Clustering of Floating Tracer in the Random Velocity Field Modulated by an Ellipsoidal Vortex Flow

Abstract

The influence of a background vortex flow on clustering of floating tracer is addressed. The vortex flow considered is induced by an ellipsoidal vortex evolving in a deformation. The system exhibits various vortex motion regimes: (i) steady state, (ii) oscillation and (iii) rotation of the ellipsoidal vortex core. The latter two induce unsteady velocity field for the tracer thus leading to irregular (chaotic) tracer motion. Superimposing a stochastic divergent velocity field onto the deterministic vortex flow allows us to observe significantly different tracer evolution. We use the method of characteristics to integrate the floating tracer density evolution equation and the Euler-Ito scheme for obtaining the floating tracer trajectories with the random velocity field. The cluster area and cluster mass from the statistical topography were used as the quantitative diagnostics of floating-tracer’s clustering. For the case of the steady ellipsoidal vortex embedded into the deformation flow with a random velocity field component we found that clustering characteristics are weakened by the steady vortex. For the cases of an unsteady ellipsoidal vortex, we observed clustering in the floating-tracer density field if the contribution of the divergent component is higher or equal to that of the rotational (nondivergent) component. Even when the initial floating tracer patch was set on the boundary of oscillating ellipsoidal vortex, we observed formation of clusters. In the case of a rotating ellipsoidal vortex, we also observed pronounced clustering. Thus, we argue that unsteady ellipsoidal vortex regimes (oscillation and rotation), which induce chaotic motion of the nearby passive tracer’s trajectories, are still conducive to clustering of floating tracer observed in the density field despite the intense deformation introduced by strain and shear.