Dispersion of tracer particles in a compressible flow

Abstract

The turbulent diffusion of Lagrangian tracer particles has been studied in a flow on the surface of a large tank of water and in computer simulations. The effect of flow compressibility is captured in images of particle fields. The velocity field of floating particles has a divergence, whose probability density function shows exponential tails. Also studied is the motion of pairs and triplets of particles. The mean square separation ∆(t) 2 is fitted to the scaling form ∆(t) 2 ∝ t α , and in contrast with the Richardson-Kolmogorov prediction, an extended range with a reduced scaling exponent of α = 1.65 ± 0.1 is found. Clustering is also manifest in strongly deformed triangles spanned within triplets of tracers.

Three-dimensional structures in a shallow flow

“…Since the vertical velocities are zero at the free surface these particles cannot escape and aggregate in the regions around sinks thus depopulating the vorticity dominated regions of the surface flow. Similar unequal distributions of passive floaters at the free surface of a deep fluid layer were already demonstrated by Cressman et al (2004).…”

Submesoscale evolution of surface drifter triads in the Gulf of Mexico

“…In both S 1 and S 2, however, there is no tendency for Λ( t ) to relax back toward higher values consistent with Gaussian statistics. In this sense, the behavior of Λ( t ) in both S 1 and S 2 is more consistent with compressible surface turbulence results [e.g., Cressman et al , ], where surface convergence zones act to maintain elongation in the presence of fluctuations.…”

“…The second metric is based on the fact that self-similar triangle shape, independent of size and orientation, can be uniquely defined by two quantities. Several shape metrics have been proposed in the literature [e.g., Pumir et al, 2000;Cressman et al, 2004a]. Here following Merrifield et al [2010] and de Chaumont Quitry et al [2011], we use a two-parameter metric that has an intuitive interpretation for the case of triangles.…”

“…In 2-D divergent flows, such as those advecting buoyant tracers at the ocean's surface (e.g., oil and drifters), the picture is modified due to the clustering and trapping of particles in convergence zones [Falkovich et al, 2001;Cressman et al, 2004a]. Clustering acts to reduce dispersion and increase the tendency of triangles to remain elongated for long times, delaying and possibly inhibiting transition toward the diffusive limit [Boffetta et al, 2004;Cressman et al, 2004aCressman et al, , 2004b].…”

Anisotropy and Inhomogeneity in Drifter Dispersion

“…Thus, shape deformation can be used as an isotropy metric. A variety of different metrics have been suggested in the literature (Cressman et al, 2004;Merrifield et al, 2010;Pumir et al, 2000). Here we consider two.…”