Form, function, and divergence of a generic fin shape in small cetaceans.

Tail flukes as well as the dorsal fin are the apomorphic traits of cetaceans which appeared during the evolutionary process of adaptation to the aquatic life. Both appendages present a wing-like shape associated with lift generation and low drag. We hypothesized that the evolution of fins as lifting structures led to a generic wing design, where the dimensionless parameters of the fin cross-sections are invariant with respect to the body length and taxonomy of small cetaceans (Hypothesis I). We also hypothesized that constraints on variability of a generic fin shape are associated with the primary function of the fin as a fixed or flapping hydrofoil (Hypothesis II). To verify these hypotheses, we examined how the variation in the fin's morphological traits is linked to the primary function, species and body length. Hydrodynamic characteristics of the fin cross-sections were examined with the CFD software and compared with similar engineered airfoils. Generic wing design of both fins was found in a wing-like planform and a streamlined cross-sectional geometry optimized for lift generation. Divergence in a generic fin shape both on the planform and cross-sectional level was found to be related with the fin specialization in fixed or flapping hydrofoil function. Cross-sections of the dorsal fin were found to be optimized for the narrow range of small angles of attack. Cross-sections of tail flukes were found to be more stable for higher angles of attack and had gradual stall characteristics. The obtained results provide an insight into the divergent evolutionary pathways of a generic wing-like shape of the fins of cetaceans under specific demands of thrust production, swimming stability and turning control.