Lagrangian statistics of two–dimensional turbulence in a square container

Abstract

Two-dimensional decaying turbulence is studied in a square domain to investigate the influence of solid boundaries on the Lagrangian dynamics. It was shown in [1] for a circular geometry, that the vorticity generation at the walls and subsequent detachment strongly influence the velocity increment and acceleration statistics. In the present work we assess the influence of the geometry by considering a square domain. The recirculation zones in the corners and the generation of a large-scale swirling flow [2, 3] could influence the statistics. Therefore we compare the Lagrangian statistics of decaying flows in a square and in a circular domain. The numerical set-up is described in [1, 4] and the Lagrangian statistics are averaged over 104 trajectories. The numerical resolution is N = 1024². The initial eddy turn over time is $T_{e} = 1/\sqrt{2Z} = 0.12$ and the initial Reynolds number is $Re = L\sqrt{E}/v = 3 \cdot 10^{4}$, where E is the initial kinetic energy and $L = 2\pi \ast 10/11$ is the size of the square.