Falkovich Gregory
Weizmann Institute of Science, Rehovot 76100, Israel; Institute for Information Transmission Problems, Moscow 127994, Russia.
Proc Math Phys Eng Sci. 2016 Jul;472(2191):20160287. doi: 10.1098/rspa.2016.0287.
This short note is written to call attention to an analytic approach to the interaction of developed turbulence with mean flows of simple geometry (jets and vortices). It is instructive to compare cases in two and three dimensions and see why the former are solvable and the latter are not (yet). We present the analytical solutions for two-dimensional mean flows generated by an inverse turbulent cascade on a sphere and in planar domains of different aspect ratios. These solutions are obtained in the limit of small friction when the flow is strong while turbulence can be considered weak and treated perturbatively. I then discuss when these simple solutions can be realized and when more complicated flows may appear instead. The next step of describing turbulence statistics inside a flow and directions of possible future progress are briefly discussed at the end.
本短文旨在提请注意一种分析方法，用于研究充分发展的湍流与简单几何形状（射流和涡旋）的平均流之间的相互作用。比较二维和三维的情况并探究为何前者可解而后者（目前）不可解是很有启发性的。我们给出了由球体上的反向湍流级联以及不同纵横比的平面域中产生的二维平均流的解析解。这些解是在小摩擦极限下得到的，此时流动很强，而湍流可视为弱湍流并采用微扰法处理。然后我讨论了这些简单解何时能够实现，以及何时可能出现更复杂的流动。最后简要讨论了描述流体内湍流统计量的下一步工作以及未来可能的进展方向。
