Sensitivity of stratified turbulence to the buoyancy Reynolds number
Sensitivity of stratified turbulence to the buoyancy Reynolds number
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DOI：
10.1017/jfm.2013.170
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发表时间：
2013-05
影响因子：
3.7
通讯作者：
P. Bartello;S. Tobias
中科院分区：
文献类型：
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作者：
P. Bartello;S. Tobias
摘要在这篇文章中，我们提出了分层流的直接数值模拟，分辨率高达204 {8}^{2} × 513$，以探索稳定分层湍流动力学的标度。最近的研究表明，对于足够强的层结，湍流的垂直积分尺度在足够高的Reynolds数下调整到产生一个阶数单位的垂直Froude数${F}_{v} $，而水平Froude数${F}_{h} $随着层结的增加而减小。我们的数值模拟与Lindborg（J. Fluid Mech.，第550卷，2006年，第207-242页），并采用较低分辨率的数值模拟，因为水平动能谱遵循Kolmogorov谱（用水平波数替换波数后），并且水平势能谱类似地遵循被动标量的Corrsin-Obukhov谱。最重要的是，我们建立在这些以前的结果，通过彻底探索水平动能的水平谱的分层和垂直耗散项的相对大小的依赖关系，量化的浮力雷诺数。我们最重要的结果是，幂律指数尺度的变化完全与浮力雷诺数有关，而与分层本身无关，这为Lindborg（2006）的假设提供了相当大的支持，即水平谱在大雷诺数下与分层无关。我们进一步证明，即使在大的数值分辨率的这项研究，频谱，因此，动态的浮力雷诺数的影响，除非它是大于O（10）$，这表明，在评估索赔时，必须格外小心从以前的数值模拟分层流在低或中等分辨率和外推的结果，地球物理或天体物理雷诺数。
Abstract In this article we present direct numerical simulations of stratified flow at resolutions of up to $204{8}^{2} \times 513$ , to explore scalings for the dynamics of stably stratified turbulence. Recent work suggests that for strong enough stratification, the vertical integral scale of the turbulence adjusts to yield a vertical Froude number, ${F}_{v} $ , of order unity at high enough Reynolds number, whilst the horizontal Froude number, ${F}_{h} $ , decreases as stratification is increased. Our numerical simulations are consistent with predictions by Lindborg (J. Fluid Mech., vol. 550, 2006, pp, 207–242), and with numerical simulations at lower resolution, in that the horizontal kinetic energy spectrum follows a Kolmogorov spectrum (after replacing the wavenumber with the horizontal wavenumber) and that the horizontal potential energy spectrum similarly follows the Corrsin–Obukhov spectrum for a passive scalar. Most importantly, we build upon these previous results by thoroughly exploring the dependence of the horizontal spectrum of horizontal kinetic energy on both the stratification and the relative size of the vertical dissipation terms, as quantified by the buoyancy Reynolds number. Our most important result is that variations in the power-law exponent scale entirely with the buoyancy Reynolds number and not with the stratification itself, lending considerable support to the Lindborg (2006) hypothesis that horizontal spectra are independent of stratification at large Reynolds numbers. We further demonstrate that even at the large numerical resolution of this study, the spectrum and hence the dynamics are affected by the buoyancy Reynolds number unless it is larger than $O(10)$ , indicating that extreme care must be taken when assessing claims made from previous numerical simulations of stratified flow at low or moderate resolution and extrapolating the results to geophysical or astrophysical Reynolds numbers.