Equilibria and condensates in Rossby and drift wave turbulence

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 (e.g. temperature).

Soliton generation and drift wave turbulence spreading via geodesic acoustic mode excitation

The two-field equations governing fully nonlinear dynamics of the drift wave (DW) and geodesic acoustic mode (GAM) interaction in toroidal geometry are derived in the nonlinear gyrokinetic framework. Two stages with distinctive features are identified and analyzed by both analytical and numerical approaches. In the linear growth stage, the derived set of nonlinear equations can be reduced to the intensively studied parametric decay instability (PDI), accounting for the spontaneous resonant excitation of GAM by DW. The main results of previous works on spontaneous GAM excitation, e.g., the much enhanced GAM group velocity and the nonlinear growth rate of GAM, are reproduced from the numerical solution of the two-field equations. In the fully nonlinear stage, soliton structures are observed to form due to the balancing of the self-trapping effect by the spontaneously excited GAM and kinetic dispersiveness of DW. The soliton structures enhance turbulence spreading from DW linearly unstable to stable region, exhibiting convective propagation instead of typical linear dispersive process, and is thus, expected to induce core-edge interaction and nonlocal transport.

Investigation of tokamak turbulent avalanches using wave-kinetic formulation in toroidal geometry

The interplay between toroidal drift-wave turbulence and tokamak profiles is investigated using a wave-kinetic description. The coupled system is used to investigate the interplay between marginally stable toroidal drift-wave turbulence and geodesic acoustic modes (GAMs). The coupled system is found to be unstable. Notably, the most unstable mode corresponds to the resonance between the turbulent wave radial group velocity and the GAM phase velocity. For a low-field-side ballooned drift-wave growth, a background flow shear breaks the symmetry between inwards- and outwards-travelling instabilities. Although this turbulence–GAM coupling may not be the primary driver for avalanches in standard core ion temperature gradient simulations, this mechanism is generic and displays many of the expected features, and should be of interest in several other regimes, which include towards the edge or in the presence of energetic particles.