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Coherence of temperature and velocity superstructures in turbulent Rayleigh–Bénard flow

  • Dominik Krug (a1), Detlef Lohse (a1) (a2) and Richard J. A. M. Stevens (a1)

Abstract

We investigate the interplay between large-scale patterns, so-called superstructures, in the fluctuation fields of temperature $\unicode[STIX]{x1D703}$ and vertical velocity $w$ in turbulent Rayleigh–Bénard convection at large aspect ratios. Earlier studies suggested that velocity superstructures were smaller than their thermal counterparts in the centre of the domain. However, a scale-by-scale analysis of the correlation between the two fields employing the linear coherence spectrum reveals that superstructures of the same size exist in both fields, which are almost perfectly correlated. The issue is further clarified by the observation that, in contrast to the temperature, and unlike assumed previously, superstructures in the vertical-velocity field do not result in a peak in the power spectrum of $w$ . The origin of this difference is traced back to the production terms of the $\unicode[STIX]{x1D703}$ and $w$ variance. These results are confirmed for a range of Rayleigh numbers $Ra=10^{5}{-}10^{9}$ ; the superstructure size is seen to increase monotonically with $Ra$ . Furthermore, the scale distribution of the temperature fluctuations in particular is pronouncedly bimodal. In addition to the large-scale peak caused by the superstructures, there exists a strong small-scale peak. This ‘inner peak’ is most intense at a distance of $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D703}}$ from the wall and is associated with structures of size ${\approx}10\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D703}}$ , where $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D703}}$ is the thermal boundary layer thickness. Finally, based on the vertical coherence relative to a reference height of $\unicode[STIX]{x1D6FF}_{\unicode[STIX]{x1D703}}$ , a self-similar structure is identified in the velocity field (vertical and horizontal components) but not in the temperature.

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Copyright

This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.

Corresponding author

Email address for correspondence: d.j.krug@utwente.nl

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Coherence of temperature and velocity superstructures in turbulent Rayleigh–Bénard flow

  • Dominik Krug (a1), Detlef Lohse (a1) (a2) and Richard J. A. M. Stevens (a1)

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