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 $Z:= \{{\bf{k}}\,:| {k}_{y}| \gt \sqrt{3}{k}_{x}\}$ and $M:= \{{\bf{k}}\,:| {k}_{y}| \lt \sqrt{3}{k}_{x}\}$ respectively, where ${\bf{k}}=({k}_{x},{k}_{y})$ 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 $M\leftrightarrow M+Z$ and $Z\leftrightarrow Z+Z$ . 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 ${\bf{k}}$ -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.

Keywords

• Rossby waves
• drift waves
• turbulence
• energy cascade
• zonal jets
• 47.27.E