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Drag for wall-bounded flows is directly related to the spatial flux of spanwise vorticity outward from the wall. In turbulent flows a key contribution to this wall-normal flux arises from nonlinear advection and stretching of vorticity, interpretable as a cascade. We study this process using numerical simulation data of turbulent channel flow at friction Reynolds number$$Re_\tau =1000$$. The net transfer from the wall of spanwise vorticity created by downstream pressure drop is due to two large opposing fluxes, one which is ‘down-gradient’ or outward from the wall, where most vorticity concentrates, and the other which is ‘up-gradient’ or toward the wall and acting against strong viscous diffusion in the near-wall region. We present evidence that the up-gradient/down-gradient transport occurs by a mechanism of correlated inflow/outflow and spanwise vortex stretching/contraction that was proposed by Lighthill. This mechanism is essentially Lagrangian, but we explicate its relation to the Eulerian anti-symmetric vorticity flux tensor. As evidence for the mechanism, we study (i) statistical correlations of the wall-normal velocity and of wall-normal flux of spanwise vorticity, (ii) vorticity flux cospectra identifying eddies involved in nonlinear vorticity transport in the two opposing directions and (iii) visualizations of coherent vortex structures which contribute to the transport. The ‘D-type’ vortices contributing to down-gradient transport in the log layer are found to be attached, hairpin-type vortices. However, the ‘U-type’ vortices contributing to up-gradient transport are detached, wall-parallel, pancake-shaped vortices with strong spanwise vorticity, as expected by Lighthill's mechanism. We discuss modifications to the attached eddy model and implications for turbulent drag reduction.
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Vorticity Statistics and Distributions in Drag Reduced Turbulent Pipe Flow with Transverse Wall Oscillations
Presented are vorticity statistics in drag reduced turbulent pipe flow at low and moderate Reynolds number. Drag reduction is achieved by transverse wall oscillations. Quantities of interest are the distributions of streamwise vorticity in the viscous and lower part of the buffer layer of the flow. We observe a sinusoidal pattern appearing in the distribution that is associated with the strengthening and weakening of counter-rotating vortex pairs. Presented alongside the phase varying distributions of vorticity are the phase averaged distribution of azimuthal and radial velocity fluctuations. The information presented provides a statistical evidence for the new proposed model for the near wall vortex distortion.
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- Award ID(s):
- 1707075
- PAR ID:
- 10112473
- Publisher / Repository:
- Eleventh International Symposium on Turbulence and Shear Flow Phenomena
- Date Published:
- Journal Name:
- Turbulence and shear flow phenomena
- ISSN:
- 2642-0554
- Format(s):
- Medium: X
- Location:
- Southampton, UK
- Sponsoring Org:
- National Science Foundation
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