Roughness-Facilitated Local 1/2 Scaling Does Not Imply the Onset of the Ultimate Regime of Thermal Convection

Xiaojue Zhu, Richard J. A. M. Stevens, Roberto Verzicco, and Detlef Lohse
Phys. Rev. Lett. 119, 154501 – Published 11 October 2017

Abstract

In thermal convection, roughness is often used as a means to enhance heat transport, expressed in Nusselt number. Yet there is no consensus on whether the Nusselt vs Rayleigh number scaling exponent (NuRaβ) increases or remains unchanged. Here we numerically investigate turbulent Rayleigh-Bénard convection over rough plates in two dimensions, up to Ra1012. Varying the height and wavelength of the roughness elements with over 200 combinations, we reveal the existence of two universal regimes. In the first regime, the local effective scaling exponent can reach up to 1/2. However, this cannot be explained as the attainment of the so-called ultimate regime as suggested in previous studies, because a further increase in Ra leads to the second regime, in which the scaling saturates back to a value close to the smooth wall case. Counterintuitively, the transition from the first to the second regime corresponds to the competition between bulk and boundary layer flow: from the bulk-dominated regime back to the classical boundary-layer-controlled regime. Our study demonstrates that the local 1/2 scaling does not necessarily signal the onset of ultimate turbulence.

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  • Received 27 March 2017

DOI:https://doi.org/10.1103/PhysRevLett.119.154501

© 2017 American Physical Society

Physics Subject Headings (PhySH)

  1. Research Areas
Fluid DynamicsNonlinear Dynamics

Authors & Affiliations

Xiaojue Zhu1,*, Richard J. A. M. Stevens1, Roberto Verzicco2,1, and Detlef Lohse1,3,†

  • 1Physics of Fluids Group and Max Planck Center Twente, MESA+ Institute and J. M. Burgers Centre for Fluid Dynamics, University of Twente, P.O. Box 217, 7500AE Enschede, Netherlands
  • 2Dipartimento di Ingegneria Industriale, University of Rome “Tor Vergata,” Via del Politecnico 1, Roma 00133, Italy
  • 3Max Planck Institute for Dynamics and Self-Organization, 37077 Göttingen, Germany

  • *xiaojue.zhu@utwente.nl
  • d.lohse@utwente.nl

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Vol. 119, Iss. 15 — 13 October 2017

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