Gyrokinetic simulations of turbulent transport; Size scaling and chaotic behaviour

Villard, L.*; Bottino, A.*; Brunner, S.*; Casati, A.*; Chowdhury, J.*; Dannert, T.*; Ganesh, R.*; Garbet, X.*; Grler, T.*; Grandgirard, V.*; Hatzky, R.*; Idomura, Yasuhiro   ; Jenko, F.*; Jolliet, S.; Khosh Aghdam, S.*; Lapillonne, X.*; Latu, G.*; McMillan, B. F.*; Merz, F.*; Sarazin, Y.*; Tran, T. M.*; Vernay, T.*

This paper presents some of the main recent advances in gyrokinetic theory and computing of turbulence. A past controversy regarding the finite size (finite ) effect in ITG turbulence has now been resolved. Now, both Eulerian and Lagrangian global codes are shown to agree and to converge to the flux-tube result in the 0 limit. It is found, however, that an appropriate treatment of geometrical terms is necessary. Turbulent processes are characterized by a chaotic behavior, often accompanied by bursts and avalanches. Performing ensemble averages of statistically independent simulations, starting from different initial conditions, is presented as a way to assess the intrinsic variability of turbulent fluxes and obtain reliable estimates of the standard deviation.