Numerous species of aquatic invertebrates, including crustaceans, swim by oscillating multiple closely spaced appendages. The coordinated, out-of-phase motion of these appendages, known as "metachronal paddling", has been well-established to improve swimming performance relative to synchronous paddling. Invertebrates employing this propulsion strategy cover a wide range of body sizes and shapes, but the ratio of appendage spacing (G) to the appendage length (L) has been reported to lie in a comparatively narrow range of 0.2 < G/L ≤ 0.65. The functional role of G/L on metachronal swimming performance is unknown. We hypothesized that for a given Reynolds number and stroke amplitude, hydrodynamic interactions promoted by metachronal stroke kinematics with small G/L can increase forward swimming speed. We used a dynamically scaled self-propelling robot to comparatively examine swimming performance and wake development of metachronal and synchronous paddling under varying G/L, phase lag, and stroke amplitude. G/L was varied from 0.4 to 1.5, with the expectation that when G/L is large, there should be no performance difference between metachronal and synchronous paddling due to a lack of interaction between vortices that form on the appendages. Metachronal stroking at non-zero phase lag with G/L in the biological range produced faster swimming speeds than synchronous stroking. As G/L increased and as stroke amplitude decreased, the influence of phase lag on the swimming speed of the robot was reduced. For smaller G/L, vortex interactions between adjacent appendages generated a horizontally-oriented wake and increased momentum fluxes relative to larger G/L, which contributed to increasing swimming speed. We find that while metachronal motion augments swimming performance for closely spaced appendages (G/L < 1), moderately spaced appendages (1.0 ≤ G/L ≤ 1.5) can benefit from metachronal motion only when the stroke amplitude is large.

中文翻译：

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较近的肢体间距通过促进尖端涡旋相互作用而提高了异时游泳速度

许多水生无脊椎动物，包括甲壳类，都通过振荡多个紧密间隔的附肢而游动。这些附属物的协调的，异相的运动被称为“同步划水”，已经建立起来，可以相对于同步划水提高游泳性能。采用这种推进战略无脊椎动物覆盖大范围的身体大小和形状的，但附属物间距（之比G ^），以附肢长度（大号）已在比较窄的范围内的0.2 <被报道谎言ģ /大号≤0.65。G / L的功能作用关于异时游泳的表现还不得而知。我们假设，对于给定的雷诺数和中风的幅度，水动力相互作用促进与小metachronal冲程运动摹/大号可以增加前进的游泳速度。我们使用了动态缩放的自推式机器人来比较地考察游泳性能以及在变化的G / L，相位滞后和行程幅度下进行同步划水和同步划水的发展。G / L从0.4到1.5不等，期望当G / L如果幅度很大，则由于在肢体上形成的涡流之间缺乏相互作用，因此在同步和同步划桨之间应该没有性能差异。在生物范围内，G / L处于非零相位滞后的准时冲程比同步冲程产生更快的游泳速度。随着G / L的增加和冲程幅度的减小，相位滞后对机器人游泳速度的影响减小了。对于较小的G / L，相对较大的G / L而言，相邻附肢之间的涡旋相互作用产生了水平方向的尾流并增加了动量通量。，这有助于提高游泳速度。我们发现，虽然metachronal运动增强件游泳紧密间隔的附肢（性能ģ /大号<1），中度隔开附属物（1.0≤ ģ /大号≤1.5）可从metachronal运动受益只有当行程振幅大。