The total turbulent energy in the ITG case is significantly reduced compared to the ETG case.
The rate of change of energy in the ETG case, divided into various components as defined in Eq. (15).
The net heat flux (drive) , the high k dissipation D, and the dissipation at zonal wavenumbers when the zonal flows are “turned on” at time . The zonal flows are turned on by changing from 1 to 0.
The rate of change of energy in the ITG case, divided into various components as defined in Eq. (15).
The rate of change of the unstable mode energy, , divided into the various coupling terms as a function of time. (a) is for ETG case and (b) is for ITG case. The legend is the same for both plots.
The zonal field couplings of the unstable mode energy in ITG case.
A cartoon showing the nonlinear energy transfer rates for the unstable mode (a) and the zonal flow (b).
The rate of change of energy terms for the zonal pressure (a) and zonal flow (b) for ITG case.
The rate of change of energy of the unstable mode in ITG, explicitly showing calculation of the energy transfer from the unstable to stable mode via zonal flows ().
The nonlinear transfer function spectrum for modes at different wavenumbers.
The nonlinear growth rate of the stable modes derived from the different nonlinear couplings of the stable mode which are similar to Eq. (17). The second panel is a continuation of the first panel with the y axis magnified and x axis shrunk.
The frequency sum using linear frequencies, for k = (−0.08,0.2).
The frequency sum using the nonlinear frequencies, for k = (−0.08,0.2).
Frequency sum for k = (−0.08,0.2) and k′ = (0.0,0.2).
Zonal field energy levels.
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