Abstract This paper analyzes the influence of turbulence on a wake-oscillator model. Turbulence is introduced by randomizing the model proposed by Facchinetti et al. under the quasi-steady assumption. A multiple scale analysis of the deterministic model shows that the response is governed by a dimensionless group D , expressed as a function of the amplitudes of the forcing terms in the two governing equations, the total (aerodynamic plus structural) damping and the parameter e of the fluid Van der Pol oscillator. The influence of turbulence is interpreted as a stochastic noise of small intensity and with a slower timescale than the (fast) oscillations, which is typical of wind engineering applications. A slow phase model of the problem is then derived by assuming that the small turbulence drives the system only slightly away from its limit cycle in smooth flow conditions. Standard modeling techniques borrowed from other fields of physics, in particular the observation of phase shifts and their accumulation, are used to highlight conditions under which the turbulence of the oncoming flow might reduce the amplitudes of vibrations of the body. The slow phase model is derived in smooth flow conditions, then extended to turbulent flow. It recalls that the phase plays a central role in synchronization problems, and that the response amplitude should only be considered as a sub-product of the slow phase. The slow phase model is expressed by means of a first order nonlinear differential equation for the phase and a memoryless transformation for the response amplitudes. Its solution is explicit and simple in some limiting cases. In particular, for small turbulence intensity, the response is shown to be insensitive to turbulence when its frequency content is not low enough. This major dependence upon the frequency content of the turbulence explains that the reduction of VIV due to turbulence cannot be explained by the turbulence intensity only, as usually considered today. The required relative smallnesses of the turbulence and its frequency content naturally appear in the derivation, which is led in a dimensionless manner. Finally, the present study constitutes an analysis of a phenomenological model which could be used in a much wider concept than of the elastically-mounted circular cylinder.

中文翻译：

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用于平滑和湍流迎面而来的流动的涡激振动的慢相模型的推导

摘要 本文分析了湍流对尾流振荡模型的影响。通过随机化 Facchinetti 等人提出的模型来引入湍流。在准稳态假设下。确定性模型的多尺度分析表明响应由无量纲组 D 控制，表示为两个控制方程中强迫项幅度的函数，总（空气动力学加结构）阻尼和参数 e流体范德波尔振荡器。湍流的影响被解释为强度小且时间尺度比（快速）振荡慢的随机噪声，这是风工程应用的典型特征。然后通过假设小湍流驱动系统在平滑流动条件下仅略微偏离其极限环来推导出该问题的慢相模型。从其他物理学领域借用的标准建模技术，特别是对相移及其累积的观察，用于强调即将到来的流动的湍流可能会降低身体振动幅度的条件。慢相模型是在平滑流动条件下导出的，然后扩展到湍流。它回忆起相位在同步问题中起着核心作用，响应幅度应仅被视为慢相位的子产品。慢相位模型通过相位的一阶非线性微分方程和响应幅度的无记忆变换表示。在某些限制情况下，它的解决方案是明确而简单的。特别是，对于小湍流强度，当湍流的频率成分不够低时，响应显示对湍流不敏感。这种对湍流频率内容的主要依赖解释了由于湍流引起的 VIV 的降低不能仅用湍流强度来解释，正如今天通常认为的那样。所需的相对较小的湍流及其频率成分自然出现在以无量纲方式导出的推导中。最后，