Computational and Information Systems Laboratory, National Center for Atmospheric Research, PO Box 3000, Boulder, CO 80307-3000, USA.
Philos Trans A Math Phys Eng Sci. 2010 Apr 13;368(1916):1635-62. doi: 10.1098/rsta.2009.0284.
Invariance properties of physical systems govern their behaviour: energy conservation in turbulence drives a wide distribution of energy among modes, as observed in geophysical or astrophysical flows. In ideal hydrodynamics, the role of the invariance of helicity (correlation between velocity and its curl, measuring departures from mirror symmetry) remains unclear since it does not alter the energy spectrum. However, in the presence of rotation, significant differences emerge between helical and non-helical turbulent flows. We first briefly outline some of the issues such as the partition of energy and helicity among modes. Using massive numerical simulations, we then show that small-scale structures and their intermittency properties differ according to whether helicity is present or not, in particular with respect to the emergence of Beltrami core vortices that are laminar helical vertical updraft vortices. These results point to the discovery of a small parameter besides the Rossby number, a fact that would relate the problem of rotating helical turbulence to that of critical phenomena, through the renormalization group and weak-turbulence theory. This parameter can be associated with the adimensionalized ratio of the energy to helicity flux to small scales, the three-dimensional energy cascade being weak and self-similar.
湍流中的能量守恒会导致能量在模式之间广泛分布，这在地球物理或天体物理流动中得到了观察。在理想的流体动力学中，由于旋度（速度与其旋度的相关性，用于衡量偏离镜像对称的程度）的不变性不会改变能量谱，因此其作用仍然不清楚。然而，在旋转的情况下，螺旋和非螺旋湍流之间会出现显著差异。我们首先简要概述了一些问题，例如能量和旋度在模式之间的分配。然后，我们使用大规模数值模拟表明，小尺度结构及其间歇性特性根据是否存在旋度而有所不同，特别是在出现 Beltrami 核涡旋（层流螺旋垂直上升涡旋）方面。这些结果表明，除了罗斯比数之外，还发现了一个小参数，这一事实将通过重整化群和弱湍流理论将旋转螺旋湍流的问题与临界现象联系起来。这个参数可以与能量和旋度通量到小尺度的无量纲比相关联，三维能量级联是弱且自相似的。
