在惯性驱动的von Karman封闭流中向turbulence的超临界转变
Supercritical transition to turbulence in an inertially-driven von Karman closed flow
摘要：
本文研究了在雷诺数100 - 1000000范围内，两个装有弯曲叶片的反向旋转大叶轮之间的惯性驱动von Karman流动从层流到充分发展的湍流的转变。这种转变是由方位角剪切层的不稳定性驱动的，即，Kelvin-Helmholtz不稳定性，表现出行波/漂移波，调制行波和湍流谱下出现的混沌。一个局部量-在一个给定的点的速度波动的能量-和一个全局量-所施加的扭矩-被用来监测动态。当地的数量定义了临界雷诺数Rec的时间依赖性的流量的开始，和一个上限阈值/交叉Ret的能量级联的饱和。无量纲阻力系数，即，湍流耗散在该有限Ret之上达到平台，如对于Re ->无穷大的“Kolmogorov”类湍流所预期的。我们的观察结果表明，在这个封闭的流动中，湍流的过渡是全球超临界的：速度波动的能量可以被认为是一个序参量，其特征在于从第一层流的时间依赖性到充分发展的湍流的动态。此外，在时间域中的频谱分析表明，几乎所有的波动能量存储在时间尺度的一个或两个数量级慢于基于叶轮频率的时间尺度。
英文摘要：
We study the transition from laminar flow to fully developed turbulence for an inertially-driven von Karman flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (100 - 1 000 000). The transition is driven by the destabilisation of the azimuthal shear-layer, i.e., Kelvin-Helmholtz instability which exhibits travelling/drifting waves, modulated travelling waves and chaos below the emergence of a turbulent spectrum. A local quantity -the energy of the velocity fluctuations at a given point- and a global quantity -the applied torque- are used to monitor the dynamics. The local quantity defines a critical Reynolds number Rec for the onset of time-dependence in the flow, and an upper threshold/crossover Ret for the saturation of the energy cascade. The dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence for Re -> infinity. Our observations suggest that the transition to turbulence in this closed flow is globally supercritical: the energy of the velocity fluctuations can be considered as an order parameter characterizing the dynamics from the first laminar time-dependence up to the fully developed turbulence. Spectral analysis in temporal domain moreover reveals that almost all of the fluctuations energy is stored in time-scales one or two orders of magnitude slower than the time-scale based on impeller frequency.
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