Coherent structure formation, phase correlations, and finite-size effects in 2D turbulence

Abstract

General conditions for the formation of long-lived coherent vortices in decaying and force-driven 2-D turbulence are investigated. It is shown by a series of numerical simulations that the emergence of closed streamlines leading to the trapped trajectories of vorticity is a necessary, but not sufficient condition for this phenomenon, so that these trapped trajectories may be considered only as “seed vortices.” Numerical experiments which demonstrate the relations between phase correlations, finite-size effects, and the formation of coherent vortices in 2-D decaying turbulence are presented. It is shown that there is a universal dimensionless time for the onset of intermittency in the flow which corresponds to the time of establishment of phase correlations. The stricter conditions for appearance of coherent vortices in forced turbulence in comparison with decaying turbulence are associated with phase mixing introduced by random forcing. The universal features of decaying turbulence are discussed in terms of phase portraits based on inviscid constants of motion and their decay rates.