Based on a high-order implicit discontinuous Galerkin method, numerical simulations of a two-dimensional oscillating foil are performed to explore the origin of basic aspects of the flow such as the generation of interesting flow structures in the wake and the associated aerodynamic forces. Dimensional arguments suggest that the flow is characterized by non dimensional aerodynamic coefficients depending on the kinematics of the oscillation, such its frequency and amplitude, and on the dynamics of the flow, such as the Reynolds number. Most of the studies have concentrated their attention on the role played by the kinematic of the oscillation with less or no attention to the effect of the Reynolds number. Here, we show that this effect cannot be neglected in the study of the phenomena at the basis of the generation of lift and thrust. We found that the Reynolds number plays a fundamental role for the development of thrust by defining critical values $R{e}_c$ for the switch from drag to thrust conditions. It is also shown that for $Re>R{e}_c$, the Reynolds number defines additional subcritical values which are at the basis of flow instabilities leading to smooth and sharp transitions of the structure of the wake and of the related aerodynamic forces. For the analysis of the behaviour of the flow, the space of phases composed by the instantaneous lift and thrust $(c_L,c_T)$ is introduced. It is shown how the orbits in the $(c_L,c_T)$-space allow us for a clear understanding of the physical evolution of the flow system and of the cyclical phenomena composing it.

基于高阶隐式不连续Galerkin方法，对二维振荡箔进行了数值模拟，以探索流动基本方面的起源，例如尾流中有趣的流动结构的产生以及相关的空气动力。尺寸论据表明，流动的特征在于无量纲的空气动力学系数，这取决于振动的运动学，例如其频率和幅度，以及流动的动力学，例如雷诺数。大多数研究都将注意力集中在振荡运动学上所起的作用，而很少或根本没有注意雷诺数的影响。在这里，我们表明在产生升力和推力的基础上对现象的研究中不能忽略这种影响。$\mathrm{[R}{Ë}_C$从阻力状态切换到推力状态。还表明，对于$\mathrm{[R}Ë>\mathrm{[R}{Ë}_C$雷诺数定义了其他次临界值，这些次临界值是基于流动不稳定性的基础，从而导致尾流结构和相关的空气动力平稳而急剧地过渡。为了分析流动特性，由瞬时升力和推力组成的相空间$（C_{\mathrm{大号}}，C_{Ť}）$介绍。它显示了如何在轨道$（C_{\mathrm{大号}}，C_{Ť}）$空间使我们能够清楚地了解流动系统的物理演化及其组成的周期性现象。