Kinematic modeling and motion algorithm for long undulatory fins
仿生波动长鳍运动学建模及算法研究

Studies have shown that undulatory propulsion with long fins has advantages in stability, maneuverability, and low-speed retaining. By using the differential geometry, we develop a rules-surface-based kinematic model for a zero-depth fin. This model characterizes the undulatory properties, including the non-uniform height and the non-uniform amplitude. It has also been studied in-depth in Cartesian coordinates to reflect the curve-based and non-zero-depth properties. The corresponding undulation algorithm is proposed and implemented in the dynamic mesh analysis of computational fluid dynamics (CFD). To validate the effectiveness and feasibility of the proposed undulatory model and algorithm, simulations of an ideal zero-depth waving plate and the Gymnarchus niloticus (a freshwater fish which is pushed forward by undulations caused by a long dorsal fin) are given respectively, with specified morphological and undulatory parameters. This study may serve as a good platform for dynamic analysis of undulations.