Bulletin of the American Physical Society
77th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 24–26, 2024; Salt Lake City, Utah
Session T40: Turbulent Wall Bounded Flow II
4:45 PM–6:42 PM,
Monday, November 25, 2024
Room: 355 F
Abstract: T40.00002 : GENERALIZED SCALING OF THE TURBULENCE STRUCTURE IN WALL-BOUNDED FLOWS
4:58 PM–5:11 PM
Presenter:
T.-W. Lee
(Arizona State University)
Authors:
T.-W. Lee
(Arizona State University)
J.E. Park
(Arizona State University)
If we take the first gradient of u’2 profiles, then self-similarity is found across a large range of Reynolds numbers and different wall-bounded (flat-plate and channel) flows. The fixed peak location (y+~ 15) serves as a pivot (zero-crossing) point for positive and negative segments. Also, the maxima and minima in the gradients vary with the Reynolds number (Lee, 2021a; Lee, 2021b), asymmetrically (steeper for the positive segments) but both in a monotonic manner so that scaling factors can be introduced to collapse the profiles. The maximum u’2 variation with the Reynolds number has been correlated using DNS data (Keirsbulck et al., 2012). Similarly, maxima (peak) and minima (nadir) for du’2/dy+ can be tabulated as a function of the Reynolds number. We have used the DNS data of Iwamoto et al. (2002) and Graham et al. (2016) for channel flows (Ret= 110-5200), and also of Spalart (1998) for boundary-layer flow over a flat plate (Ret=300 – 1410), for the turbulence profiles including evaluations of the maxima and minima in du’2/dy+. The profiles are thus scaled in the y+ axis through the d/dy+ operation, and normalized by the absolute values of the extrema (maxima/minima), (du’2/dy+)ext, in the vertical direction. Upon doing so, we can see that in Figure 3 the collapse of the profiles is nearly perfect, universal across the Reynolds number for both the channel and boundary-layer flows, and covers the entire flow width. Segmented, partial scaling rules are no longer necessary with the universal gradient (d/dy+) scaling.
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