Dynamic properties of eta(i)-mode weak turbulence

The turbulence of the toroidal eta(i) mode has a forward spectral cascade. This means that, most of the energy initially placed in the low-wavenumber region (the linear instability region) will be spread out towards high-wavenumber modes. Therefore the linear instability may be reduced by this energy cascade. An elementary estimate of the critical amplitude for nonlinear mode coupling to balance the linear growth rate is given. As a consequence of three wave cascade process derivable from the fully toroidal fluid model equations, the formation of zonal flows in eta(i)-mode turbulence is predicted.