Noise amplification in open Taylor-Couette flow.
Noise amplification in open Taylor-Couette flow.
复制标题
开放 Taylor-Couette 流中的噪声放大。
DOI：
10.1103/physreve.50.3670
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发表时间：
1994
期刊：
影响因子：
--
通讯作者：
D. Cannell
中科院分区：
文献类型：
--
作者：
Kenneth L. Babcock;Guenter Ahlers;D. Cannell
在半径比r 1/r 2= 0.738的开放Taylor-Couette装置中，我们对施加轴向通流的流动进行了广泛的实验和理论研究。重点讨论了基流对流不稳定时观测到的噪声放大。在轴向雷诺数R > 4的情况下，通过实验和理论确定了轴对称扰动下绝对不稳定和对流不稳定的参数边界，实验和理论的一致性很好。在起始点以上，在入口下游观察到持续的移动泰勒涡模式。在绝对不稳定的情况下，这种模式在实验分辨率内是周期性的，这一点在泰勒涡速度时间序列中的窄频谱证明了这一点。相反，在对流不稳定的情况下，模式是通过微观噪声的空间放大而产生的。结果表明，模式相位执行伪随机漫步导致频谱变宽。实际上，观察到的行为的所有方面都可以通过将复杂的金兹堡-朗道（CGL）方程与附加的、空间分布的随机项进行数值积分来定量地捕获。使用不同粘度的流体对空间振幅剖面进行了精确测量。拟合数据所需的噪声功率具有与热噪声一致的粘度依赖性，即，它在频率上具有至少十年的“白”谱。在我们的实验不确定度范围内，噪声功率与轴向雷诺数在1.5≤R≤4范围内无关。随机CGL方程的模拟表明，噪声对应于均方根速度波动，这比我们实验中典型的完全发育的二次流小约10.5倍。然而，最近对Taylor-Couette几何中无通流的热噪声功率的理论计算结果的数值评估结果比实验结果小约270倍。
We present an extensive experimental and theoretical study of the flow in an open Taylor-Couette apparatus with radius ratio r 1/r 2= 0.738 and imposed axial through-flow. Emphasis is given to the amplification of noise observed when the base flow is convectively unstable. Parameter boundaries for absolute and convective instability with respect to axisymmetric disturbances are determined experimentally and theoretically for axial Reynolds numbers R≲ 4, with excellent agreement between experiment and theory. Above onset a sustained pattern of traveling Taylor vortices is observed downstream of the inlet. In the case of absolute instability, the pattern is periodic within experimental resolution as evidenced by a narrow frequency spectrum in the time series of the Taylor-vortex velocity at a fixed point. In contrast, the patterns in the convectively unstable case arise via spatial amplification of microscopic noise. There results a broadened frequency spectrum caused by the pattern phase executing a pseudorandom walk. Virtually all aspects of the observed behavior are captured quantitatively by numerically integrating a complex Ginzburg-Landau (CGL) equation with an additive, spatially distributed, stochastic term. Precise measurements of the spatial amplitude profiles were made using fluids of various viscosities. The noise power required to fit the data has a viscosity dependence consistent with thermal noise, ie, it has a ‘‘white’’spectrum over at least a decade in frequency. Within our experimental uncertainty, the noise power is independent of the axial Reynolds number over the range 1.5≲ R≲ 4. Simulations of the stochastic CGL equation indicate that the noise corresponds to rms velocity fluctuations, which are smaller than typical fully developed secondary flows in our experiment by a factor of about 10 5. However, numerical evaluation of a recent theoretical result for the thermal noise power in the Taylor-Couette geometry with no through-flow turns out to be about 270 times smaller than the experimental result.