Fish swim by undulating their body to ensure propulsion. In steady state, thrust is balanced by a total drag force, whose dominant terms depend on the Reynolds number and on the flow regime. If skin friction prevails on pressure drag in the laminar regime, and conversely in the turbulent regime, it is not clear how important is the contribution of the vortex-induced drag in both regimes. In this article, we tackle both flow regimes within the same numerical framework to address this question and the relevant scaling laws at play. In particular, we show in the turbulent regime that the combination of both the pressure and vortex-induced drags sets the Strouhal number between 0.2 and 0.4 following the thrust and drag balance, in very good agreement with natural swimmers. In the laminar regime, the vortex-induced drag can be neglected in most cases. If not, we rationalize the correction and show that our two-dimensional swimmer needs to account for a significant amplification of the drag force to match the biological data.

中文翻译：

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自推式灵活游泳者的阻力分析

鱼会通过波动其身体来游动以确保推进。在稳态下，推力由总阻力平衡，总阻力取决于雷诺数和流动状态。如果在层流状态下压力拖曳中普遍存在皮肤摩擦，而在湍流状态下则相反，尚不清楚涡流诱导的阻力在这两种情况下的重要性有多重要。在本文中，我们将在同一个数值框架内处理两种流动形式，以解决该问题以及相关的比例定律。特别是，我们在湍流状态下表明，压力和涡流阻力的组合使推力和阻力平衡后的Strouhal数在0.2到0.4之间，这与自然游泳者非常吻合。在层流状态下，大多数情况下可以忽略涡流引起的阻力。