Richard J.A.M. Stevens

Professor at the University of Twente

Wind energy · Turbulence · Environmental flows

Publication 91 · Wall-shear turbulence

How wall friction sets passive-scalar transport

G.S. Yerragolam, R.J.A.M. Stevens, R. Verzicco, D. Lohse, and O. Shishkina, Journal of Fluid Mechanics 943, A17 (2022).

Read the article Open-access version

The article and figure are open access under CC BY 4.0.

Main finding

Passive-scalar transport in smooth turbulent Couette flow followed Nu ≈ 0.015 Pr^(1/2) Re_b^(3/4) over the tested intermediate range. The scaling is consistent with a Reynolds-analogy link between scalar flux and wall stress, not a universal high-Reynolds-number asymptote.

Nusselt number versus bulk Reynolds number for five Prandtl numbers, alongside the Prandtl-compensated collapse and three-quarter-power fit
How to read the figure. Panel (a) shows the raw Nusselt number against bulk Reynolds number for Pr = 0.1, 0.3, 1, 3, and 10. The dotted line marks the laminar value Nu = 1; the dashed lines show the finite-range fit Nu = 0.015 Pr1/2 Reb3/4. In panel (b), dividing Nu by Pr1/2 collapses the turbulent data around a common Reb3/4 line, while the compensated laminar plateaus remain separated. Figure 5 shows the resulting transport scaling; the friction law and the boundary-layer assumptions that motivate the Reynolds-analogy interpretation are documented separately in Figures 2–4. Open the full-resolution figure. Figure 5, cropped. G.S. Yerragolam et al. (2022), CC BY 4.0.

Why this matters

The study links scalar flux to wall stress through Nu ≈ (Cf/4) Pr1/2 Reb. Combining this Reynolds-analogy relation with the measured finite-range friction fit Cf = 0.060 Reb−1/4 gives Nu = 0.015 Pr1/2 Reb3/4. This provides a controlled bridge from wall-shear turbulence to scalar and thermal transport, but the exponent follows from the friction law used over the tested intermediate range and is not claimed as a universal high-Reynolds-number asymptote.

Research context

The direct numerical simulations resolve smooth plane Couette flow between plates moving at opposite velocities, with a passive scalar maintained by a fixed difference between the walls and no buoyancy. They cover 81 ≤ Reb ≤ 22,361, 0.1 ≤ Pr ≤ 10, and 7.07 ≤ Reτ ≤ 546 in a wall-parallel periodic domain. A larger-domain check changed the reported global Nu, Reτ, and Cf values by less than 1%. The lowest-Prandtl-number data deviate most from the collapse, transition cases converge less well, and no averaging-time uncertainty bands or independent experiments validate the full parameter plane.

View in the complete publication list Related sheared-convection research