Wave induced barrier transparency and melting of quasi-crystalline structures in two dimensional plasma turbulence

Abstract

The conservation of energy and enstrophy in two dimensional inviscid hydrodynamics leads to dual cascade behavior. The energy cascades towards long scales and the enstrophy is transferred to shorter scales. The interplay of these dynamical processes leads to self organization and formation of coherent patterns in the two dimensional hydrodynamic turbulence. It was shown by Kukharkin et al. [Phys. Rev. Lett. 25, 2486 (1995)] that this process of self organization occurs in an even more interesting fashion in the Hasegawa Mima (HM) equation [Phys. Fluids 21, 21 (1978)] This equation is a generalization of the two dimensional Navier Stokes hydrodynamics model in which there is a characteristic natural scale in the system (e.g., Larmor radius in the drift wave context). Kukharkin et al. observed that this scale acts as a barrier in the energy cascade, such that the cascade rate at the longer wavelength side of the barrier is smaller. This work has also shown that the accumulation of energy around the intrinsic scale leads to the formation of quasi-crystalline patterns. In the present paper it has been demonstrated that the presence of wave excitations leads to an increased cascade towards longer scales past the natural length scale barrier. It has also been demonstrated that wave excitations lead to the melting of quasi-crystalline structures. Another intriguing but interesting observation is that even though the faster cascade is induced by waves arising through an anisotropic inhomogeneity in one of the plasma parameters, the spectrum of the fluctuations continues to remain predominantly isotropic. A physical understanding of the observations is provided by illustrating a close connection between the Kelvin–Helmholtz destabilization of shear flows and the phenomenon of inverse cascade in 2D fluid flows.