in the white shark: relationship between the denticle morphology and swimming speed of sharks

Shotaro Sayama et al. J R Soc Interface. 2024 Aug.

Abstract

The ridges of the dermal denticles of migratory sharks have inspired riblets to reduce the frictional drag of a fluid. In particular, the dermal denticles of white sharks (Carcharodon carcharias) are characterized by a high middle ridge and low side ridges. The detailed morphology of their denticles and their variation along the body, however, have never been investigated. Moreover, the hydrodynamic function of high-low combinations of ridges is unknown. In this article, the ridge spacings and heights of the white shark denticles were three-dimensionally quantified using microfocus X-ray computed tomography. Then, the swimming speed at which the ridges would reduce drag was hydrodynamically calculated with a flat plate body model and previous riblet data. High ridges with a large spacing were found to effectively reduce drag at a migration speed of 2.3 m s-1, while adjacent high and low ridges with a small spacing reduced drag at a burst hunting speed of 5.1 m s-1. Moreover, the above hydrodynamic calculation method was also applied to the shortfin mako shark and an extinct giant shark (called megalodon) with known ridge spacings, resulting in the estimated hunting speeds of 10.5 m s-1and 5.9 m s-1, respectively.

Keywords: Carcharodon carcharias; drag reduction; shark skin; turbulent boundary layer.

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Conflict of interest statement

We declare we have no competing interests.

Figures

Side view of a white shark (NSMT-P 125500) showing skin sampling locations with the representative denticle taken by micro X-ray CT..
Figure 1.
Side view of a white shark (NSMT-P 125500) showing skin sampling locations with the representative denticle taken by X-ray CT. The shark image was cropped from a side-view photo. Note that the sampling was conducted on the right side of the body.
(a) Example denticle at L3 illustrating the definition of ridge spacing and height.
Figure 2.
(a) Example denticle at L3 illustrating the definition of ridge spacing and height. s 1 is the spacing between the neighbouring high middle ridge and low side ridge. h 1 is the height of the low side ridge. h 2 is the height of the middle high ridge. Details of the measurement methods, such as the orientation of the denticle and the measured positions, are given in Appendix A. (b) Schematics of a scalloped riblet with h/s = 0.5 viewed from the flow direction.
Example of a staggered array of denticles at D4.
Figure 3.
Example of a staggered array of denticles at D4 ((a) front top view, (b) lateral view). s 2 is the spacing between the high middle ridges.
Schematic of the size relationship between the ridge spacing and streamwise vortices in the turbulent boundary layer.
Figure 4.
Schematic of the size relationship between the ridge spacing and streamwise vortices in the turbulent boundary layer. A large streamwise vortex of slow flow ( U = 2 m s−1) is pushed away from the bottom surface by the high middle ridges, resulting in a reduction in friction drag. On the other hand, the small streamwise vortex of fast flow ( U = 5 m s−1) is pushed away by the neighbouring ridges. The denticles in this figure are replicas of one denticle at L3.
Top views of the denticles measured by X-ray micro-CT.
Figure 5.
Top views of the denticles measured by X-ray CT. The locations are indicated on a model of our shark obtained by three-dimensional surface scanning. x1 and x2 denote the distances from the leading edge of the snout and the caudal fin, respectively. Note that the sampling was conducted on the right side of the body. The sampling locations were identified using photographs.
Mean ridge spacing of S1 (n = 12) for each measured location.
Figure 6.
Mean and s.d. of the ridge spacing of s 1 (n = 12) for each measured location.
Mean and s.d. of the ridge heights h1 (n = 12) (a)and h2 (n = 6) (b)for each location.
Figure 7.
Mean and s.d. of the ridge heights h 1 (n = 12) (a) and h2 (n = 6) (b) for each location.
Ratio of the height of the high middle ridge to that of the low side ridge at each location.
Figure 8.
Ratio of the height of the high middle ridge to that of the low side ridge at each location.
Ratio of the ridge height to the ridge spacing for the high middle ridge.
Figure 9.
Ratio of the ridge height to the ridge spacing for the high middle ridge (a) and the low side ridge (b) at each location.
Non-dimensional ridge spacing
Figure 10.
Mean and s.d. of the non-dimensional ridge spacing s 1 + at U = 1 m s−1 (a), 2 m s−1 (b), 5 m s−1 (c) and 10 m s−1 (d). The grey shaded area indicates the range at which s 1 + values are less than 27.5, representing the range of reduced drag. The black horizontal line indicates the optimal s 1 + value of 17, which corresponds to the maximum drag reduction.
Non-dimensional low side ridge height
Figure 11.
Mean and s.d. of the non-dimensional low side ridge height h 1 + at U = 1 m s−1 (a), 2 m s−1 (b), 5 m s−1 (c) and 10 m s−1 (d).
Non-dimensional high middle ridge height.
Figure 12.
Mean and s.d. of the non-dimensional high middle ridge height h 2 + at U = 1 m s−1 (a), 2 m s−1 (b), 5 m s−1 (c) and 10 m s−1 (d).
Non-dimensional ridge spacing s2+.
Figure 13.
Mean and s.d. of the non-dimensional ridge spacing s 2 + at U = 1 m s−1 (a), 2 m s−1 (b), 5 m s−1 (c) and 10 m s−1 (d). The grey shaded area indicates the range where s 2 + values are less than 27.5, representing the range of reduced drag. The black horizontal line indicates the optimal s 2 + value of 17, which corresponds to the maximum drag reduction.
Comparison between the theoretical ridge spacing for
Figure 14.
Comparison between the theoretical ridge spacing for s + = 17 and the measured s 1 and s 2 values for each U .
Schematic of the denticle array model of the hammerhead shark, with seven ridges for each denticle.
Figure 15.
Schematic of the denticle array model of the hammerhead shark, with seven ridges for each denticle.
Definition of the angles and viewpoints for measuring denticles.
Figure 16.
Definition of the angles and viewpoints for measuring denticles. (a) Frontal view. The bottoms of the two grooves were aligned parallel to the y-axis. (b) Top view. The denticle was rotated so that the three ridges became parallel to the x-axis. (c) Side cross section at the bottom of the groove. Approximately 10–50% of the region from the posterior edge was flat. The denticle was rotated so that the flat region became parallel to the x-axis. (d) Side view of the denticle.

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