Chaotic advection of fluid particles at different Reynolds numbers by two-dimensional smoothed particle hydrodynamics

We perform turbulence simulations through the smoothed particle hydrodynamics (SPH) in a two-dimensional (2D) reduced geometry. By starting from a simple Taylor-Green vortex, we vary the Reynolds number, following the transition of the flow dynamics to turbulence. The same Reynolds numbers are reproduced for random initial conditions, which show an easier triggering of turbulence. The statistical analysis of the pair-particles distance separation is performed in order to characterize such transition, revealing that, in the more viscous case, the large-scale main structures of the initial vortex survive to the cascade, as typical of low-order, chaotic systems. At high Reynolds numbers, instead, the initial structure is broken and the system experiences turbulence. In this regime, the SPH particles manifest the classical Richardson law of turbulence, with an explosive pair-particles departure. This work might be relevant for 2D applications of hydrodynamics, to understand the chaos-turbulence transitions.