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Predicting transition ranges to fully turbulent viscous boundary layers in low Prandtl number convection flows

Janet D. Scheel1,* and Jörg Schumacher2

  • 1Department of Physics, Occidental College, 1600 Campus Road, M21, Los Angeles, California 90041, USA
  • 2Institut für Thermo- und Fluiddynamik, Technische Universität Ilmenau, Postfach 100565, D-98684 Ilmenau, Germany

  • *Corresponding author: jscheel@oxy.edu
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Phys. Rev. Fluids 2, 123501 – Published 6 December, 2017

DOI: https://doi.org/10.1103/PhysRevFluids.2.123501

Abstract

We discuss two aspects of turbulent Rayleigh-Bénard convection (RBC) on the basis of high-resolution direct numerical simulations in a unique setting: a closed cylindrical cell of aspect ratio of one. First, we present a comprehensive comparison of statistical quantities such as energy dissipation rates and boundary layer thickness scales. Data are used from three simulation run series at Prandtl numbers Pr that cover two orders of magnitude. In contrast to most previous studies in RBC the focus of the present work is on convective turbulence at very low Prandtl numbers including Pr=0.021 for liquid mercury or gallium and Pr=0.005 for liquid sodium. In this parameter range of RBC, inertial effects cause a dominating turbulent momentum transport that is in line with highly intermittent fluid turbulence both in the bulk and in the boundary layers and thus should be able to trigger a transition to the fully turbulent boundary layers of the ultimate regime of convection for higher Rayleigh number. Second, we predict the ranges of Rayleigh numbers for which the viscous boundary layer will transition to turbulence and the flow as a whole will cross over into the ultimate regime. These transition ranges are obtained by extrapolation from our simulation data. The extrapolation methods are based on the large-scale properties of the velocity profile. Two of the three methods predict similar ranges for the transition to ultimate convection when their uncertainties are taken into account. All three extrapolation methods indicate that the range of critical Rayleigh numbers Rac is shifted to smaller magnitudes as the Prandtl number becomes smaller.

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Phys. Rev. Fluids 2, 123501– Published 6 December, 2017
  • Received 12 July 2017
Article part of CHORUS

©2017 American Physical Society

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