We investigate the interplay between large-scale patterns, so-called superstructures, in the fluctuation fields of temperature $\theta$ and vertical velocity $w$ in turbulent Rayleigh-B\'{e}nard convection at large aspect ratios. Earlier studies suggested that velocity superstructures were smaller than their thermal counterparts in the center 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 $\theta$- 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 particularly the temperature fluctuations 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 $\delta_\theta$ from the wall and associated with structures of size $\approx 10 \delta_\theta$, where $\delta_\theta$ is the thermal boundary layer thickness. Finally, based on the vertical coherence relative to a reference height of $\delta_\theta$, a self-similar structure is identified in the velocity field (vertical and horizontal components) but not in the temperature.

中文翻译：

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湍流瑞利-贝纳流中温度和速度上层结构的相干性

我们研究了大纵横比下湍流 Rayleigh-B\'{e}nard 对流中温度 $\theta$ 和垂直速度 $w$ 波动场中的大规模模式（所谓的上层结构）之间的相互作用。早期的研究表明，速度上层结构比域中心的热结构小。然而，使用线性相干谱对两个场之间的相关性进行逐尺度分析表明，两个场中都存在相同大小的上层结构，它们几乎完全相关。观察到与温度相反，与之前假设的不同，垂直速度场中的上层结构不会导致功率谱中的峰值 w ，从而进一步澄清了这个问题。这种差异的起源可以追溯到 $\theta$- 和 $w$- 方差的产生项。这些结果在一系列瑞利数 $Ra = 10^5$--$10^9$ 中得到证实，上层建筑的尺寸可以看到随着 $Ra$ 单调增加。此外，特别是温度波动的尺度分布明显是双峰的。除了上层结构引起的大尺度峰外，还存在一个强的小尺度峰。这个“内峰”在距离壁 $\delta_\theta$ 处最为强烈，并且与尺寸为 $\approx 10 \delta_\theta$ 的结构相关，其中 $\delta_\theta$ 是热边界层厚度. 最后，基于相对于参考高度 $\delta_\theta$ 的垂直相干性，