Rossby wave, drift wave and zonal flow turbulence

Abstract

An extensive qualitative and quantitative study of Rossby wave, drift wave and zonal flow turbulence in the Charney-Hasegawa-Mima model is presented. This includes details of two generation mechanisms of the zonal flows, evidence of the nonlocal nature of this turbulence and of the energy exchange between the small and large scales. The modulational instability study shows that for strong primary waves the most unstable modes are perpendicular to the primary wave, which corresponds to the generation of a zonal flow if the primary wave is purely meridional. For weak waves, the maximum growth occurs for off-zonal modulations that are close to being in three-wave resonance with the primary wave. Nonlinear jet pinching is observed for all nonlinearity levels but the subsequent dynamics differ between strong and weak primary waves. The jets of the former further roll up into Kármán-like vortex streets and saturate, while for the latter, the growth of the unstable mode reverses and the system oscillates between a dominant jet and a dominant primary wave. A critical level of nonlinearity is defined which separates the two regimes. Some of these characteristics are captured by truncated models. Numerical proof of the extra invariant in Rossby and drift wave turbulence is presented. While the theoretical derivations of this invariant stem from the wave kinetic equation which assumes weak wave amplitudes, it is shown to be relatively-well conserved for higher nonlinearities also. Together with the energy and enstrophy, these three invariants cascade into anisotropic sectors in the k-space as predicted by the Fjørtoft argument. The cascades are characterised by the zonostrophy pushing the energy to the zonal scales. A small scale instability forcing applied to the model has demonstrated the wellknown drift wave - zonal flow feedback loop. The drift wave turbulence is generated from this primary instability. The zonal flows are then excited by either one of the generation mechanisms, extracting energy from the drift waves as they grow. Eventually the turbulence is completely suppressed and the zonal flows saturate. The turbulence spectrum is shown to diffuse in a manner which has been mathematically predicted. The insights gained from this simple model could provide a basis for equivalent studies in more sophisticated plasma and geophysical fluid dynamics models in an effort to fully understand the zonal flow generation, the turbulent transport suppression and the zonal flow saturation processes in both the plasma and geophysical contexts