A self-sustaining process theory for uniform momentum zones and internal shear layers in high Reynolds number shear flows

Abstract

Abstract

Properties of turbulent channel flow similarity solutions

“…(2017), Hall (2018) and Montemuro et al. (2020). More broadly, there is now an overwhelming weight of evidence that the dynamics and energetics of wall turbulence are inextricably linked to its underlying hierarchical structure, e.g.…”

Cause-and-effect of linear mechanisms sustaining wall turbulence

“…Subsequent developments of the VWI theory include extensions to multiscale motions consistent with the logarithmic layer (Hall 2018). Other descriptions of self-sustaining turbulence in the vein of vortex-wave interactions are the studies by Deguchi, Hall & Walton (2013) and Deguchi & Hall (2015), the high-Reynolds-number theory by Ozcakir et al (2016); Ozcakir, Hall & Tanveer (2019), and the semi-analytic model by Chini et al (2017) and Montemuro et al (2020); the latter devoted to the formation and maintenance of uniform momentum zones and interlaced vortical fissures studied by asymptotic analysis. While the theories above could provide a plausible explanation for how turbulence self-sustains, we are still lacking direct cause-and-effect evidence regarding whether one or a combination of the abovementioned mechanisms are actually at work in realistic turbulent flows.…”

“…Next, we briefly describe mechanisms (i), (ii) and (iii). In mechanism (i), it is hypothesised that the energy is transferred from the mean flow U ( y, z, t) to the fluctuating flow through modal instability in the form of strong inflectional variations in the spanwise direction (Hamilton et al 1995;Waleffe 1997;Karp & Cohen 2017) or wall-normal direction (Chini et al 2017;Montemuro et al 2020), corrugated vortex sheets (Kawahara et al 2003), or intense localised patches of low-momentum fluid (Andersson et al 2001;Hack & Moin 2018). These exponential instabilities are markedly robust at all times (Lozano-Durán, Karp & Constantinou 2018) and, therefore, their excitation has been proposed to be the mechanism that replenishes the perturbation energy of the turbulent flow (Hamilton et al 1995;Waleffe 1997;Andersson et al 2001;Kawahara et al 2003;Marquillie et al 2011;Hack & Zaki 2014;Hack & Moin 2018).…”

“…(2017) and Montemuro et al. (2020); the latter devoted to the formation and maintenance of uniform momentum zones and interlaced vortical fissures studied by asymptotic analysis. While the theories above could provide a plausible explanation for how turbulence self-sustains, we are still lacking direct cause-and-effect evidence regarding whether one or a combination of the abovementioned mechanisms are actually at work in realistic turbulent flows.…”

“…2017; Montemuro et al. 2020), corrugated vortex sheets (Kawahara et al. 2003), or intense localised patches of low-momentum fluid (Andersson et al.…”