Richard J.A.M. Stevens

Physics of Fluids · University of Twente

Publication 57 · Thermal convection

Nu ∼ Ra^1/2 scaling enabled by multiscale wall roughness in Rayleigh-Bénard turbulence

X. Zhu, R.J.A.M. Stevens, O. Shishkina, R. Verzicco, D. Lohse, J. Fluid Mech. 869, R4 (2019).

Main finding

Multiscale roughness provides strong bounded evidence for extending a finite roughness-induced near-half-power interval. It does not establish turbulent boundary layers, asymptotic scaling, or the ultimate regime. The paper explicitly supports that negative distinction.

Heat transport against Rayleigh number for smooth, uniformly rough and multiscale rough plates
How to read the figure. (a) Nusselt number against Rayleigh number for smooth walls, uniform roughness and multiscale roughness. (b) The same data compensated by Ra^0.49: the multiscale case holds a plateau over a finite range of Rayleigh number and then falls away, so the near-half-power scaling is extended but does not continue indefinitely. Open the full-resolution figure. Figure 3. X. Zhu et al. (2019). No separate licence is stated here; consult the original publication and credited source before reuse.

Why this matters

A hierarchy of surface sizes can prolong an apparent scaling law without proving a new asymptotic regime.

Research context

Earlier paper it builds on: Roughness-facilitated local 1/2 scaling does not imply the onset… establishes that mono-scale roughness produces a finite near-half-power interval and then returns to an approximately one-third regime. Its simulations appear in Figure 3 here and must count once across the pair.

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