Two-dimensional turbulent flows on a bounded domain

Large-scale flows in the oceans and the atmosphere reveal strong similarities with purely two-dimensional flows. One of the most typical features is the cascade of energy from smaller flow scales towards larger scales. This is opposed to three-dimensional turbulence where larger flow structures collapse into smaller structures. The inverse energy cascade in two-dimensional turbulence leads to a self-organization of the flow in large scale vortices. For instance in the Adriatic Sea an array of large-size circulations cells can be observed. We have investigated the influence of no-slip walls on two-dimensional turbulent flows by performing direct numerical simulations for a periodic channel domain. The collision of a dipolar vortex with a no-slip wall is used as a model to investigate the interaction between the no-slip wall and a vortex structure. In another type of simulations energy is injected by a forcing mechanism which leads to the development of a turbulent flow. Results are compared with theoretical predictions for infinite domains to reveal the different flow dynamics for bounded domains.