Condensation in Quasi-Geostrophic and Drift Wave Turbulence

Jonathan Skipp

A landmark result in the theory of turbulence is Kraichnan’s 1967 prediction that for 2D inviscid flows, statistical equilibrium is reached when the largest scales of the system contain most of the energy and the smallest scales contain most of the enstrophy. Kraichnan termed the limit of this equilibrium state ‘condensation’. Here we carry out an analogous investigation of quasi-geostrophic and drift wave turbulence within the Charney-Hasegawa-Mima (CHM) model, in the weakly nonlinear limit. As well as energy and enstrophy, a third adiabatic invariant of this equation, zonostrophy, is known to exist. The presence of zonostrophy allows for a richer variation of equilibrium states, including the isotropic condensates observed in 2D flows, but also those in which the spectrum of waves condenses at zonal scales. The latter are important in the formation of atmospheric blocking in geophysical flows, and barriers to the transport of heat and particles in fusion plasmas.