Contributions of Vortical/Non-Vortical Structures to Velocity–Vorticity Correlations and Net Force in 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.…”

“…Although we attempt here no detailed statistical analysis, the D-type vortices pictured in figure 13 appear indeed to be wall-attached structures, with feet of one or both legs planted in the near-wall region. These observations agree with the suggestion of Eyink (2008) and others (Chen et al 2014(Chen et al , 2018b that the down-gradient transport of vorticity should be supplied by attached hairpin-type structures, although we recall the evidence from the previous subsection that D-type vortices are not self-similar at Re τ = 1000. An interesting fact that may be inferred from the colour plot in figure 13 is that Σ D yz is not down-gradient (red colour) at every point on the D-vortices.…”

“…Because of the availability of full 3-D velocity fields, Chen et al (2018b) could apply the swirling strength criterion for various choices of β in both 2-D planes and in three dimensions and they found that comparable results were obtained for both, although the 3-D criterion identified more coherent vortices than did the 2-D criterion. Chen et al (2018b) could also study the stretching flux −wω y and the full nonlinear flux vω z − wω y and then investigate the coherent vortex contribution to each of these. In fact, Chen et al (2018b) decomposed the entire space domain into four exclusive point sets consisting of 'filamentary vortices' (FV), 'non-filamentary vortices' (NFV), 'non-swirling vortex structures' (NSVS) and 'irrotational structures', and all of these except the latter can contribute to vorticity flux.…”

“…Chen et al (2018b) could also study the stretching flux −wω y and the full nonlinear flux vω z − wω y and then investigate the coherent vortex contribution to each of these. In fact, Chen et al (2018b) decomposed the entire space domain into four exclusive point sets consisting of 'filamentary vortices' (FV), 'non-filamentary vortices' (NFV), 'non-swirling vortex structures' (NSVS) and 'irrotational structures', and all of these except the latter can contribute to vorticity flux. The FV structures correspond roughly to our vortex cores, but identified by swirling strength and a region growing algorithm, and the other structure types are precisely defined by Chen et al (2018a,b).…”

“…The FV structures correspond roughly to our vortex cores, but identified by swirling strength and a region growing algorithm, and the other structure types are precisely defined by Chen et al (2018a,b). Thus, Chen et al (2018b) determined the fractional contributions of each of the first three types of structures (FV, NFV, NSVS) to the three fluxes (advective, stretching, total nonlinear) and they emphasized the dominant role of the FV structures. For the region y + > 300 of their simulation where wω y > 0 (down-gradient), FV structures contribute more than 80 % while occupying only 15 % of the volume.…”