Richard J.A.M. Stevens

Physics of Fluids

University of Twente

Publication 67 · 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).

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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