Kinematic simulation of multi point turbulent dispersion
As three particles are advected by a turbulent flow, they separate from each other and develop non trivial geometries, which effectively reflect the structure of the turbulence. We investigate here the geometry, in a statistical sense, of three Lagrangian particles advected, in 2-dimensions, by Kinematic Simulation (KS). KS is a Lagrangian model of turbulent diffusion that makes no use of any delta correlation in time at any level. With this approach, situations with a very large range of inertial scales and varying persistence of spatial flow structure can be studied. We first show numerically that the model flow reproduces recent experimental results at low Reynolds numbers. The statistical properties of the shape distribution at much higher Reynolds number is then considered. Even at the highest available inertial range, of scale, corresponding to a ratio between large and small scales of $L/\eta \approx 17,000$, we find that the radius of gyration of the three points does not precisely follow Richardson's prediction. The shapes of the triangles have a high probability to be elongated. The corresponding shape distribution is not found to be perfectly self similar, even for our highest ratio of inertial scales. We also discuss how the parameters of the synthetic flow, such as the exponent of the spectrum and the effect of the sweeping affect our results. Our results suggest that a non trivial distribution of shapes will be observed at high Reynolds numbers, although it may not be exactly self similar. Special attention is given to the effects of persistence of spatial flow structure.