Two-dimensional turbulence on a bounded domain : the role of angular momentum

In contrast to its counterpart in the 3D world, turbulence in 2D is characterized by an inverse energy cascade. The presence of this inverse cascade in 2D turbulence is visible in the so-called self-organization of such flows: larger vortices and structures are observed to emerge from initially random flow fields. The lecture will address the evolution of 2D turbulent flows on a finite domain with no-slip walls. The organized state consists of a large, domain-filling cell whose motion can be considered as inviscid. Results of both laboratory experiments in rotating / stratified fluids and numerical simulations, however, reveal the crucial role played by the unsteady boundary layers: the domain boundaries act as important sources of large-amplitude vorticity filaments that may influence the motion in the interior. Attention will be given to global flow quantities like the kinetic energy, the enstrophy, and the total angular momentum. In the case of forced 2D turbulence, the latter quantity may show a remarkable flip-flopping behaviour, associated with a collapse of the organized flow state followed by its re-organisation.