Since the early work of Johnston [Johnston, Halleent, and Lezius, J. Fluid Mech. 56, 533 (1972)], the mean flow scaling in a spanwise rotating channel has received much attention. While it is known that the mean velocity near the pressure, turbulent side follows a linear scaling $U=2\mathrm{\Omega }y+C$ at high rotation speeds, the functional dependence of $C$ on the Reynolds number and the rotation number has been an open question. Here, $U$ is the mean velocity, $\mathrm{\Omega }$ is the constant rotating speed in the spanwise direction, and $C$ is a constant. In this work, we show that $C^{+}=log\left(l_{\mathrm{\Omega }}^{+}\right)/K$, where the superscript $+$ denotes normalization using wall units at the pressure side; $l_{\mathrm{\Omega }}=u_{\tau ,p}/2\mathrm{\Omega }$ is a rotation-induced length scale; $K$ is a constant and $K\approx \kappa$, where $\kappa$ is the von Kármán constant; and $u_{\tau ,p}$ is the wall friction velocity at the pressure side.

中文翻译：

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翼展方向旋转通道中的平均流量缩放

自约翰斯顿（Johnston，Halleent，and Lezius，J. Fluid Mech。 [ J.Am.Chem.Soc.56，533（1972）]中，翼展方向旋转通道中的平均流量缩放倍受关注。虽然已知压力附近的平均速度，湍流侧遵循线性比例$ü=2\mathrm{\Omega }ÿ+C$ 在高转速下， $C$雷诺数和转数是一个悬而未决的问题。这里，$ü$ 是平均速度， $\mathrm{\Omega }$ 是在翼展方向上的恒定转速，并且 $C$是一个常数。在这项工作中，我们表明$C^{+}=日志（{升}_{\mathrm{\Omega }}^{+}）/ķ$，上标 $+$ 表示使用压力侧壁单元进行归一化； ${升}_{\mathrm{\Omega }}={ü}_{\tau ，p}/2\mathrm{\Omega }$ 是旋转引起的长度刻度； $ķ$ 是一个常数， $ķ\approx \kappa$，在哪里 $\kappa$是vonKármán常数；和${ü}_{\tau ，p}$ 是压力侧的壁摩擦速度。