Configuration-space behaviour of scale-to-scale energy transfer in anisotropic fluid and plasma turbulence

Investigating how energy is transferred in turbulent flows is critical to understand the dynamics of multi-scale geophysical fluids and space plasmas. High Reynolds number flows often support the propagation of waves, the latter competing with turbulent motions in transferring the energy across scales. In presence of coherent structures and strong anisotropy, classical paradigms of direct/inverse, constant-flux, local (in Fourier space) cascades do not necessarily hold anymore, and the overall energy transfer may become strongly localized and structured in configuration space.

In order to identify and quantify the coupling of wave vectors belonging to different regions of the spectrum in magnetohydrodynamic (MHD) and kinetic plasmas, as well as in stratified fluids (with or without rotation), we developed a methodology based on the filtering of the governing MHD/kinetic and Boussinesq equations. The method is usually referred to as ``space-filtered approach'', and it is based on the following idea. First, a low-pass spatial filter is applied to all quantities, and then these filtered quantities are employed to construct equations for the conservation laws of interest. In this procedure, quadratic terms give rise to the so-called sub-grid terms, which represent a source/sink term that couples energy flux transfer at a given spatial scale. The interesting aspect of this approach is that sub-grid terms are not defined in Fourier but in configuration space. As a result, one can evaluate and study how the scale-to-scale energy transfer is related to other spatial-dependent quantities.