In this dissertation, the ITG and ETG turbulence are explored based on nonlinear gyrokinetic theory and direct numerical simulations. Then, the results concerning (i) formation of coherent vortex streets and the resultant transport reduction, (ii) effects of parallel dynamics on the zonal flow generation, and (iii) nonlinear entropy transfer among turbulent vortices, streamers, and zonal flows, are presented.

First, vortex structures in the slab ETG turbulence are investigated, including comparisons with those in the slab ITG case. Depending on parameters which determine the growth rate of linear ETG modes, two different flow structures are observed, i.e., statistically steady turbulence with a weak zonal flow and coherent vortex streets along a strong zonal flow. The former involves many isolated vortices and their mergers with complicated motion, and leads to steady electron heat transport. When the latter is formed, the high wavenumber components of potential and temperature fluctuations are reduced, and the electron heat transport decreases significantly. It is found that the transport reduction is mainly associated with the phase matching between the potential and temperature fluctuations rather than the reduction of fluctuation amplitudes. A traveling wave solution of a Hasegawa-Mima type equation derived from the gyrokinetic equation with the electron temperature gradient agrees well with the coherent vortex streets found in the slab ETG turbulence.

Second, effects of parallel dynamics on transition of vortex structures and zonal flows, which are closely associated with transport reduction found in the slab ETG turbulence, are intensively examined. Numerical results show three different types of vortex structures, i.e., coherent vortex streets accompanied with the transport reduction, turbulent vortices with steady transport, and a zonal-flow-dominated state, depending on the relative magnitude of the parallel compression to the diamagnetic drift. In particular, the formation of coherent vortex streets is correlated with strong generation of zonal flows for the cases with weak parallel compression, even though the maximum growth rate of linear ETG modes is relatively large. A physical mechanism of the secondary growth of zonal flows is discussed based on the modulational instability analysis with a truncated fluid model, where the parallel dynamics with acoustic modes is incorporated. The modulational instability for zonal flows is found to be stabilized by the effect of the finite parallel compression. The theoretical analysis qualitatively agrees with the secondary growth of zonal flows found in the slab ETG turbulence simulations, where the transition of vortex structures is observed.

Finally, the investigations of vortex structures and zonal flows are extended to toroidal ITG and ETG turbulence by means of five-dimensional nonlinear gyrokinetic simulations. In the steady state, the formation of the strong zonal flow is observed in the toroidal ITG turbulence, while the radially elongated streamers, which yield the significant enhancement of heat transport, develop in the toroidal ETG case. Gyrokinetic entropy balance relations for zonal and non-zonal modes, and the nonlinear entropy transfer function, which is regarded as a kinetic extension of the zonal-flow energy production due to the hydrodynamic Reynolds stress, are carefully examined. The different entropy transfer processes in saturation and steady phases are revealed for the ITG turbulence. The entropy transfer from non-zonal to zonal modes is substantial in the saturation phase of the instability growth, while the entropy variable of the low radial-wavenumber modes driving the heat transport are successively transferred to the higher radial-wavenumber modes with less turbulent heat flux via the non-local interaction with zonal flows in the steady phase. On the other hand, in both the saturation and steady phases of the ETG turbulence, the role of zonal flows in the entropy transfer to the higher radial-wavenumber modes is much weaker than that in the ITG case. Instead, the nearly isotropic entropy transfer within the low wavenumber modes occurs dominantly through the nonlinear interactions among non-zonal modes.

The formation of vortices and zonal flows, and the related entropy transfer processes in the ITG and ETG turbulence are comprehensively examined in this study, then the detailed mechanisms of the turbulence suppression due to the nonlinear interactions with zonal flows are clarified in the framework of kinetic theory. The results obtained by a novel method of the entropy transfer analysis provide one with not only deeper understandings of the fundamental physics of the turbulent transport and zonal flows, but fruitful suggestions for advanced turbulence measurement methods such as the bicoherence analysis.

, application/pdf, 総研大甲第1410号}, title = {Vortices, Zonal Flows, and Transport in Gyrokinetic Plasma Turbulence}, year = {} }