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

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].