On uniqueness of transfer rates in magnetohydrodynamic turbulence

Abstract

In hydrodynamic and magnetohydrodynamic turbulence, expressions for the transfer rates rely on integrals over wavenumber triads (k,p,q) satisfying k+p+q=0. As an example SuuE(k|p,q) denotes the kinetic energy transfer rate to the mode k, from the two other modes in the triad, p and q. As noted by Kraichnan (1958), in SuuE(k|p,q), what fraction of the energy transferred to the mode k originated from p and which from q is unknown . Such an expression is thus incongruent with the customary description of turbulence in terms of two-scale energy exchange. Notwithstanding this issue, Dar etal. (2001) further decomposed these transfers into separate contributions from p-to-k and q-to-k, thus introducing the concept of mode-to-mode transfers that they applied to MHD turbulence. Doing so, they had to set aside additional transfers circulating within each triad, but failed to calculate them.