This paper considers a single-sensor estimation of vortex shedding in cylinder wakes at $\text{Re}=100$ in simulations and at $\text{Re}=1036$ in experiments. A model based on harmonic decomposition is developed to capture the periodic dynamics of vortex shedding. Two model-based methods are proposed to estimate time-resolved flow fields. First, linear estimation (LE), which implements a Kalman filter to estimate the flow. Second, linear-trigonometric estimation (LTE), which utilizes the same Kalman filter together with a nonlinear relationship between harmonics of the vortex shedding frequency. LTE shows good performance and outperforms LE regarding the reconstruction of vortex shedding. Physically this suggests that, at the Reynolds numbers considered, the higher harmonic motions in the cylinder wake are slave to the fundamental frequency.

中文翻译：

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基于模型的非恒定圆柱尾流中涡流脱落的估计

本文考虑了汽缸尾流处涡旋脱落的单传感器估计 $\text{回覆}=100$ 在模拟和 $\text{回覆}=1036$在实验中。建立了基于谐波分解的模型来捕获涡旋脱落的周期性动力学。提出了两种基于模型的方法来估计时间分辨流场。首先是线性估计（LE），它实现了卡尔曼滤波器来估计流量。第二，线性三角估计（LTE），它利用相同的卡尔曼滤波器以及涡旋脱落频率的谐波之间的非线性关系。在涡旋脱落的重建方面，LTE表现出良好的性能，并且优于LE。从物理上讲，这表明，考虑到雷诺数，圆柱尾流中的高次谐波运动是基频的从动。