An improved version of the non-equilibrium theory of non-homogeneous turbulence of Chen & Vassilicos (J. Fluid Mech., vol. 938, 2022, A7) predicts that an intermediate range of length scales exists where the interscale turbulence transfer rate, the two-point interspace turbulence transport rate and the two-point pressure gradient velocity correlation term in the two-point small-scale turbulent energy equation are all proportional to the turbulence dissipation rate and independent of length scale. Particle image velocimetry measurements in a field of view under the turbulence-generating impellers in a baffled water tank support these predictions and show that the measured small-scale turbulence is significantly non-homogeneous. The particle image velocimetry measurements also suggest that the rate with which large scales lose energy to the small scales in the two-point large-scale turbulent energy equation also appears to be approximately proportional to the turbulence dissipation rate and independent of length scale in the same intermediate range and that this rate may not balance the interscale turbulence transfer rate in the two-point small-scale turbulent energy equation because of turbulent energy transport caused by the non-homogeneity.

中文翻译：

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非均匀稳态湍流中具有类柯尔莫哥洛夫尺度的逐尺度非平衡

Chen 和 Vassilicos 的非均匀湍流非平衡理论的改进版本（J.流体机械。，卷。 938, 2022, A7) 预测存在一个中间长度尺度范围，其中尺度间湍流传递速率、两点空间湍流传递速率和两点小尺度湍流能量中的两点压力梯度速度相关项方程均与湍流耗散率成正比且与长度尺度无关。在有挡板的水箱中产生湍流的叶轮下的视场中进行的粒子图像测速测量支持了这些预测，并表明测量的小规模湍流明显不均匀。粒子图像测速测量还表明，在两点大尺度湍流能量方程中，大尺度向小尺度损失能量的速率似乎也近似与湍流耗散率成正比，并且与同一尺度的长度尺度无关。由于湍流能量传输的非均匀性，该速率可能无法平衡两点小尺度湍流能量方程中的尺度间湍流传输速率。