Dynamics of second-order phase transitions in resistive pressure-gradient-driven turbulence

The phase transition model for the transition from a low-confinement to a high-confinement regime is based on general properties of the coupling between turbulence and averaged sheared flows. To extract these generic properties several turbulence models have been investigated. In particular, the structure of the turbulent Reynolds stress tensor is crucial to the phase transition model. For a broad range in parameters of the resistive pressure-gradient-driven turbulence, we find a strong competition in the Reynolds stress tensor between the dynamo instability term and the turbulent viscosity. This result is contrary to expectations based on simplified local models. This competition allows the transition to take place only near marginal stability. The particle flux is calculated, and its reduction at the transition is caused not only by fluctuation suppression but also by the change in the relative phase of the pressure and potential fluctuations. The results obtained with this turbulence model are presented here, with special emphasis on the structure of the Reynolds stress and the existence of limit cycle solutions, which may be related to the observed phenomenon of dithering.