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

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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.