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A hierarchical entropy balance equation retaining the dynamics in the radial direction is introduced to study non-local turbulent transport and the associated global profile relaxation. It consists of firstand second-order equations that describe the entropy dynamics related to thermodynamics/fluid quantity and the corresponding micro-scale phase space fluctuations, respectively. Specifically, the second-order equation describes not only a local entropy production related to heat and density flux (i.e., zonal flow), but also the spatial convection of perturbed entropy. We investigated the entropy dynamics in ion-temperature-gradient driven turbulence based on a global gyrokinetic Vlasov simulation in slab geometry. Entropy convection plays an important role in the relaxation dynamics dominated by the avalanche process. A self-organized relaxed state is established, in which short-wavelength temperature corrugation, i.e., zonal pressure, is regulated by zonal flow shear.

Global Profile Relaxation and Entropy Dynamics in Turbulent Transport