Triple cascade behaviour in QG and drift turbulence and generation of zonal jets

TL;DR

This study investigates the cascade behavior of energy, enstrophy, and zonostrophy in quasi-geostrophic and plasma drift turbulence using the CHM model, highlighting the conservation and role of zonostrophy in forming zonal jets.

Contribution

It generalizes the Fjørtoft argument for the CHM model at small scales and demonstrates numerically that zonostrophy is conserved and influences cascade directions even under strong nonlinearity.

Findings

Zonostrophy is well conserved in the CHM model.

The three invariants cascade as predicted by the generalized Fjørtoft argument.

Triple cascade remains accurate even with strong initial nonlinearity.

Abstract

We study quasi-geostrophic turbulence and plasma drift turbulence within the Charney-Hasegawa-Mima (CHM) model. We focus, theoretically and using numerical simulations, on conservation of {\em zonostrophy} and on its role in the formation of the zonal jets. The zonostrophy invariant was first predicted in \cite{perm,BNZ_invariant} in two special cases -- large-scale turbulence and anisotropic turbulence. Papers \cite{perm,BNZ_invariant} also predicted that the three invariants, energy, enstrophy and zonostrophy, will cascade anisotropically into non-intersecting sectors in the $k$-space, so that the energy cascade is "pushed" into the large-scale zonal scales. In the present paper, we consider the scales much less than the Rossby deformation radius and generalise the Fj{\o}rtoft argument of \cite{perm,BNZ_invariant} to find the directions of the three cascades in this case. For the first time, we demonstrate numerically that zonostrophy is well conserved by the CHM model, and that the energy, enstrophy and zonostrophy cascade as prescribed by the Fj{\o}rtoft argument if the nonlinearity is sufficiently weak. Moreover, numerically we observe that zonostrophy is conserved surprisingly well at late times and the triple-cascade picture is rather accurate even if the initial nonlinearity is strong.