Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results

The basic entity of nonlinear interaction in Navier-Stokes and the magnetoh ydrodynamic (MHD) equations is a wavenumber triad (k, p, q) satisfying k p + q = 0. The expression for the combined energy transfer from two of thes e wavenumbers to the third wavenumber is known. In this paper, we introduce the idea of an effective energy transfer between a pair of modes by the me diation of the third mode, and find an expression for it. Then, we apply th is formalism to compute the energy transfer in the quasi-steady-state of tw o-dimensional MHD turbulence with large-scale kinetic forcing. The computat ion of energy fluxes and the energy transfer between different wavenumber s hells is done using the data generated by the pseudo-spectral direct numeri cal simulation. The picture of energy flux that emerges is quite complex - there is a forward cascade of magnetic energy, an inverse cascade of kineti c energy, a flux of energy from the kinetic to the magnetic field, and a re verse flux which transfers the energy back to the kinetic from the magnetic . The energy transfer between different wavenumber shells is also complex - local and non-local transfers often possess opposing features, i.e., energ y transfer between some wavenumber shells occurs from kinetic to magnetic, and between other wavenumber shells this transfer is reversed. The net tran sfer of energy is from kinetic to magnetic. The results obtained from the s tudies of flux and shell-to-shell energy transfer are consistent with each other. (C) 2001 Elsevier Science B.V. All rights reserved.