In the absence of large-scale dissipation, forced two-dimensional turbulence in a square box leads to the accumulation of energy in the largest available scale: after some transient, a global circulation fills the entire box. I will present numerical simulations of this phenomenon, before introducing a quasilinear approximation that gives an analytic prediction of the amplitude of the large-scale flow at high Reynolds number. Somewhat surprisingly, this amplitude depends sensitively on the form of the dissipation, even in the undamped limit.
In the second part of the seminar I will present some experimental results on forced rotating turbulence. Rotation tends to two-dimensionalize the flow while favoring cyclonic vorticity. Combining the phenomenologies of 2D and 3D turbulence, I will explain the different scaling regimes observed in the experiment.