Turbulent Bursts in Couette-Taylor Flow.
Turbulent Bursts in Couette-Taylor Flow.
复制标题
库埃特-泰勒流中的湍流爆发。
DOI：
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发表时间：
1996
影响因子：
8.6
通讯作者：
P. Marcus
中科院分区：
文献类型：
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作者：
K. Coughlin;P. Marcus
提出了同心旋转圆柱体之间的三维流动（库埃特-泰勒流）中的湍流爆发的新数学模型。在一定的流态内，如果参数保持固定，则流动会在空间层流相（时间上混沌的互穿螺旋涡流）和湍流相之间及时振荡。我们的数学模型基于我们之前发布的 [1] 完全解析的直接数值模拟（即使用没有湍流建模的纳维-斯托克斯方程）。根据这些模拟，我们开发了一个物理模型 [2]，将循环分解为四个物理过程：(1) 流动建立了涡流的层流平衡（互穿螺旋涡流）； (2) 平衡对于线性 Floquet 模式变得不稳定，该模式从随机的、小的初始条件呈指数增长； (3) 该模式充当剪切驱动不稳定性的有限振幅触发器，从而导致大振幅、充满空间的湍流； (4)在湍流耗尽了流动的平均方位角分量中存储的能量之后，耗散导致其崩溃并且循环重复。在这里，我们使用基于物理模型的近似值从纳维-斯托克斯方程导出数学模型。我们展示了该模型与数值计算速度的吻合程度，它如何解释数值计算场的相关性和其他属性，以及它如何做出可以在未来实验中测试的预测。
A new mathematical model for turbulent bursts in the three-dimensional flow between concentric, rotating cylinders (Couette-Taylor flow) is presented. Within a certain flow regime, if the parameters are held fixed, the flow oscillates in time between a spatially laminar phase (temporally chaotic Interpenetrating Spiral Vortex flow) and a turbulent phase. Our mathematical model is based on our previously published [1] fully-resolved, direct numerical simulation (i.e., using the Navier-Stokes equation with no turbulence modeling). Prom these simulations we developed a physical model [2] that breaks up the cycle into four physical processes: (1) the flow sets up a laminar equilibrium of vortices (Interpenetrating Spiral Vortex flow); (2) the equilibrium becomes unstable to a linear Floquet mode which grows exponentially from random, small initial conditions; (3) this mode acts as a finite–amplitude trigger for a shear-driven instability which results in large–amplitude, space–filling turbulence; and (4) after the turbulence exhausts the energy stored in the mean azimuthal component of the flow, dissipation causes it to collapse and the cycle repeats. Here, we derive a mathematical model from the Navier–Stokes equations using approximations based on the physical model. We show how well the model agrees with the numerically computed velocities, how it explains correlations and other properties of the numerically computed fields, and how it makes predictions that could be tested in future experiments.