Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Publication 97 · 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).

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.

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