Population trends of spanwise vortices in wall turbulence

Abstract

The present effort documents the population trends of prograde and retrograde spanwise vortex cores in wall turbulence outside the buffer layer. Large ensembles of instantaneous velocity fields are acquired by particle-image velocimetry in the streamwise-wall-normal plane of both turbulent channel flow at Re τ ≡ u * δ/ν = 570, 1185 and 1760 and a zero-pressure-gradient turbulent boundary layer at Re τ = 1400, 2350 and 3450. Substantial numbers of prograde spanwise vortices are found to populate the inner boundary of the log layer of both flows and most of these vortices have structural signatures consistent with the heads of hairpin vortices. In contrast, retrograde vortices are most prominent at the outer edge of the log layer, often nesting near clusters of prograde vortices. Appropriate Reynolds-number scalings for outer-and inner-scaled population densities of prograde and retrograde vortices are determined. However, the Re τ = 570 channel-flow case deviates from these scalings, indicating that it suffers from low-Re effects. When the population densities are recast in terms of fractions of resolved prograde and retrograde spanwise vortices, similarity is observed for 100 < y + < 0.8δ + in channel flow and in both flows for 100 < y + < 0.3δ + over the Re τ range studied. The fraction of retrograde vortices increases slightly with Re τ beyond the log layer in both flows, suggesting that they may play an increasingly important role at higher Reynolds numbers. Finally, while the overall prograde and retrograde population trends of channel flow and the boundary layer show little difference for y < 0.45δ, the retrograde populations differ considerably beyond this point, highlighting the influence of the opposing wall in channel flow. IntroductionThe results of many recent experimental and computational studies suggest that wall turbulence is populated by hairpin vortices that tend to streamwise-align into larger-scale coherent groups termed vortex packets. The phrase 'hairpin vortex' is used herein to describe both symmetric and asymmetric hairpin-, lambda-and arch-like structures that are composed of either one or two streamwise-oriented legs connected to a spanwise-oriented head whose rotation is of the same sense as the mean shear. (Spanwise vortices with rotation in the same sense as the mean shear, hairpin heads or otherwise, are hereafter referred to as 'prograde' spanwise vortices.) These structures are qualitatively consistent with the horseshoe vortex first proposed by Theodorsen

The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence

“…28 As such, only the necessary experimental details are presented and the reader is directed to Ref. 28 for further information.…”

“…28 As such, only the necessary experimental details are presented and the reader is directed to Ref. 28 for further information. The boundary-layer measurements were made in a low turbulence, open-circuit boundary layer wind tunnel under zeropressure-gradient conditions.…”

“…This spatial resolution is adequate enough to resolve the vortical structures germane to this study. 28,30 Standard two-frame cross-correlation methods were used to analyze the PIV images with 50% overlap to satisfy Nyquist's criterion and the time delay between images was chosen to minimize the relative velocity measurement error to less that 1%. Table I summarizes the flow parameters for the experiment.…”

A doubly localized equilibrium solution of plane Couette flow

“…Swirling strength is defined as the magnitude of the imaginary part of the complex eigenvalues of the velocity gradient tensor ∇u (Zhou et al 1999). Signed swirling strength includes a ± sign indicating the orientation of swirling (Wu & Christensen 2006), here the sign of the x component of the swirling axis when oriented with the right-hand-rule. The swirling is highly localized: the magnitude of swirling drops by a factor of roughly ten between the X-shaped isosurfaces and the edges of the dotted box that marks a 40 × 16 subdomain.…”

Polymer-induced turbulence modifications in an impinging jet

“…In the two-dimensional measurement planes garnered from PIV swirling strength can be calculated from an equivalent two-dimensional version of the velocity gradient tensor (Adrian et al, 2000). Further, since λ ci does not embody the sense of the rotation (as the complex eigenvalues occur in complex-conjugate pairs), the sign of the local in-plane fluctuating vorticity can be used to distinguish clockwise from counter-clockwise rotating motions in the measurement plane (Wu and Christensen, 2006). This vortex identification scheme reveals the boundaries of the jet prior to impingement to be populated by counter-rotating vortical structures, with the left portion of the jet occupied by clockwise-rotating (blue) vortices while the right portion is populated with counter-clockwise rotating (red) vortices.…”