Large-scale vortical structure, supported by small-scale turbulent motions. Helicity as a cause for inverse energy cascade (Q1204032)

In this article we demonstrate that turbulent stress contributions which depend on the rotation of the frame of reference (and therefore are system dependent) give rise to the inverse energy cascade, and thus introduce an ordering in the structure of turbulence. We first demonstrate that a non-rotating Boussinesq fluid subject to an artificial force that is not invariant under parity changes of the orthogonal group has a destabilizing effect in the Bénard problem. This destabilization is due to helicity, and the stability regimes are divided into two regions. For a rotating turbulent Boussinesq fluid we derive the most simple rotation dependent expression for the stress divergence and demonstrate that it leads quantitatively to a similar helicity dependent force. In the Bénard problem it gives rise to an analogous division of the stability/instability regime as obtained for non-rotating fluids subject to the artificial helicity dependent force.