Helicity transfer in turbulent models

Helicity transfer in a shell model of turbulence is investigated. We show that a Reynolds-independent helicity flux is present in the model when the large scale forcing breaks inversion symmetry. The equivalent in shell models of the “$2/15$ law,” obtained from helicity conservation in Navier-Stokes equations, is derived and tested. The odd part of the helicity flux statistics is found to be dominated by a few very intense events. In a particular model, we calculate analytically leading and subleading contributions to the scaling of triple velocity correlation.