Enstrophy non-conservation and the forward cascade of energy in two-dimensional electrostatic magnetized plasma turbulence

TL;DR

This paper introduces a fluid model for electrostatic magnetized plasma turbulence that does not conserve enstrophy, leading to a forward energy cascade and a shallower energy spectrum, supported by numerical simulations.

Contribution

It derives a new fluid system related to the Hasegawa-Mima equation that exhibits non-conservation of enstrophy and a forward energy cascade, explaining observed turbulence spectra.

Findings

The energy spectrum is shallower than -11/3 power law.

Numerical simulations confirm the forward cascade of energy.

The model explains fluctuation spectra in plasma turbulence observations.

Abstract

A fluid system is derived to describe electrostatic magnetized plasma turbulence at scales somewhat larger than the Larmor radius of a given species. It is related to the Hasegawa- Mima equation, but does not conserve enstrophy, and, as a result, exhibits a forward cascade of energy, to small scales. The inertial-range energy spectrum is argued to be shallower than a -11/3 power law, as compared to the -5 law of the Hasegawa-Mima enstrophy cascade. This property, confirmed here by direct numerical simulations of the fluid system, may help explain the fluctuation spectrum observed in gyrokinetic simulations of streamer-dominated electron-temperature-gradient driven turbulence [Plunk et al., 2019], and also possibly some cases of ion-temperature-gradient driven turbulence where zonal flows are suppressed [Plunk et al., 2017].