Inertial transfers in the helical decomposition

The directions of the triadic energy transfers assumed in a previous paper agree with the spectral closures, in a similarity range, if the exponent of the power-law energy spectrum is less than unity. The helical interactions showing a strong local energy transfer when the triad is nonlocal, sum up to a reverse cascade unless the spectrum falls off faster than a -7/3 power of the wave number. The energy cascades from each type of helical interaction are calculated for a -5/3 inertial range using the eddy damped quasinormal Markovian model. One type of interaction is responsible for 86 percent of the cascade. The contributions of the two classes of helical interactions to the subgrid-scale eddy viscosity are presented, together with the contributions from the forward and reverse cascading interactions. An application of the assumption on the triadic energy transfers to turbulence under rapid rotation gives a simple argument for the tendency toward nonlinear two-dimensionalization of the flow.