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Oscillation in the temperature profile of the large-scale circulation of turbulent convection induced by a cubic container

Dandan Ji1 and Eric Brown2,*

  • 1Department of Physics, Yale University, New Haven, Connecticut 06520, USA
  • 2Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA

  • *ericmichealbrown@gmail.com
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Phys. Rev. Fluids 5, 063501 – Published 18 June, 2020

DOI: https://doi.org/10.1103/PhysRevFluids.5.063501

Abstract

We present observations of oscillations in the shape of the temperature profile of the large-scale circulation (LSC) of turbulent Rayleigh-Bénard convection. Temperature measurements are broken down into Fourier moments as a function of θ−θ0, where θ is the azimuthal angle in a horizontal plane at midheight, and θ0 is the LSC orientation. The oscillation structure is dominated by a third-order sine moment and third-order cosine moment in a cubic cell. In contrast, these moments are not found to oscillate in a cylindrical cell. This geometry-dependent behavior can be explained by a minimal model that assumes that the heat transported by the LSC is conducted from the thermal boundary layers, and is proportional to the pathlength of the LSC along boundary layers at the top and bottom plates. In a noncircular cross-section cell, oscillations of the LSC orientation θ0 result in an oscillation in the container shape in the reference frame of the LSC, resulting in an oscillation in the pathlength of the LSC at a given θ−θ0. In a square-cross-section cell, this model predicts the dominant third-order sine moment and third-order cosine moment with magnitudes within 50% of measured values, when using the amplitude of the oscillation of θ0 as input. A cylindrical cell is special in that the pathlength is independent of θ0, and so these oscillating moments are not induced. In a cylindrical cell, the model reproduces the sinusoidal mean temperature profile with a sloshing oscillation dominated by the second-order sine moment, consistent with previous observations in that geometry.

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Phys. Rev. Fluids 5, 063501– Published 18 June, 2020
  • Received 28 February 2020
  • Accepted 20 May 2020
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