Flow over a fish-like airfoil is numerically investigated to elaborate the hydrodynamics of the undulatory braking locomotion for an elongated eel-like body or long-based fin. For undulation with low frequency, we find that boundary layer separation occurs in a parameter region with wakes in which two vortex pairs are formed per undulatory period. The physical mechanism of separation is governed by the slip (the ratio of swimming-to-body-wave speed), and the critical value of the slip in an inertial flow regime is approximately 4/3 rather than 1, which is independent of steepness (or amplitude). The relationship between pressure drag and relative velocity (between phase speed and free stream velocity) changes from linear to quadratic, corresponding to two different flow structures; this happens due to boundary layer separation, and the piecewise scaling relationship between pressure drag and relative velocity is explicitly clarified. Considering the viscosity effects, the separation criterion and the scaling relationship in the case of an undulatory brake are both synthetically modified using the Reynolds number, with all the required parameters clearly expressed. The results of this study provide physical insight into understanding the flow structures and hydrodynamics of the undulatory braking locomotion, which has instructional significance to brake design.

对鱼状机翼上的流动进行了数值研究，以阐述细长的鳗鱼状身体或长基鳍的波动制动运动的流体动力学。对于低频波动，我们发现边界层分离发生在具有尾流的参数区域，其中每个波动周期形成两个涡旋对。分离的物理机制由滑移（游泳与体波速度的比值）控制，惯性流态滑移的临界值约为 4/3 而不是 1，与陡度无关（或振幅）。压力阻力与相对速度（相速度与自由流速度之间）的关系由线性变为二次，对应两种不同的流动结构；这是由于边界层分离而发生的，明确阐明了压力阻力与相对速度之间的分段缩放关系。考虑到粘度影响，波动制动情况下的分离标准和比例关系都使用雷诺数进行了综合修改，并清楚地表达了所有所需的参数。这项研究的结果为理解波动制动运动的流动结构和流体动力学提供了物理洞察力，这对制动设计具有指导意义。清楚地表达了所有必需的参数。这项研究的结果为理解波动制动运动的流动结构和流体动力学提供了物理洞察力，这对制动设计具有指导意义。清楚地表达了所有必需的参数。这项研究的结果为理解波动制动运动的流动结构和流体动力学提供了物理洞察力，这对制动设计具有指导意义。