There have been significant efforts recently aimed at improving the aerodynamic performance of aerofoils through the modification of their surfaces. Inspired by the drag-reducing properties of the tooth-like denticles that cover the skin of sharks, we describe here experimental and simulation-based investigations into the aerodynamic effects of novel denticle-inspired designs placed along the suction side of an aerofoil. Through parametric modelling to query a wide range of different designs, we discovered a set of denticle-inspired surface structures that achieve simultaneous drag reduction and lift generation on an aerofoil, resulting in lift-to-drag ratio improvements comparable to the best-reported for traditional low-profile vortex generators and even outperforming these existing designs at low angles of attack with improvements of up to 323%. Such behaviour is enabled by two concurrent mechanisms: (i) a separation bubble in the denticle's wake altering the flow pressure distribution of the aerofoil to enhance suction and (ii) streamwise vortices that replenish momentum loss in the boundary layer due to skin friction. Our findings not only open new avenues for improved aerodynamic design, but also provide new perspective on the role of the complex and potentially multifunctional morphology of shark denticles for increased swimming efficiency.

We present unifying rules governing the efficient locomotion of swimming fish and marine mammals. Using scaling and dimensional analysis, supported by new experimental data, we show that efficient locomotion occurs when the values of the Strouhal (St) number St(=f A/U) and A * (=A/L), two nondimensional numbers that relate forward speed U , tail-beat amplitude A, tail-beat frequency f , and the length of the swimmer L are bound to the tight ranges of 0.2-0.4 and 0.1-0.3, respectively. The tight range of 0.2-0.4 for the St number has previously been associated with optimal thrust generation. We show that the St number alone is insufficient to achieve optimal aquatic locomotion, and an additional condition on A * is needed. More importantly, we show that when swimming at minimal power consumption, the Strouhal number of a cruising swimmer is predetermined solely by the shape and drag characteristics of the swimmer. We show that diverse species of fish and cetaceans cruise indeed with the St number and A * predicted by our theory. Our findings provide a physical explanation as to why fast aquatic swimmers cruise with a relatively constant tail-beat amplitude of approximately 20% of the body length, and their swimming speed is nearly proportional to their tail-beat frequency.

Biomechanists and biologists alike have yet to fully understand the complex morphology and function of shark denticles, morphologically intricate tooth-like structures embedded into the skin of sharks. Denticles vary in many ways (such as size and shape) depending on shark species, and studies on denticle hydrodynamics have suggested that they may aid in drag reduction as well as increase both lift and thrust. Although previous studies have analyzed the effect of different denticle patterns on hydrodynamic performance, no previous work has focused on the effects of denticle size. Here, we report on the hydrodynamic properties of 3D printed shark skin foils with rigid denticles embedded into a flexible substrate. The patterning of these denticles was based on previously reported designs exhibiting the greatest hydrodynamic performance (which also most closely mimics real shark skin). The size of the denticles and the speed of the flow were varied, and the foils were evaluated under both static and dynamic conditions. Static tests showed drag reduction compared to a smooth control foil (without denticles) for the smallest denticle size, while medium and large denticles exhibited increased drag. Under dynamic testing conditions, the smallest denticles increased the self-propelled swimming speed, while the largest denticles reduced swimming performance. At higher speeds, the smallest denticles were also able to reduce power consumption compared to the control, demonstrating that their hydrodynamic effect depends on both denticle size and swimming speed. Our results thus provide new insights into the role of denticle size in shark swimming hydrodynamics across a range of locomotory modes, while simultaneously providing new design guidelines for the production of high performance low drag surface coatings for aquatic and aerospace applications.