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Nu ∼ Ra1/2 scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence

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Shishkina,  Olga
Laboratory for Fluid Physics, Pattern Formation and Biocomplexity, Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Lohse,  Detlef
Max Planck Institute for Dynamics and Self-Organization, Max Planck Society;

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Citation

Zhu, X., Stevens, R. J. A. M., Shishkina, O., Verzicco, R., & Lohse, D. (2019). Nu ∼ Ra1/2 scaling enabled by multiscale wall roughness in Rayleigh–Bénard turbulence. Journal of Fluid Mechanics, 869: R4. doi:10.1017/jfm.2019.228.


Cite as: http://hdl.handle.net/21.11116/0000-0003-91C3-C
Abstract
In turbulent Rayleigh–Bénard (RB) convection with regular, mono-scale, surface roughness, the scaling exponent β in the relationship between the Nusselt number Nu and the Rayleigh number Ra, Nu ∼ Raβ can be ≈1/2 locally, provided that Ra is large enough to ensure that the thermal boundary layer thickness λθ is comparable to the roughness height. However, at even larger Ra, λθ becomes thin enough to follow the irregular surface and β saturates back to the value for smooth walls (Zhu et al., Phys. Rev. Lett., vol. 119, 2017, 154501). In this paper, we prevent this saturation by employing multiscale roughness. We perform direct numerical simulations of two-dimensional RB convection using an immersed boundary method to capture the rough plates. We find that, for rough boundaries that contain three distinct length scales, a scaling exponent of β = 0.49 ± 0.02 can be sustained for at least three decades of Ra. The physical reason is that the threshold Ra at which the scaling exponent β saturates back to the smooth wall value is pushed to larger Ra, when the smaller roughness elements fully protrude through the thermal boundary layer. The multiscale roughness employed here may better resemble the irregular surfaces that are encountered in geophysical flows and in some industrial applications.