Coherent vortices

The decay of two-dimensional turbulence has the fascinating property of organizing into coherent structures from a disordered background. This feature has been observed in laboratory experiments [22] as well as in numerical simulations [23,24]. In a first stage the system self-organizes into a set of coherent vortices containing most of the flow vorticity, surrounded by an incoherent sea of small scale vorticity. The vortices mutually advect each other and their dynamics is well represented by the Hamiltonian point-vortex model. When two vortices of the same sign come close to each other they can merge in a bigger one, and the total number of vortices decay algebraically [25,26] as $n(t) \sim t^{-\xi}$. In the final state remains only a survivor dipole, which decay diffusively.

Figure 1.6: The formation of coherent structures in decaying two-dimensional turbulence.

The interest for this process is clearly motivated by its relation with the formation of large vortices in atmosphere, which play a fundamental role in our weather and our climate. As I will show, the presence of friction or polymers strongly modifies the classical picture of decaying turbulence, and may completely suppress the self-organization into large scale vortices.