The influence of walls on Lagrangian statistics in two-dimensional turbulence

Abstract

The influence of solid walls on the Lagrangian statistics of statistically stationary two-dimensional turbulence is investigated by comparing the flow in a circular wall-bounded and in an unbounded periodic domain. A Fourier pseudo-spectral method is used, which is combined in the wall bounded case with a volume penalization technique to impose no-slip conditions. A particular emphasis is put on the acceleration of fluid particles. It is investigated to what extent the impact of the boundaries influences the shape of the probability density functions of Lagrangian velocity increments. It is shown that the influence of walls is not confined to a small near-wall region but alters the statistics in the entire flow domain. This can be explained by the vorticity generation in the turbulent boundary layer which destabilizes and leads to the formation of vortices that subsequently detach and travel into the bulk flow. The enstrophy level is thus increased with respect to the one in the unbounded periodic domain.