Since the early work of Johnston (Johnston, Halleent, and Lezius, J. Fluid Mech., 1996, 315, 1-29), 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 $U=2\Omega y+C$ 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, $\Omega$ is the {constant rotating speed in spanwise direction}, and $C$ is a constant. In this work, we show that $C^{+}=log(l_{\Omega }^{+})/K$, where the superscript $+$ denotes normalization using wall units at the pressure side, $l_{\Omega }=u_{\tau ,p}/2\Omega$ is a rotation-induced length scale, $K$ is a constant and $K\approx \kappa$, $\kappa$ is the von K{'a}rm{'a}n 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

自从约翰斯顿（Johnston，Halleent，and Lezius，J. Fluid Mech。，1996，315，1-29）的早期工作以来，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$ü=2\Omega ÿ+C$ 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， $\Omega$ 是{沿翼展方向恒定的旋转速度}，并且 $C$是一个常数。在这项工作中，我们表明$C^{+}=日志（{升}_{\Omega }^{+}）/ķ$，上标 $+$ 表示使用压力侧的壁单元进行归一化， ${升}_{\Omega }={ü}_{\tau ，p}/2\Omega$ 是旋转引起的长度刻度， $ķ$ 是一个常数， $ķ\approx \kappa$， $\kappa$ 是von K {'a} rm {'a} n常数，并且 ${ü}_{\tau ，p}$ 是压力侧的壁摩擦速度。