论文标题
快速旋转的湍流中三维的发作
Onset of three-dimensionality in rapidly rotating turbulent flows
论文作者
论文摘要
通过上限理论，通过垂直不变的体力驱动的湍流被证明是二维旋转率的二维。湍流的维度过渡对能量耗散率有关键的后果。但是，边界过程未提供其在参数空间中的位置。为了确定正好2D和部分3D流之间的精确阈值，我们对完全湍流的2D基态执行线性稳定性分析。这需要在数千个失误时间内数字地集成一组准2D方程，以准确平均3D扰动的平均生长速度在湍流2DBase流的统计数据上。我们利用现代GPU的功能来实现此任务，这使我们能够研究参数空间，直到RE = 10^5。在典型的3D DNS和实验室实验的雷诺数中，在[10^2，5x10^3]中，湍流的2D流通过离心型不稳定而对3D运动变得不稳定。但是，在更高的雷诺数中，另一个不稳定接管了。后一种不稳定性的候选机制是通过调制的2D流对惯性波的参数激发，这是我们用振荡性的2D Kolmogorov流量来说明的现象。
Turbulent flows driven by a vertically invariant body force were proven to become exactly two-dimensional above a critical rotation rate, using upper bound theory. This transition in dimensionality of a turbulent flow has key consequences for the energy dissipation rate. However, its location in parameter space is not provided by the bounding procedure. To determine this precise threshold between exactly 2D and partially 3D flows, we perform a linear stability analysis over a fully turbulent 2D base state. This requires integrating numerically a quasi-2D set of equations over thousands of turnover times, to accurately average the growth rate of the 3D perturbations over the statistics of the turbulent 2Dbase flow. We leverage the capabilities of modern GPUs to achieve this task, which allows us to investigate the parameter space up to Re = 10^5. At Reynolds numbers typical of 3D DNS and laboratory experiments, Re in [10^2, 5x10^3], the turbulent 2D flow becomes unstable to 3D motion through a centrifugal-type instability. However, at even higher Reynolds number another instability takes over. A candidate mechanism for the latter instability is the parametric excitation of inertial waves by the modulated 2D flow, a phenomenon that we illustrate with an oscillatory 2D Kolmogorov flow.
