@techreport{oai:nifs-repository.repo.nii.ac.jp:00010431,
 author = {"Yagi,  M. and Itoh,  S.-I. and Kawasaki,  M. and Itoh,  K. and Fukuyama,  A."},
 month = {Jan},
 note = {"In this paper, we analyze the turbulence composed of collective modes with different scale lengths. The hierarchical model for multiple-scale turbulence is developed. Nonlinear interactions between different scale length are modeled as turbulent drag, nonlinear noise and nonlinear drive and a set of Langevin equations is formulated. Using this model, a case where two driving mechanisms coexist (one for the micro mode and the other for semi-micro mode) is investigated. It is found that a new type of turbulence transition and a cusp-type catastrophe exist in some parameter regime. Numerical simulations are also performed for neighboring multiple-scale turbulence such as ion temperature gradient driven drift wave(ITG) ( kappa_y rho_i <1) and short wavelength ITG( kappa_y rho_i >1) modes in the shearless slab geometry. The cascade and inverse cascade in multiple-scale turbulence are investigated. The cascade is mainly observed ina( kappa parallel)?  space. On the other hand, the cascade and the inverse cascade are observed in   (kappa perp)?space. Another interesting result is that the particle flux is negative (inward pinch) due to the short wavelength ITG modes, while the ion and electron heat flux are positive, which indicates nonlinear interaction between different scale length mode might affect transport."},
 title = {Multiple-Scale Turbulence and Bifurcaion},
 year = {2003}
}