In competitive swimming, most swimmers utilize a propulsion technique known as Underwater Undulatory Swimming (UUS) in the initial 15-m section following the start and after each turn. UUS mirrors the propulsion technique of cetaceans, wherein swimmers propel themselves through the water by rhythmically raising and lowering both lower limbs while maintaining both upper limbs in an erect and streamlined position. Previous studies have demonstrated that swimmers at higher competitive levels employ UUS to achieve greater swimming velocity following the start (Marinho et al., 2021, Pla et al., 2021). Consequently, increasing UUS speed is considered a crucial factor for competitive swimmers to gain an advantage in competitive races.

A review article that examined the factors determining UUS velocity reported that the kick frequency and vertical toe velocity as the primary kinematic variables (Ruiz-Navarro et al., 2022). Similarly, in a UUS experiment conducted in a water flume with flow velocities set at 70, 80 and 90 % of the maximum swimming velocity achievable by each swimmer, both kick frequency and mean toe vertical velocity during up-kick and down-kick increased significantly with increasing mainstream velocity (Yamakawa et al., 2022). These findings from previous studies clearly emphasize the significance of lower-limb velocity in determining UUS velocity.

So how does increasing the lower-limb movement speed increase the UUS velocity? Based on the principles of hydrodynamics, swimmers transfer momentum to the water through their swimming movement and gain propulsion through the reaction of the water. In other words, in swimming movement, unlike land movement, the swimmer is not propelled by a direct push against the ground but through the medium of water. Consequently, when focusing only on lower-limb movement, it remains unclear how much propulsive force is generated, and the precise mechanism by which the velocity of UUS increased eludes us. To shed light on this mechanism, it is necessary to quantitatively observe the water flow around the swimmer (velocity and vortex) when the swimmer performs a swimming movement. Therefore, recent attempts have employed the particle image velocimetry (PIV) method to visualize the flow around swimmers (Hochstein and Blickhan, 2011, Matsuuchi et al., 2009, Shimojo et al., 2019, Takagi et al., 2014b). In a previous study investigating the flow field around the foot during UUS using the PIV method in a water flume, a strong flow was observed in the ventral posterior direction (mainstream and vertical) from the end of the down-kick to the start of the up-kick. Conversely, they reported that a vertical upward flow was observed from the end of the up-kick to the beginning of the down-kick (Shimojo et al., 2019). However, in this study by Shimojo et al. (2019), only one test flow velocity (U) condition was set (0.8 m/s), and it remains to be determined how the velocity vector distribution in the flow field changes when U is varied. Therefore, although it is known that varying U increases the speed of movement of the lower limb, it is not yet clear how the velocity vector distribution changes in the process.

Therefore, the primary objective of this study was to determine the relationship between the changes in the kinematic characteristics of the lower limb and the resulting changes the velocity vector distribution in the flow field when U was varied using a controllable water flume.

Similar to previous studies that have varied U in the water flume (Yamakawa et al., 2022), it was hypothesized that the swimmer's toe velocity would increase as the U increased. Previous research has also shown that propulsion is acquired during both down-kick and up-kick, but up-kick acquire less propulsion than down-kick (Atkison et al., 2014). Mainly backward and vertical downward flow was observed after down-kick, whereas mainly vertical upward flow was observed after up-kick (Shimojo et al., 2019). Therefore, two effects were expected: (1) the vector of the flow field increases and body acceleration increases during the down-kick, and (2) the vector of the flow field increases (mainly the vertical upward vector increases) and body acceleration increases slightly during the up-kick.