×

zbMATH — the first resource for mathematics

Uniform momentum zone scaling arguments from direct numerical simulation of inertia-dominated channel turbulence. (English) Zbl 1460.76528
Summary: Inertia-dominated wall-sheared turbulent flows are composed of an inner and outer layer, where the former is occupied by the well-known autonomous inner cycle while the latter is composed of coherent structures with spatial extent comparable to the flow depth. In arbitrary streamwise-wall-normal planes, outer-layer structures instantaneously manifest as regions of quasi-uniform momentum – relative excesses and deficits about the Reynolds average – and for this reason are termed uniform momentum zones (UMZs). By virtue of this attribute, the interfacial zones between successive UMZs exhibit abrupt wall-normal gradients in streamwise momentum; these interfacial gradients cannot be explained by the notion of attached eddies, for which the vertical gradient goes as \((x_3^+)^{-1}\) in the outer layer, where \(x_3^+\) is inner-normalized wall-normal position. Using data from direct numerical simulation (DNS) of channel turbulence across inertial regimes, we recover vertical profiles of Kolmogorov length a posteriori and show that \(\eta^+ \sim (x_3^+)^{1/4}\), thereby requiring that ambient wall-normal gradients in streamwise velocity must scale as \((x_3^+)^{-1/2}\). The data reveal that UMZ interfaces are responsible for these relatively larger wall-normal gradients. The DNS data afford a unique opportunity to interpret inner- and outer-layer structures simultaneously: we propose that UMZs – and the associated outer-layer dynamics – can be explained as the product of inner-layer bluff-body-like interactions, wherein wakes of quasi-uniform momentum emanate from the inner layer; wake-scaling arguments agree with observations from DNS.

MSC:
76F65 Direct numerical and large eddy simulation of turbulence
76F40 Turbulent boundary layers
76F25 Turbulent transport, mixing
PDF BibTeX Cite
Full Text: DOI
References:
[1] Adrian, R. J., Meinhart, C. D. & Tomkins, C. D.2000Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech.422, 1-54. · Zbl 0959.76503
[2] Bautista, J. C. C., Ebadi, A., White, C. M., Chini, G. P. & Klewicki, J. C.2019A uniform momentum zone-vortical fissure model of the turbulent boundary layer. J. Fluid Mech.858, 609-633. · Zbl 1415.76329
[3] Fan, D., Xu, J., Yao, M. X. & Hickey, J.-P.2019On the detection of internal interfacial layers in turbulent flows. J. Fluid Mech.872, 198-217. · Zbl 1419.76313
[4] Heisel, M., De Silva, C. M., Hutchins, N., Marusic, I. & Guala, M.2020On the mixing length eddies and logarithmic mean velocity profile in wall turbulence. J. Fluid Mech.887, R1.
[5] Hutchins, N & Marusic, I2007Evidence of very long meandering features in the logarithmic region of turbulent boundary layers. J. Fluid Mech.579, 1-28. · Zbl 1113.76004
[6] Jimenez, J. & Pinelli, A.1999The autonomous cycle of near-wall turbulence. J. Fluid Mech.389, 335-359. · Zbl 0948.76025
[7] Lee, M. & Moser, R. D.2015Direct numerical simulation of turbulent channel flow up to \(Re_\tau = 5200\). J. Fluid Mech.774, 395-415.
[8] Lee, M. & Moser, R. D.2019Spectral analysis of the budget equation in turbulent channel flows at high Reynolds number. J. Fluid Mech.860, 886-938. · Zbl 1415.76350
[9] Marusic, I., Mathis, R. & Hutchins, N.2010Predictive model for wall-bounded turbulent flow. Science329, 193-196. · Zbl 1226.76015
[10] Meinhart, C. D. & Adrian, R. J.1995On the existence of uniform momentum zones in a turbulent boundary layer. Phys. Fluids7, 694-696.
[11] Pope, S. B.2000Turbulent Flows. Cambridge University Press.
[12] Schoppa, W. & Hussain, F.2002Coherent structure generation in near-wall turbulence. J. Fluid Mech.453, 57-108. · Zbl 1141.76408
[13] De Silva, C. M., Philip, Jimmy, Hutchins, N. & Marusic, I.2017Interfaces of uniform momentum zones in turbulent boundary layers. J. Fluid Mech.820, 451-478. · Zbl 1383.76257
[14] Tennekes, H. & Lumley, J. L.1972A First Course in Turbulence. MIT Press. · Zbl 0285.76018
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.