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

该提案的主要出发点是申请人小组最近在发现粘性和非粘性螺旋流的新守恒定律方面取得的突破，这很可能是在60年代发现螺旋度之后的第一次。事实上，这包括了平面和轴对称流的新守恒定律。在目前的建议中，湍流的应用是在前景。从湍流应用的角度来看，螺旋对称湍流介于完全三维湍流和平面二维湍流之间，完全三维湍流决定了我们对湍流的经典认识，而平面二维湍流则截然不同。与3D湍流类似，螺旋湍流允许三维速度场，最重要的是，可以确定涡度输运方程中负责产生小尺度的涡拉伸项。然而，螺旋流存在于二维流形上，有点类似于平面二维湍流。采用一个专门设计的模拟程序来模拟螺旋流，我们打算准确地回答这个关键问题，即螺旋湍流在多大程度上更接近于2D或3D湍流，或者换句话说，螺旋流是否优先将能量从小尺度传递到大尺度，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.