Comparison of swirling strengths derived from two- and three-dimensional velocity fields in channel flow

Abstract

Swirling strength is an effective vortex indicator in wall turbulence, and it can be determined based on either two-dimensional (2D) or three-dimensional (3D) velocity fields, written as λci2D and λci3D, respectively. A comparison between λci2D and λci3D has been made in this paper in sliced XY, YZ, and XZ planes by using 3D DNS data of channel flow. The magnitude of λci2D in three orthogonal planes differs in the inner region, but the difference tends to diminish in the outer flow. The magnitude of λci3D exceeds each λci2D, and the square of λci3D is greater than the summation of squares of three λci2D. Extraction with λci2D in XY, YZ, and XZ planes yields different population densities and vortex sizes, i.e., in XZ plane, the vortices display the largest population density and the smallest size, and in XY and YZ planes the vortices are similar in size but fewer vortices are extracted in the XY plane in the inner layer. Vortex size increases inversely with the threshold used for growing the vortex region from background turbulence. When identical thresholds are used, the λci3D approach leads to a slightly smaller population density and a greater vortex radius than the λci2D approach. A threshold of 0.8 for the λci3D approach is approximately equivalent to a threshold of 1.5 for the λci2D approach.

Vorticity cascade and turbulent drag in wall-bounded flows: plane Poiseuille flow

“…(2018 b ) (see also Chen et al. 2018 a ) verified the results of Chen et al. (2014), but in the channel-flow simulation of Del Alamo et al.…”

“…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. (2018 a , b ). Thus, Chen et al.…”

“…The following paper of Chen et al (2018b) (see also Chen et al 2018a) verified the results of Chen et al (2014), but in the channel-flow simulation of Del Alamo et al (2004) at Re τ = 934. 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.…”

“…Since the vorticity magnitudes decrease rapidly with y, this normalization permits uniform visualization of coherent vortices at all wall distances. The imposed level is somewhat arbitrary but we choose here β = 1 which is in the range of earlier related studies (Wu & Christensen 2006;Chen et al 2014Chen et al , 2018a, which we discuss at length below.…”

“…The imposed level is somewhat arbitrary but we choose here which is in the range of earlier related studies (Wu & Christensen 2006; Chen et al. 2014, 2018 a , b ), which we discuss at length below.…”