We investigate experimentally three-dimensional (3D) hydrodynamic turbulence at scales larger than the forcing scale. We manage to perform a scale separation between the forcing scale and the container size by injecting energy into the fluid using centimetric magnetic particles. We measure the statistics of the fluid velocity field at scales larger than the forcing scale (energy spectra, velocity distributions, and energy flux spectrum). In particular, we show that the large-scale dynamics are in statistical equilibrium and can be described with an effective temperature, although not isolated from the turbulent Kolmogorov cascade. In the large-scale domain, the energy flux is zero on average but exhibits intense temporal fluctuations. Our Letter paves the way to use equilibrium statistical mechanics to describe the large-scale properties of 3D turbulent flows.

中文翻译：

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三维流体动力湍流中大尺度的统计平衡

我们在大于强迫尺度的尺度上通过实验研究三维 (3D) 流体动力湍流。我们通过使用厘米磁性粒子向流体中注入能量，设法在强制刻度和容器尺寸之间进行刻度分离。我们以大于强迫尺度（能量谱、速度分布和能量通量谱）的尺度测量流体速度场的统计数据。特别是，我们表明大尺度动力学处于统计平衡，并且可以用有效温度来描述，尽管没有与湍流 Kolmogorov 级联隔离。在大尺度域中，能量通量平均为零，但表现出强烈的时间波动。