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

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.