Equilibria and condensates in Rossby and drift wave turbulence

TL;DR

This paper analyzes the equilibrium spectra of the Charney-Hasegawa-Mima equation, revealing how a third invariant leads to diverse condensate formations that explain observed large-scale structures in geophysical and plasma turbulence.

Contribution

It characterizes the equilibrium spectra and condensates of the CHM system, highlighting the role of the third invariant in enriching the turbulence dynamics.

Findings

Identification of equilibrium spectra with condensates in the CHM system

Explanation of large-scale structures as condensates of invariants

Role of negative thermodynamic potentials in condensate formation

Abstract

We study the thermodynamic equilibrium spectra of the Charney- Hasegawa-Mima (CHM) equation in its weakly nonlinear limit. In this limit, the equation has three adiabatic invariants, in contrast to the two invariants of the 2D Euler or Gross-Pitaevskii equations, which are examples for comparison. We explore how the third invariant considerably enriches the variety of equilibrium spectra that the CHM system can access. In particular we characterise the singular limits of these spectra in which condensates occur, i.e. a single Fourier mode (or pair of modes) accumulate(s) a macroscopic fraction of the total invariants. We show that these equilibrium condensates provide a simple explanation for the characteristic structures observed in CHM systems of finite size: highly anisotropic zonal flows, large-scale isotropic vortices, and vortices at small scale. We show how these condensates are associated with combinations of negative thermodynamic potentials (viz. temperature).