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In the present paper, we use a coarse-graining approach to investigate thenonlinear redistribution of free energy in both position and scale space forweakly collisional magnetised plasma turbulence. For this purpose, we usehigh-resolution numerical simulations of gyrokinetic (GK) turbulence that spanthe proton-electron range of scales, in a straight magnetic guide fieldgeometry. Accounting for the averaged effect of the particles' fast gyro-motionon the slow plasma fluctuations, the GK approximation captures the dominantenergy 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 fromthe coarse-grid-scales and the sub-grid-scales (SGS). We concentrate on theanalysis of nonlinear SGS effects. Not only that this allows us to investigatethe flux of free energy across the scales, but also to now analyse its spatialdensity. We find that the net value of scale flux is an order of magnitudesmaller than both the positive and negative flux density contributions. Thedependence of the results on the filter type is also analysed. Moreover, weinvestigate the advection of energy in position space. This rather novelapproach for GK turbulence can help in the development of SGS models thataccount for advective unstable structures for space and fusion plasmas, andwith the analysis of the turbulent transport saturation.

Sub-grid-scale effects in magnetised plasma turbulence