Large-scale drift and Rossby wave turbulence

Abstract

We study drift/Rossby wave turbulence described by the large-scale limit of the Charney-Hasegawa-Mima equation. We define the zonal and meridional regions as and respectively, where is in a plane perpendicular to the magnetic field such that k x is along the isopycnals and k y is along the plasma density gradient. We prove that the only types of resonant triads allowed are and . Therefore, if the spectrum of weak large-scale drift/Rossby turbulence is initially in Z it will remain in Z indefinitely. We present a generalised FjØrtoft's argument to find transfer directions for the quadratic invariants in the two-dimensional -space. Using direct numerical simulations, we test and confirm our theoretical predictions for weak large-scale drift/Rossby turbulence, and establish qualitative differences with cases when turbulence is strong. We demonstrate that the qualitative features of the large-scale limit survive when the typical turbulent scale is only moderately greater than the Larmor/Rossby radius.