Vorticity fluxes: A tool for three-dimensional and secondary flows in turbulent shear flows

In this work we extend the vorticity-flux approach, proposed by Brown and Roshko (2012) for the analysis of turbulent shear layers and wakes, to the study of secondary flows of Prandtl’s second kind. To this end, we assess direct numerical simulations (DNSs) of turbulent flow through sinusoidal channels (Vidal et al., 2018a) at bulk Reynolds numbers R e h = 2500 and 5000, and with various wall wave parameters, leading to a range of secondary flow intensities. We find that the fluctuating vorticity-flux difference w ′ ω y ′ ¯ + − v ′ ω z ′ ¯ + is closely connected to the in-plane cross-flow, in particular the large negative values present around the wall peak, which enhance the transport of near-wall momentum towards the channel core. The tilting of sweep events at the wall valley is also connected to the secondary flow magnitude, and is associated with positive values of the fluctuating vorticity-flux difference. Furthermore, conditionally averaged fields show that, unlike what is observed in channels with flat walls, the behavior in the vorticity-flux field at the peak is mostly due to Q 1 and Q 4 events, which essentially tilt momentum towards the peak.