Zonal flows driven by energy and zonostrophy conservations in Charney-Hasegawa-Mima turbulence*

Although zonal flows are ubiquitous in planetary systems, driving mechanisms of them in turbulence still remain poorly understood. Our present investigation focuses on the relations between zonal flows and inviscid invariants. Zonal flows owe their existence to the anisotropisation of energy transfer. Rotation facilitates two-dimensionalisation of turbulence and leads to the inverse energy cascade, driving the formations of large-scale structures.

The Charney-Hasegawa-Mima (CHM) equation is one of the simplest useful nonlinear models describing the interaction between zonal flows and turbulence. We performed DNSs of the CHM equation. Zonal structures in the real space have different appearance among vortex, stream, and pressure fields. The 2D energy spectra show dumbbell structure in low-k range and peaks on/around k_y-axis, corresponding to zonal flows. The local-flux vectors proposed in [1] [2]show consistent directional structures with the energy-enstrophy double cascade, critical balance and weak turbulence theory. The convergence points of these vector fields suggest there exist two kind of driving mechanisms for zonal flows: those owing to energy and zonostrophy conservations. The effect of finite Rossby deformation radius on the driving mechanisms will also be discussed.[3]