Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence
Reynolds-number dependency in homogeneous, stationary two-dimensional turbulence
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DOI：
10.1017/s0022112009993661
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发表时间：
2010-03
影响因子：
3.7
通讯作者：
A. Bracco;J. McWilliams
中科院分区：
文献类型：
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作者：
A. Bracco;J. McWilliams
二维纳维-斯托克斯方程的湍流解是大水平尺度上湍流地球物理和天体物理“稀”流的混沌时空模式和平衡分布的范例。在这里，我们研究了具有大规模、随机强迫和粘性扩散的静态解决方案中均匀、静态二维湍流如何随雷诺数 (Re) 变化，还包括限制逆能量级联的低粘性扩散。这项调查是在 Re ≫ 1 的计算可行范围内进行的，大约在 1.5 × 103 到 5.6 × 106 之间。随着 Re 的增加，我们看到细丝和涡核内出现了涡度精细结构。在大 Re 处，能谱形状接近正熵惯性范围 k−3 形式，并且速度结构函数与 Re 无关。本研究中研究的所有其他统计测量都表现出随 Re 的幂律缩放，包括能量、熵、耗散率和涡度结构函数。标度指数取决于强迫特性对大规模相干结构的影响，而大规模相干结构的特定分布是非通用的。一个引人注目的结果是流动的间歇性测量的 Re 独立性，这与渐近增加间歇性的三维均匀湍流的已知行为形成鲜明对比。这是大规模相干涡旋控制分布函数尾部的结果。我们的分析允许外推到 Re → ∞ 的渐近极限，这是地球物理和天体物理体系及其大规模模拟模型的基础，其中湍流输运和耗散必须参数化。
Turbulent solutions of the two-dimensional Navier–Stokes equations are a paradigm for the chaotic space–time patterns and equilibrium distributions of turbulent geophysical and astrophysical ‘thin’ flows on large horizontal scales. Here we investigate how homogeneous, stationary two-dimensional turbulence varies with the Reynolds number (Re) in stationary solutions with large-scale, random forcing and viscous diffusion, also including hypoviscous diffusion to limit the inverse energy cascade. This survey is made over the computationally feasible range in Re ≫ 1, approximately between 1.5 × 103 and 5.6 × 106. For increasing Re, we witness the emergence of vorticity fine structure within the filaments and vortex cores. The energy spectrum shape approaches the forward-enstrophy inertial-range form k−3 at large Re, and the velocity structure function is independent of Re. All other statistical measures investigated in this study exhibit power-law scaling with Re, including energy, enstrophy, dissipation rates and the vorticity structure function. The scaling exponents depend on the forcing properties through their influences on large-scale coherent structures, whose particular distributions are non-universal. A striking result is the Re independence of the intermittency measures of the flow, in contrast with the known behaviour for three-dimensional homogeneous turbulence of asymptotically increasing intermittency. This is a consequence of the control of the tails of the distribution functions by large-scale coherent vortices. Our analysis allows extrapolation towards the asymptotic limit of Re → ∞, fundamental to geophysical and astrophysical regimes and their large-scale simulation models where turbulent transport and dissipation must be parameterized.