Turbulent transport in mixed states of convective cells and sheared flows

Low-order mode coupling equations are used to describe recent computer simulations of resistive-g turbulent convection that show bifurcations for the onset of steady and pulsating sheared mass flows. The three convective transport states are identified with the tokamak confinement regimes called low-mode (L-mode), high-mode (H-mode), and edge-localized modes (ELMs). The first bifurcation (L→H) and the second bifurcation (H→ELMs) conditions are derived analytically and compared with direct solutions of the 6-ODE mode coupling equations. First an exact expression is given for the energy transfer rate from the fluctuations to the sheared mass flow through the triplet velocity correlation function. Then the time scale expansion required to derive the Markovian closure formula is given. Markovian closure formulas form the basis for the thermodynamic-like L–H models used in several recently proposed models.