Title: Coherent structures and spectral energy transfer in turbulent plasma: a space-filter approach,
Abstract: Plasma turbulence at scales of the order of the ion inertial length is
mediated by several mechanisms, including linear wave damping, magnetic
reconnection, formation and dissipation of thin current sheets, stochastic
heating. It is now understood that the presence of localized coherent
structures enhances the dissipation channels and the kinetic features of the
plasma. However, no formal way of quantifying the relationship between
scale-to-scale energy transfer and the presence of spatial structures has so
far been presented. In this letter we quantify such relationship analyzing the
results of a two-dimensional high-resolution Hall-MHD simulation. In
particular, we employ the technique of space-filtering to derive a spectral
energy flux term which defines, in any point of the computational domain, the
signed flux of spectral energy across a given wavenumber. The characterization
of coherent structures is performed by means of a traditional two-dimensional
wavelet transformation. By studying the correlation between the spectral energy
flux and the wavelet amplitude, we demonstrate the strong relationship between
scale-to-scale transfer and coherent structures. Furthermore, by conditioning
one quantity with respect to the other, we are able for the first time to
quantify the inhomogeneity of the turbulence cascade induced by topological
structures in the magnetic field. Taking into account the low filling-factor of
coherent structures (i.e. they cover a small portion of space), it emerges that
80% of the spectral energy transfer (both in the direct and inverse cascade
directions) is localized in about 50% of space, and 50% of the energy transfer
is localized in only 25% of space.