快速旋转对流中的内部加热并非地转湍流的捷径

中文摘要 AI 辅助

行星和恒星中的对流湍流通常由内部加热驱动，这种强迫机制也被提出作为一种在适度强迫下获取地转湍流（GT）区域无扩散标度的手段。我们采用渐近约化的准地转模型对此进行检验，该模型在埃克曼数趋于零（$Ek \rightarrow 0$）的极限下形式上有效，且保留普朗特数作为独立参数。我们未发现此类捷径：努塞尔数（Nusselt）和雷诺数与无扩散预测值的接近程度并不比边界加热情形更好，且在$Pr = 7$时偏离程度更大；预测的$Pr^{-1/2}$塌缩失效；前置因子取决于加热形式。我们的无滑移/无应力情形与Hadjerci等人（2024）的辐射驱动模拟逐案匹配，但在相同约化瑞利数和普朗特数下，埃克曼数不同的扫描之间仍存在25%的努塞尔数（Nu）变化。这些数据仅覆盖了补偿努塞尔数恒定的窄强迫范围；在约化模型可及的更宽范围内，补偿努塞尔数先升至最大值后下降。我们认为，整体输运标度并非GT的完整诊断指标，而内部平均温度梯度和垂直速度峰度的饱和仍是可靠指标。

英文摘要

Convective turbulence in planets and stars is often driven by internal heating. This forcing mechanism has also been proposed as a means of accessing the diffusion-free scalings of the geostrophic turbulence (GT) regime at modest forcing. We test this with the asymptotically reduced quasi-geostrophic model, which is formally valid in the limit of vanishing Ekman number, $Ek \rightarrow 0$, and retains the Prandtl number as an independent parameter. We find no such shortcut: the Nusselt and Reynolds numbers are no closer to their diffusion-free predictions than in the boundary-heated case, and at $Pr = 7$ they are further from them; the predicted $Pr^{-1/2}$ collapse fails; and the prefactor depends on the form of the heating. Our no-slip/stress-free cases track the radiatively driven simulations of Hadjerci et al. (2024) case by case, yet a $25\%$ variation in $Nu$ persists between sweeps that share the same reduced Rayleigh and Prandtl numbers but differ in Ekman number. Those data span only the narrow range of forcing over which the compensated Nusselt number is stationary; across the wider range accessible to the reduced model it rises to a maximum and then falls. We argue that bulk transport scalings are incomplete diagnostics of GT, whereas the saturation of the interior mean temperature gradient and of the vertical velocity kurtosis remain reliable indicators.

发表机构

• University of Colorado, Boulder（科罗拉多大学博尔德分校）
• ETH Zurich（苏黎世联邦理工学院）

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