Characteristics of Momentum Sources and Sinks in Turbulent Channel Flow

Vorticity cascade and turbulent drag in wall-bounded flows: plane Poiseuille flow

“…In addition, we have calculated the separate contributions of the advective (vω z ) and stretching/tilting (−wω y ) terms to the nonlinear flux, for which no exact predictions exist. However, our results for these two quantities plotted also in figure 6 agree well with those earlier reported by Monty et al (2011), Brown et al (2015 and Chen et al (2018b) from the channel-flow simulation of Del Alamo et al (2004) at Re τ = 934 and also with the experimental results of Chen et al (2014) for an open channel flume at somewhat lower Re τ = 740. Similar observations have been made both at lower and at higher Reynolds numbers, but we postpone until our conclusions section the discussion of the important issue of Re-dependences.…”

“…We are aware of no prior studies which computed spanwise cospectra for channel flows, although analogous cospectra were calculated by Wu et al (2012) for pipe flows as a function of azimuthal angle. Therefore, we have validated our calculations of spanwise cospectra by comparing with the corresponding spatial two-point velocity-vorticity correlations in the spanwise direction obtained from channel-flow DNS at Re τ = 934 by Del Alamo et al (2004), as reported in Monty et al (2011). This comparison, shown in figure B.3 in the supplementary materials, confirms our own data presented here.…”

“…The sensitivity of the nonlinear vorticity transport to such small scales for y > y p has important implications for physical phenomena such as polymer drag reduction since modifications of the flux cospectrum at very small scales can alter the delicate balance between down-gradient and up-gradient transport and lead to a drastic reduction of drag (cf. Crawford & Karniadakis 1997;Monty et al 2011).…”

“…The correlations between velocity and vorticity were seen to arise from a 'scale selection' associated with peaks in the velocity and vorticity streamwise spectra. Monty, Klewicki & Ganapathisubramani (2011) interpret the TI term as a momentum source/sink (depending upon the sign) and carried out detailed calculations of the streamwise and spanwise two-point correlations of v with ω z and w with ω y in a DNS of channel flow. They drew an important conclusion, which anticipates our own, that 'the mean Reynolds stress gradient at any wall-normal location is a direct result of a slight asymmetry in the characteristic vortical motions of the flow'.…”