Dispersion of finite-size particles probing inhomogeneous and anisotropic turbulence

Abstract

A series of 8 laboratory experiments was used to investigate the dynamics of a few almost neutrally-buoyant finite-size particles in the entire volume of a rectangular tank open to air and filled with water. Stirring was achieved by a cylinder executing a two-dimensional periodic Lissajoux figure. The rate and direction of stirring by the cylinder was varied. The particle motions were analysed using a tracking method developed for the experimental design. The Reynolds number associated with the large-scale stirring motion was in a turbulent range of [5,693–11,649] across all experiments. The absence of stirring in the direction of the cylinder axis, the constant interference of the cylinder with the eddies and the presence of walls and the free-surface resulted in a flow that was both inhomogeneous and anisotropic as recorded by the particle motion. Despite these unusual conditions, the single-particle dispersion across all experiments could be seen to follow a ballistic regime until about two-fifths of the particle Lagrangian velocity auto-correlation time TL. It was followed by a brief diffusive regime between TL and 2.5TL, after which the presence of the boundaries prevented further dispersion. Such evolution is consistent with classic predictions for fluid tracer dispersion in homogeneous and isotropic turbulence. Particle-pair dispersion was more complex. Both the fixed time-averaged and length-scale-dependent particle-pair dispersion rates averaged across pairs showed the ballistic dispersion regime, whereas the subsequent diffusive regime was better borne out by the length-scale-dependent particle-pair dispersion. A super-diffusive Richardson regime was not unmistakably detected. Substantial variability was however found across the different pairs of particles, which was linked to differences in the decorrelation time of the velocity difference as a result of the inhomogeneity of the turbulence. For short initial separations, some particle pairs had a better separation of the time scales delimiting the ballistic and diffusive regimes and showed hints of a brief Richardson regime.