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.

• Received 16 January 2020
• Accepted 16 June 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.074603