Local patches of turbulent boundary layer behaviour in classical-state vertical natural convection

ORAL

Abstract

We present evidence of local patches in vertical natural convection that are reminiscent of Prandtl--von K{\'a}rm{\'a}n turbulent boundary layers, for Rayleigh numbers $10^5$--$10^9$ and Prandtl number 0.709. These local patches exist in the classical state, where boundary layers exhibit a laminar-like Prandtl--Blasius--Polhausen scaling at the global level, and are distinguished by regions dominated by high shear and low buoyancy flux. Within these patches, the locally averaged mean temperature profiles appear to obey a log-law with the universal constants of Yaglom (1979). We find that the local Nusselt number versus Rayleigh number scaling relation agrees with the logarithmically corrected power-law scaling predicted in the ultimate state of thermal convection, with an exponent consistent with Rayleigh--B{\'e}nard convection and Taylor--Couette flows. The local patches grow in size with increasing Rayleigh number, suggesting that the transition from the classical state to the ultimate state is characterised by increasingly larger patches of the turbulent boundary layers.

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Authors

  • Chong Shen Ng

    The University of Melbourne

  • Andrew Ooi

    The University of Melbourne

  • Detlef Lohse

    University of Twente, Physic of Fluids Group, University of Twente, Physics of Fluids Group, Mesa+ Institute and J.M. Burgers Centre for Fluid Dynamics, University of Twente, The Netherlands, Physics of Fluids, MESA+ institute, University of Twente, the Netherlands, Physics of Fluids Group, University of Twente, The Netherlands, Physics of Fluids group, Faculty of Science and Technology, University of Twente, The Netherlands, Physics of Fluids, Faculty of Science \& Technology, University of Twente, The Netherlands, Physics of Fluids Group, Faculty of Science and Technology, J. M. Burgers Center for Fluid Dynamics and MESA+ Institute, University of Twente, Physics of Fluids Group, University of Twente, The Netherlands., Physics of Fluids Group, University of Twente, Physics of Fluids, University of Twente

  • Daniel Chung

    University of Melbourne, Univ of Melbourne, The University of Melbourne