Küchler Christian, Bewley Gregory P, Bodenschatz Eberhard
Max Planck Institute for Dynamics and Self-Organization, Göttingen, Germany; Institute for Dynamics of Complex Systems, University of Göttingen, Göttingen, Germany; and Max Planck University of Twente Center for Complex Fluid Dynamics, Göttingen, Germany and Twente, Netherlands.
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA.
Phys Rev Lett. 2023 Jul 14;131(2):024001. doi: 10.1103/PhysRevLett.131.024001.
In turbulent flows, kinetic energy is transferred from large spatial scales to small ones, where it is converted to heat by viscosity. For strong turbulence, i.e., high Reynolds numbers, Kolmogorov conjectured in 1941 that this energy transfer is dominated by inertial forces at intermediate spatial scales. Since Kolmogorov's conjecture, the velocity difference statistics in this so-called inertial range have been expected to follow universal power laws for which theoretical predictions have been refined over the years. Here we present experimental results over an unprecedented range of Reynolds numbers in a well-controlled wind tunnel flow produced in the Max Planck Variable Density Turbulence Tunnel. We find that the measured second-order velocity difference statistics become independent of the Reynolds number, suggesting a universal behavior of decaying turbulence. However, we do not observe power laws even at the highest Reynolds number, i.e., at turbulence levels otherwise only attainable in atmospheric flows. Our results point to a Reynolds number-independent logarithmic correction to the classical power law for decaying turbulence that calls for theoretical understanding.
在湍流中，动能从大空间尺度传递到小空间尺度，在小空间尺度处通过粘性转化为热量。对于强湍流，即高雷诺数，科尔莫戈罗夫在1941年推测，这种能量传递在中间空间尺度上由惯性力主导。自科尔莫戈罗夫的推测以来，在这个所谓的惯性范围内的速度差统计一直被期望遵循通用的幂律，多年来对其理论预测不断完善。在此，我们展示了在马克斯·普朗克可变密度湍流风洞中产生的、在前所未有的雷诺数范围内的实验结果。我们发现，测量得到的二阶速度差统计与雷诺数无关，这表明衰减湍流具有通用行为。然而，即使在最高雷诺数下，即处于通常只有在大气流动中才能达到的湍流水平时，我们也未观察到幂律。我们的结果表明，对于衰减湍流的经典幂律存在与雷诺数无关的对数修正，这需要从理论上加以理解。
