Large scale spatial structures in two-dimensional turbulent flows

Abstract

The organized motion of coherent structures in two-dimensional turbulent flows is vested with a quasi-deterministic behavior. The spontaneous formation of large-scale structures could be accounted for as a manifestation of long-wave instability of the corresponding small-scale flow. For a class of such flows, dynamics of coherent structures are modeled by the Kolmogorov-Spiegel-Sivashinsky family of partial differential equations (PDE's). We present mathematical and computational investigations of the latter. We outline how locally negative viscosity mechanisms generate coherent structures with a finite, small number of degrees of freedom. Both bursting streaks and spatially localized, temporally intermittent structures are evidenced. Although an infinity of small scales a priori dissipate energy, these are slaved by a finite number of inertial modes. Only finite dimensional dynamics and chaos subsist.