Mean flow scaling in a spanwise rotating channel

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 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 the 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 approximate to k, where K is the von Karman constant; and u(tau,p) is the wall friction velocity at the pressure side.