Ken Uzawa

Propagation of magnetic island due to self-induced zonal flow

Propagation of magnetic island caused by drift-tearing instability is numerically investigated based on a reduced set of two-fluid equations. It is found that the island propagates into the ion diamagnetic direction when the island growth is saturated, and the propagation velocity becomes small as the viscosity increases. The island propagates with zonal flow generated by drift-tearing instability, because flattening of pressure inside the island is enhanced by parallel ion velocity. The mechanism of zonal flow generation depends on the viscosity. When the viscosity is small, the flow driven by the Reynolds stress is diminished by the Maxwell stress, and the small difference between them is overcome by the ion diamagnetic stress, and thus the zonal flow directs toward the ion diamagnetic direction. When the viscosity is large, the viscous stress is counteracted by the Reynolds and the Maxwell stresses, and the small difference between them is overcome by the ion diamagnetic stress, and thus zonal flow dir...

Global characteristics of zonal flows due to the effect of finite bandwidth in drift wave turbulence

The spectral effect of the zonal flow (ZF) on its generation is investigated based on the Charney–Hasegawa–Mima turbulence model. It is found that the effect of finite ZF bandwidth qualitatively changes the characteristics of ZF instability. A spatially localized (namely, global) nonlinear ZF state with an enhanced, unique growth rate for all spectral components is created under a given turbulent fluctuation. It is identified that such state originates from the successive cross couplings among Fourier components of the ZF and turbulence spectra through the sideband modulation. Furthermore, it is observed that the growth rate of the global ZF is determined not only by the spectral distribution and amplitudes of turbulent pumps as usual, but also statistically by the turbulence structure, namely, their probabilistic initial phase factors. A ten-wave coupling model of the ZF modulation instability involving the essential effect of the ZF spectrum is developed to clarify the basic features of the global nonli...

Effect of Wave-Type Mean Flow on the Modulational Process of Zonal Flow Instability

The effects of an external mean flow on the modulational instability process of zonal flow in drift wave turbulence are theoretically studied based on Hasegawa–Mima (HM) turbulence model. Based on the coherent mode coupling approach, a dispersion relation of the zonal flow instability involving the external mean flow with a wave-type characterized by the amplitude |φ f |, radial wave number k f , and frequency ω f is derived. As an example, the zonal flow driven by ion temperature gradient (ITG) turbulence is sampled as the mean flow acting on the modulational process of zonal flow instability in electron temperature gradient (ETG) turbulence. It is shown that the growth rate of the zonal flow, γ q , is suppressed by the mean flow with a fitting relation γ q ≃γ q 0 -α|φ f | 2 k 2 f , where γ q 0 is the growth rate of the zonal flow in the absence of mean flow and α is a positive numerical constant. This formula is applicable to a strong shearing regime where the zonal flow instability is stabilized. The s...

Comparison of analytical models for zonal flow generation in ion-temperature-gradient mode turbulence

During the past years the understanding of the multi scale interaction problems have increased significantly. However, at present there exists a flora of different analytical models for investigating multi scale interactions and hardly any specific comparisons have been performed among these models. In this work two different models for the generation of zonal flows from ion‐temperature‐gradient (ITG) background turbulence are discussed and compared. The methods used are the coherent mode coupling model and the wave kinetic equation model (WKE). It is shown that the two models give qualitatively the same results even though the assumption on the spectral difference is used in the (WKE) approach.