Spatial signatures of retrograde spanwise vortices in wall turbulence

Abstract

The spatial signatures of retrograde spanwise vortices in wall turbulence are assessed from particle-image velocimetry measurements in the streamwise-wall-normal plane of a zero-pressure-gradient turbulent boundary layer at Re τ ≡ u * δ/ν = 2350. The present results suggest that a proportion of retrograde spanwise vortices have a welldefined spatial relationship with neighbouring prograde vortices. Two-point crosscorrelations and conditionally averaged velocity fields given a retrograde vortex reveal that such structures are typically oriented either upstream of and below or downstream of and above a prograde core. While these pairings are consistent with the typical-eddy patterns reported by Falco and co-workers, we offer an alternative interpretation for a proportion of these retrograde/prograde pairs. In particular, the arrangement of a retrograde spanwise vortex upstream of and below a prograde core is also consistent with the spatial signature revealed if an omega-shaped hairpin structure were sliced through its shoulder region by a fixed streamwise-wall-normal measurement plane.

Experimental study on the role of spanwise vorticity and vortex filaments in the outer region of open-channel flow

“…is the root-mean-square value of Λ ci at wall-normal position y and λ ci is the imaginary part of the complex eigenvalue of the two-dimensional velocity gradient tensor (Zhou et al 1999, Adrian et al 2000a. Similar methods were used by Natrajan et al (2007) and Herpin et al (2010) That is, spanwise vortex filaments crossing the x-y plane always have spanwise vorticity, but some portions of the regions containing spanwise vorticity do not qualify as filaments. Thus, spanwise vorticity is due to both spanwise vortex filaments and non-filamentary structures.…”

“…The backward induced motion makes a hairpin vortex convect more slowly than the surrounding flow and the upward induced motion lifts it away from the wall. Since the origion of retrograde spanwise vortex filaments in wall turbulence is still not totally clear (Natrajan et al 2007), proper interpretation of their convection velocity is not attempted in the present study. In contrast to net force, the spanwise vortex filaments contribute little to the Reynolds stress.…”

Studies of Real Roughness Effects for Improved Modeling and Control of Practical Wall-Bounded Turbulent Flows

“…Wu & Christensen (2006a) found that these counterclockwise-rotating retrograde spanwise vortices have their largest populations toward the outer edge of the log layer where they generally occur in close proximity to prograde spanwise vortices. Natrajan et al (2007) found that these spatially-coincident pairs of prograde and retrograde spanwise vortices may be linked to the measurement plane slicing through the shoulders of omega-shaped hairpin-like structures. While figures 43 and 44 illustrate the imprint of the spatial organization present in flow over both smooth and RF1 surface conditions within the x -y plane, these structures also leave a definitive imprint within velocity fields acquired in the streamwise-spanwise (x -z) plane.…”

“…More recently, Klewicki & Hirschi (2004) reported observations of hairpin vortices and retrograde structures clustered in the neighborhood of intense near-wall shear layers, with the influence of retrograde structures increasing with Reynolds number. Finally, Natrajan et al (2007) performed a detailed investigation of the spatial signatures of outer-layer retrograde spanwise vortices, particularly their propensity to occur spatially-coincident with prograde cores, and reported that such patterns are also consistent with slicing through omega-shaped hairpin structures. It should be noted that the existence of ring-like vortices is not inconsistent with the hairpin-vortex model as the origin of ring-like structures in wall turbulence has been related to the pinch-off and reconnection of the legs of existing hairpin structures (Moin et al, 1986;Smith et al, 1991;Bake et al, 2002, for example).…”

“…These negative correlation values indicate the occurrence of spatially-coincident prograde and retrograde spanwise vortices. Natrajan et al (2007) first reported these negative correlation regions in p,\,,, within the x -y plane and postulated the latter arrangement to be a slice through the shoulder of an omega-shaped hairpin-like structure while the former arrangement may be due to ring-like vortices that have been observed in the outer-layer of smooth-wall turbulence (Falco, 1991, for example). Of interest is that these regions of negative correlation in P,,4\ become smaller and weaker in the rough-wall flow.…”