Two-dimensional turbulence dispersion in a closed domain: Influence of confinement and geometry

The spreading of passive particles immersed in a two-dimensional turbulent flow confined within a closed domain is studied analytically and numerically. The primary goal is to investigate the effect of the confinement and the geometry of the container on one and two-particle Lagrangian statistics (absolute dispersion from point sources and relative dispersion of pairs of particles, respectively). The influence of the flow confinement is analysed by performing numerical experiments with numerous particles in square boxes with different sizes. The results examine the modification of the time-dependent, dispersion curves as the particles spread out (in comparison to the turbulent regimes for unbounded flows). At long times, such curves asymptotically reach a constant value of saturation as the particles fill the container. Theoretical saturation values are calculated, and the obtained formulae are tested with the numerical results. To study the influence of the domain shape, saturation values are computed analytically for different geometries (rectangles, triangles, and ellipses). To our knowledge, the obtained expressions are new. The saturation values depend on the characteristic lengths of the domain for both regular and irregular shapes. Ranges of saturated values for the different geometries are provided. The results are compared with well-known asymptotic values for unbounded flows, thus determining the influence of the closed boundaries on particle dispersion.