Bio-inspired design of body wave and morphology in fish swimming based on linear density

This paper presents a novel formula describing traveling body wave in fish swimming, offering an enhanced understanding of the locomotion and body shape of those fish swimming by body and/or caudal fin (BCF) movements. The formula is mainly determined by the linear density of the fish, under the constraint that the center of mass of the fish is fixed on the axis along the swimming direction. Further, it is shown that any pair of points on the fish body with a phase difference of 180° moves at opposite speeds, which has a constant ratio of magnitude in the lateral direction. By proper design of the body shape by an incremental approach, the lateral resistances experienced by the pair of points will be equal and opposite, so that the resultant of the lateral forces is nearly zero, minimizing the sideslip of the fish and the energy dissipation. Taking the tuna and leopard shark as examples, morphological designs for them are discussed in details. Finally, the body waves of anguilliform and thunniform are simulated.