Scale dependence of the alignment between strain rate and rotation in turbulent shear flow

Abstract

The scale dependence of the statistical alignment tendencies of the eigenvectors of the strain-rate tensor e i , with the vorticity vector ω, is examined in the self-preserving region of a planar turbulent mixing layer. Data from a direct numerical simulation are filtered at various length scales and the probability density functions of the magnitude of the alignment cosines between the two unit vectors |e i ·ω| are examined. It is observed that the alignment tendencies are insensitive to the concurrent large-scale velocity fluctuations, but are quantitatively affected by the nature of the concurrent large-scale velocity-gradient fluctuations. It is confirmed that the small-scale (local) vorticity vector is preferentially aligned in parallel with the large-scale (background) extensive strain-rate eigenvector e 1 , in contrast to the global tendency for ω to be aligned in parallel with the intermediate strain-rate eigenvector [Hamlington et al., Phys. Fluids 20, 111703 (2008)]. When only data from regions of the flow that exhibit strong swirling are included, the so-called high-enstrophy worms, the alignment tendencies are exaggerated with respect to the global picture. These findings support the notion that the production of enstrophy, responsible for a net cascade of turbulent kinetic energy from large scales to small scales, is driven by vorticity stretching due to the preferential parallel alignment between ω and nonlocal e 1 and that the strongly swirling worms are kinematically significant to this process.

The scaling of straining motions in homogeneous isotropic turbulence

“…This implies that the most extensive strain at large scales is in the ξ 2 direction (4.1). Hence, small-scale vorticity and the large scale most extensive straining direction align, which is consistent with the observations in turbulent flows (Ishihara et al 2001;Hamlington et al 2008;Leung et al 2012;Fiscaletti et al 2016). The cross-over in alignment is determined by the point where the profiles of u 1 (ξ 1 ) and u 2 (ξ 2 ) cross, which is indicated in figure 15 by ×.…”

“…Earlier work has shown that small-scale vorticity preferentially aligns with the intermediate principal strain at small scales (Ashurst et al 1987). But when considering the larger-scale strain or the non-local strain, the same small-scale vorticity preferentially aligns with the most stretching principal straining direction (Ishihara et al 2001;Hamlington et al 2008;Leung et al 2012;Fiscaletti et al 2016). However, the exact scale at which the cross-over occurs is unknown.…”

“…Dresselhaus & Tabor 1991;Nomura & Post 1998;Guala et al 2005). While vorticity aligns with the intermediate principal strain at small scales, it preferentially aligns with the most stretching principal strain at larger scales (Ishihara, Yamazaki & Kaneda 2001;Hamlington et al 2008;Leung, Swaminathan & Davidson 2012;Fiscaletti et al 2016). Because these studies did not consider Reynolds number variations, it remains unclear at what scale this cross-over in the alignment appears.…”

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

“…2012; Fiscaletti et al. 2016), which is physically related to the time lag in alignment elucidated by Xu, Pumir & Bodenschatz (2011). The Lagrangian behaviour of these terms deserves further consideration in future work.…”

Parametric numerical study of passive scalar mixing in shock turbulence interaction

“…Larger M brings the postshock PDF closer to the β vertex, while increasing Re λ opposes this trend. Prior studies in HIT (Danish & Meneveau 2018) and turbulent shear flows (Fiscaletti et al 2016) found better alignment of ω and β at small scales. Moreover, Gonzalez (2012) observed more efficient scalar mixing in HIT when ω and β are better aligned.…”