Richard J.A.M. Stevens

Professor at the University of Twente

Wind energy · Turbulence · Environmental flows

Publication 62 · Wall-shear turbulence

How curvature reorganizes Taylor-Couette mean profiles

P. Berghout, R. Verzicco, R.J.A.M. Stevens, D. Lohse, and D. Chung, Journal of Fluid Mechanics 905, A11 (2020).

Read the article Open-access version

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

Main finding

Across the tested radius ratios, a curvature length organized the transition from a near-wall shear-dominated logarithmic layer to a curvature-affected layer and an approximately constant-angular-momentum bulk.

Curvature-scaled inner-cylinder boundary-layer profiles and compensated gradients at radius ratio 0.716 across seven Taylor numbers
How to read the figure. Both panels show the inner-cylinder boundary layer at radius ratio η = 0.716 for seven Taylor numbers. In panel (a), subtracting the curvature-length-dependent offset brings the mean angular-velocity profiles toward a common curvature-scaled form; the thick grey curve is the constant-angular-momentum profile. Panel (b) shows the compensated profile gradient against y/Lc. Between the two vertical grey lines, 0.20 < y/Lc < 0.65, the curves approach the empirical curvature-log value λ−1 with λ ≈ 0.64. Figure 5 demonstrates the collapse at η = 0.716; Figures 7–8 provide the separate radius-ratio evidence, and Figures 10–11 test the global torque and friction model. Open the full-resolution figure. Figure 5, cropped. P. Berghout et al. (2020), CC BY 4.0.

Why this matters

The proposed curvature length Lc = uτ/(κωi) marks where curvature production becomes comparable to shear production in the reduced turbulent-kinetic-energy balance. The resulting framework separates a near-wall shear logarithmic layer, an empirically fitted curvature-affected logarithmic layer, and an outer region approaching constant angular momentum. This provides a common organization for mean profiles that otherwise change strongly with cylinder-radius ratio.

Research context

The paper develops an analytical similarity framework and tests it against previously published PIV and DNS data for smooth-wall Taylor–Couette flow with only the inner cylinder rotating. Profile comparisons cover radius ratios 0.5, 0.716, and 0.909; compiled global-response data extend from 0.357 to 0.909. The fitted λ ≈ 0.64 and the 0.20–0.65 interval are empirical and require sufficient scale separation. At η = 0.909 and the available driving, the data do not show a distinct curvature-log or constant-angular-momentum region. The model assumes local balance between turbulent production and dissipation, reuses its development datasets for comparison, and does not test outer-cylinder rotation, rough walls, or whether the curvature-log region persists at asymptotically high Reynolds number. “Arbitrary radius ratios” describes the functional formulation, not empirical validation at every radius ratio.

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