中文摘要：

长鳍波动推进鱼类在稳定性、机动性、低速下状态保持等方面较其它鱼类有着显著优势．本文将鱼类波动长鳍抽象为零厚度理想波动面，引入直纹面建立曲线坐标意义下波动长鳍的运动学模型，描述了长鳍波动推进时的非等幅波动、非对称波形等运动特征．面向理论分析和数值模拟，进一步扩充直纹面模型，使之满足弯曲基线、非零厚度等长鳍形态及运动特征，进而建立笛卡尔坐标系下的长鳍波动描述方程，相应地，设计了鱼类长鳍波动推进的运动描述算法．根据给定形体和运动参数，对零厚度理想波动板和弓鳍目“尼罗河魔鬼”鱼进行运动学仿真，验证了运动学模型及运动描述算法的有效性．

英文摘要：

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.