鱼类游泳速度与尾鳍摆动的动力学关系研究

摘要:

游泳能力对鱼类洄游及生境修复营造具有重要意义。该文基于鱼类巡游状态下游泳推力与鱼体阻力平衡的思路，游泳推力主要考虑尾鳍摆动“反卡门涡街”推力，根据涡运动理论推导游泳推力与尾鳍摆动参数间的关系，鱼体阻力根据边界层理论划分为3个区间，不同流动状态下分别考虑摩擦阻力或形状阻力的主导作用，建立鱼类游泳速度与尾鳍摆动参数的动力学关系，获得无量纲游泳雷诺数Re与尾鳍摆动数Sw的标度律，通过鱼类游泳二维数值模拟及文献数据统计对该标度律参数进行标定和验证。结果表明：鱼类游泳雷诺数Re与尾鳍摆动数Sw关系符合Re=k·S_\rmw^n 的标度律，游泳雷诺数110 000时，标度律指数n分别为4/3、10/9和1.00；标度律系数k随着游泳雷诺数Re的增加分为3个区间，随着鱼体相对宽度b的增加呈减小趋势，标度律关系可进一步表示为Re=k(b)·S_\rmw^n ；基于文献数据统计表明该标度律关系是存在的，能够适用于典型鲹科推进模式的鱼类。研究成果可为鱼类游泳速度计算，进而为其洄游通道和生境营造等提供支撑。

Abstract:

Swimming ability plays a crucial role in fish migration and habitat restoration. This paper focuses on the balance between swimming thrust and fish body resistance during fish cruising. The study considers the ‘anti-Kaman vortex street’ force generated by the caudal fin oscillation as the main source of swimming thrust, and the relationship between swimming thrust and caudal fin oscillation parameters is deduced by applying the theory of vortex motion. Additionally, the fish body resistance is divided into three intervals based on the boundary layer theory, with the consideration of either friction resistance or shape resistance depending on the flow state. The study establishes the dynamic relationship between swimming speed and caudal fin oscillation parameters, and derives the scaling law connecting the dimensionless swimming Reynolds number Re and the caudal fin oscillation number Sw, which is calibrated and verified by two-dimensional numerical simulation of fish swimming and statistics of the literature data. The results reveal that: The relationship of fish swimming Reynolds number Re and the caudal fin oscillation number Sw conforms to the scaling law of Re=k·S_\rmw^n , and the scaling law exponent n is 4/3, 10/9 and 1.00 for the swimming Reynolds numbers of 110 000, respectively. The coefficient k of the scaling law is divided into three intervals with the increase of the swimming Reynolds number, which shows a negative correlation with the relative width of fish body b. The relationship of the scaling law can be further expressed as Re=k(b)·S_\rmw^n . The existence of the scaling law is proved by the statistical analysis of literature data, and the scaling law applies to fish swimming with typical carangiform modes. The study can provide support for the calculation of fish swimming speed, and then for the fish migration channel and habitat construction.