Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Publication 60 · Wall-shear turbulence

How roughness strengthens plume transport and torque

P. Berghout, X. Zhu, D. Chung, R. Verzicco, R.J.A.M. Stevens, and D. Lohse, Journal of Fluid Mechanics 873, 260–286 (2019).

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

Main finding

Modeled sand-grain roughness on the inner cylinder increased plume activity, angular-momentum transport, and torque. For this surface, the equivalent sand-grain height was 1.33 times the nominal roughness height and the roughness-sublayer height was 2.78 times the equivalent height.

Instantaneous azimuthal velocity fields for smooth and increasingly rough inner cylinders in classical and ultimate Taylor-Couette turbulence
How to read the figure. Red and blue show instantaneous azimuthal-velocity fluctuations in an axial–radial section; the grey shapes are the modeled roughness elements on the inner wall. The top row is the classical state at Ta = 5 × 107: smooth, k/d = 0.039, and k/d = 0.073 from left to right. The bottom row is the ultimate state at Ta = 109: smooth, k/d = 0.035, and k/d = 0.055. Compared with the smooth cases, the rough cylinders produce more numerous and intense plume ejections and stronger mixing. This figure shows the local flow pattern; global torque is quantified separately in Figures 6–7, and the equivalent-height and roughness-sublayer constants in Figures 4–5 and 11. Open the full-resolution figure. Figure 8, cropped. P. Berghout et al. (2019), CC BY 4.0.

Why this matters

The resolved topography connects a local mechanism—form-induced motions and stronger plume ejection—to increased Reynolds transport and global torque. It also provides a quantitative bridge from the nominal geometry to an equivalent sand-grain height and to the wall-normal extent of the roughness disturbance. The fitted values describe this modeled surface and the study's threshold definition; they are not universal roughness constants.

Research context

The study uses immersed-boundary direct numerical simulation at radius ratio 0.714, with modeled monodisperse ellipsoidal roughness on the rotating inner cylinder and a smooth outer cylinder. The domain contains one periodic Taylor-roll pair and spans 107 ≤ Ta ≤ 109 and 5 ≤ k+ ≤ 92. Only the inner wall is rough, so the results do not establish the fully rough ultimate scaling expected when both cylinder boundary layers lose their viscous dependence. The simulations do not reproduce a specific experimental sand-grain surface; transfer to other topographies requires a separate roughness characterization.

Read the article Open-access version View in the complete publication list Related Taylor-Couette research