Gradient-driven flux-tube simulations of ion temperature gradient ă turbulence close to the non-linear threshold
Résumé
It is shown that Ion Temperature Gradient turbulence close to the ă threshold exhibits a long time behaviour, with smaller heat fluxes at ă later times. This reduction is connected with the slow growth of long ă wave length zonal flows, and consequently, the numerical dissipation on ă these flows must be sufficiently small. Close to the nonlinear threshold ă for turbulence generation, a relatively small dissipation can maintain a ă turbulent state with a sizeable heat flux, through the damping of the ă zonal flow. Lowering the dissipation causes the turbulence, for ă temperature gradients close to the threshold, to be subdued. The heat ă flux then does not go smoothly to zero when the threshold is approached ă from above. Rather, a finite minimum heat flux is obtained below which ă no fully developed turbulent state exists. The threshold value of the ă temperature gradient length at which this finite heat flux is obtained ă is up to 30% larger compared with the threshold value obtained by ă extrapolating the heat flux to zero, and the cyclone base case is found ă to be nonlinearly stable. Transport is subdued when a fully developed ă staircase structure in the E x B shearing rate forms. Just above the ă threshold, an incomplete staircase develops, and transport is mediated ă by avalanche structures which propagate through the marginally stable ă regions. Published by AIP Publishing.
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