  In the present paper, we use a coarse-graining approach to investigate the
nonlinear redistribution of free energy in both position and scale space for
weakly collisional magnetised plasma turbulence. For this purpose, we use
high-resolution numerical simulations of gyrokinetic (GK) turbulence that span
the proton-electron range of scales, in a straight magnetic guide field
geometry. Accounting for the averaged effect of the particles' fast gyro-motion
on the slow plasma fluctuations, the GK approximation captures the dominant
energy redistribution mechanisms in strongly magnetised plasma turbulence.
Here, the GK system is coarse-grained with respect to a cut-off scale,
separating in real space the contributions to the nonlinear interactions from
the coarse-grid-scales and the sub-grid-scales (SGS). We concentrate on the
analysis of nonlinear SGS effects. Not only that this allows us to investigate
the flux of free energy across the scales, but also to now analyse its spatial
density. We find that the net value of scale flux is an order of magnitude
smaller than both the positive and negative flux density contributions. The
dependence of the results on the filter type is also analysed. Moreover, we
investigate the advection of energy in position space. This rather novel
approach for GK turbulence can help in the development of SGS models that
account for advective unstable structures for space and fusion plasmas, and
with the analysis of the turbulent transport saturation.
