Helical invariant flows: New conservation laws and their importance for 2 1/2D turbulence

该提案的主要出发点是最近在申请人群体中发现粘性和非粘性螺旋流的新守恒定律的突破，最有可能是在60年代发现螺旋后的第一次。事实上，这包含了平面流动和轴对称流动的新守恒定律。在本方案中，紊流的应用是最重要的。鉴于湍流的应用，螺旋对称湍流被置于完全三维湍流（这决定了我们对湍流的经典认识）和平面二维湍流（这是相当不同的）之间。与三维湍流相似，螺旋湍流承认三维速度场，最重要的是，可以识别涡度输运方程中负责小尺度产生的涡拉伸项。然而，螺旋流存在于二维流形上，有点类似平面二维湍流。采用专门设计用于模拟螺旋流的模拟代码，我们打算准确地回答螺旋湍流离二维或三维湍流有多近的关键问题，或者换句话说，螺旋流是否优先将能量从小尺度转移到大尺度，反之亦然。

The principal starting point of the proposal is the recent breakthrough of finding new conservation laws for viscid and inviscid helical flows in the group of the applicant, most probably for the first time after the discovery of helicity in the 60th. This, in fact, comprised new conservation laws for plane and axisymmetric flows. In the present proposal the application to turbulence is in the foreground. In view of the turbulence application helically symmetric turbulence is placed between the fully 3D turbulence, which determines our classical knowledge of turbulence, and plane 2D turbulence, which is rather distinct. Similar to 3D turbulence, helical turbulence admits a three-dimensional velocity field and, most important, the vortex stretching term in the vorticity transport equation responsible for the generation of small scales can be identified. Nevertheless, helical flows live on a 2D manifold, somewhat analogous to plane 2D turbulence. Employing a simulation code especially designed for simulating helical flows we intend to answer exactly the key question in how far helical turbulence is closer to 2D or to 3D turbulence or in other words if helical flows have a preferential to transfer energy from small to large scales or vice versa.