Influence of flow topology on Lagrangian statistics in two-dimensional turbulence

Abstract

The influence of flow topology on Lagrangian statistics in fluid turbulence is investigated. The Weiss criterion provides a tool to split the flow into topologically different regions: elliptic (vortex dominated), hyperbolic (deformation dominated), and intermediate (turbulent background) regions. The flow corresponds to forced two-dimensional Navier-Stokes turbulence in a double periodic or a circular domain, the latter with no-slip boundary conditions. A Lagrangian approach is adopted by tracking large ensembles of passively advected tracers. The pdfs (probability density functions) of the residence time in the topologically different regions are computed introducing the Lagrangian Weiss field, i.e., the Weiss field computed along the particles' trajectories. In elliptic and hyperbolic regions, the pdfs of the residence time have self-similar algebraic decaying tails. In contrast, in the intermediate regions the pdf shows exponentially decaying tails. Furthermore, the conditional pdfs of the Lagrangian acceleration with respect to the flow topology confirm that both strong elliptic and hyperbolic regions contribute to the large values of Lagrangian acceleration.