Law of the wall for channel with spanwise rotation

Wall-bounded flow with system rotation is often encountered in nature and real-world engineering. This talk focuses on the simple channel flow with spanwise rotation. For this flow, the conventional logarithmic law of the wall holds only in the very near-wall region, and it is well known that the mean flow in the bulk follows a linear law U=2Ωy+C, where Ω is the angular velocity in the spanwise direction, U is the mean velocity, and y is the wall-normal distance. The intercept C contains all the skin friction information, but its scaling as a function of both the Reynolds number (Re_τ) and the rotation number (Ro_τ) is not entirely clear. This talk will present a mixing length model for the mean flow, which in turns leads to a scaling prediction for C, i.e., C⁺=log(Re_τ/Ro_τ)/κ. This model prediction is then compared to published DNS data, and good agreements are found.