Helicity budget in turbulent channel flows with streamwise rotation

Abstract

The streamwise rotation effects in turbulent channel flows are reflected not only in the appearance of the secondary flows but also in the weakened streamwise velocity and spanwise vorticity. In this paper, we investigate the secondary flows from three perspectives: the mean spanwise velocity, the mean streamwise vorticity, and combined mean and fluctuating helicity. We found that the combined helicity is also an alternative perspective to characterize the streamwise rotation effect, especially for the secondary flows. The budget equations of the mean and fluctuating helicity in physical space are derived theoretically and analyzed numerically. The streamwise rotation effects on the secondary flows are directly reflected on the pressure and Coriolis terms, which provides an essential source for helicity within the near-wall regions. The production term could be decomposed into two terms, which originate from the momentum and vorticity equations, respectively. The helical stress (velocity–vorticity correlation) originating from the vorticity equation shows a simple profile distribution and is dominant for the production for the helicity within the near-wall regions. The high helical structures in the core regions can be explained as an intense wall-normal transportation, which transfers produced helicity within the near-wall regions into the core regions.