Nonlinear behavior and turbulence spectra of drift waves and Rossby waves

Spectrum cascade in drift wave turbulence in a magnetized plasma as well as Rossby wave turbulence in an atmospheric pressure system are studied based on a three-wave decay process derivable from the model equation applicable to both cases. The decay in the three-way interaction occurs to smaller and larger values of ‖k‖. In a region of large wavenumbers this leads to the dual cascade; the energy spectrum cascades to smaller ‖k‖ and the enstrophy spectrum to larger ‖k‖, similar to the case of two-dimensional Navier–Stokes turbulence. In a small wavenumber region a resonant three-wave decay process dominates the cascade process, and an anisotropic spectrum develops. As a consequence of the cascade, zonal flows in the direction perpendicular to the direction of inhomogeneity appear which presents a potential implication for the particle confinement in a turbulent plasma.