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–Benard 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.
Highlights
A remarkable feature of turbulent flows is that, amid the inherent disorder in both time and space, they frequently give rise to a surprisingly organized flow motion A2-2D
The strength of the non-dimensional thermal driving in Rayleigh–Bénard convection (RBC) is given by the Rayleigh number Ra, while the dimensionless heat transfer is characterized by the Nusselt number Nu
Data are presented in premultiplied form kΦψψ, such that the area under the curve equals the variance when plotted on a logarithmic scale, according to ψ2 = Φψψ dk = kΦψψ d(log k)
Summary
A remarkable feature of turbulent flows is that, amid the inherent disorder in both time and space, they frequently give rise to a surprisingly organized flow motion. A puzzling and as yet unexplained observation is that superstructures in the temperature (θ) field are larger than in the vertical-velocity w field (Pandey et al 2018; Stevens et al 2018) when the structure size is determined based on the peaks in the power spectrum or the corresponding integral length scale. The correlation between the two quantities appears much lower than one would naively expect, given that the temperature fluctuations provide the driving of w These observations seem at odds with the notion that superstructures in RBC form large-scale convection rolls for which temperature and velocity scales should be of the same size.
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