Sensitivity of the Mediterranean circulation to horizontal space-time–dependent tracer diffusivity field in a OGCM

The sensitivity of the Mediterranean circulation to the variability of the horizontal mixing is investigated using a Bryan-Cox–type general circulation model (OGCM). Attention is focused on a parameterisation of mixing previously developed in the context of two-dimensional turbulence, that is for the first time implemented in a OGCM. This parameterisation is suitable for velocity fields characterised by the presence of geostrophic coherent structures, and it is a direct application of the well-known Taylor’s dispersion relation. Theoretical and experimental justifications of the parameterisation are discussed and results from four numerical experiments, with different tracer mixing schemes, are presented. In particular, it is shown that the proposed diffusivity parameterisation improves the tracers transport due to large eddy dynamics and, ensuring a more correct salt budget in the North western part of the basin, contributes to maintain a realistic vertical stratification and winter deep convection in long climatic integrations

Can aerosols be trapped in open flows?

The fate of aerosols in open flows is relevant in a variety of physical contexts. Previous results are consistent with the assumption that such finite-size particles always escape in open chaotic advection. Here we show that a different behavior is possible. We analyze the dynamics of aerosols both in the absence and presence of gravitational effects, and both when the dynamics of the fluid particles is hyperbolic and nonhyperbolic. Permanent trapping of aerosols much heavier than the advecting fluid is shown to occur in all these cases. This phenomenon is determined by the occurrence of multiple vortices in the flow and is predicted to happen for realistic particle-fluid density ratios.Comment: Animation available at http://www.pks.mpg.de/~rdvilela/leapfrogging.htm

Particle dispersion processes in two-dimensional turbulence: a comparison with 2-D kinematic simulation.

International audienceWe study numerically the comparison between Lagrangian experiments on turbulent particle dispersion in 2-D turbulent flows performed, on the one hand, on the basis of direct numerical simulations (DNS) and, on the other hand, using kinematic simulations (KS). Eulerian space-time structure of both DNS and KS dynamics are not comparable, mostly due to the absence of strong coherent vortices and advection processes in the KS fields. The comparison allows to refine past studies about the contribution of non-homogeneous space-time 2-D Eulerian structure on the turbulent absolute and relative particle dispersion processes. We particularly focus our discussion on the Richardson's regime for relative dispersion

A systematic correlation between two-dimensional flow topology and the abstract statistics of turbulence

Velocity differences in the direct enstrophy cascade of two-dimensional turbulence are correlated with the underlying flow topology. The statistics of the transverse and longitudinal velocity differences are found to be governed by different structures. The wings of the transverse distribution are dominated by strong vortex centers, whereas, the tails of the longitudinal differences are dominated by saddles. Viewed in the framework of earlier theoretical work this result suggests that the transfer of enstrophy to smaller scales is accomplished in regions of the flow dominated by saddles.Comment: 4 pages, 4 figure

Phase separation in a chaotic flow

The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the presence -or absence- of Lagrangian chaos. A fully chaotic flow, in particular, limits the growth of domains and for unequal volume fractions of the liquids, a characteristic exponential distribution of droplet sizes is obtained. The limiting domain size results from a balance between chaotic mixing and spinodal decomposition, measured in terms of Lyapunov exponent and diffusivity constant, respectively.Comment: Minor changes - Version accepted for publication - Physical Review Letter

Bailout Embeddings, Targeting of KAM Orbits, and the Control of Hamiltonian Chaos

We present a novel technique, which we term bailout embedding, that can be used to target orbits having particular properties out of all orbits in a flow or map. We explicitly construct a bailout embedding for Hamiltonian systems so as to target KAM orbits. We show how the bailout dynamics is able to lock onto extremely small KAM islands in an ergodic sea.Comment: 3 figures, 9 subpanel

Sand stirred by chaotic advection

We study the spatial structure of a granular material, N particles subject to inelastic mutual collisions, when it is stirred by a bidimensional smooth chaotic flow. A simple dynamical model is introduced where four different time scales are explicitly considered: i) the Stokes time, accounting for the inertia of the particles, ii) the mean collision time among the grains, iii) the typical time scale of the flow, and iv) the inverse of the Lyapunov exponent of the chaotic flow, which gives a typical time for the separation of two initially close parcels of fluid. Depending on the relative values of these different times a complex scenario appears for the long-time steady spatial distribution of particles, where clusters of particles may or not appear.Comment: 4 pages, 3 figure

Dynamics of a small neutrally buoyant sphere in a fluid and targeting in Hamiltonian systems

We show that, even in the most favorable case, the motion of a small spherical tracer suspended in a fluid of the same density may differ from the corresponding motion of an ideal passive particle. We demonstrate furthermore how its dynamics may be applied to target trajectories in Hamiltonian systems.Comment: See home page http://lec.ugr.es/~julya

Reactive dynamics of inertial particles in nonhyperbolic chaotic flows

Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular enhancement of the production caused by the universal, underlying fractal patterns. The key dynamical invariant quantities are the effective fractal dimension and effective escape rate, which are primarily determined by the hyperbolic components of the underlying dynamical invariant sets. The theory is general as it includes all previously studied hyperbolic reactive dynamics as a special case. We introduce a class of dissipative embedding maps for numerical verification.Comment: Revtex, 5 pages, 2 gif figure