Helically decomposed turbulence

Abstract

A decomposition of the energy and helicity fluxes is used to analyse turbulent hydrodynamic flows. The decomposition is based on the projection of the flow to a helical basis. This allows the roles of interactions among modes of different helicities to be investigated separately. The proposed formalism is applied to large-scale numerical simulations of non-helical and helical flows, where the decomposed fluxes are explicitly calculated. It is shown that the total energy flux can be split into three fluxes that independently remain constant in the inertial range. One of these fluxes which corresponds to the interactions of fields with the same helicity is negative, implying the presence of an inverse cascade that is ‘hidden’ inside the forward cascade. Similarly to the energy flux, it is also shown that the helicity flux can be decomposed into two fluxes that remain constant in the inertial range. Implications of these results as well as possible new directions for investigations are discussed.