Lagrangian dispersion in geophysical fluids

Lagrangian dispersion in geophysical fluids

The study of diffusion and mixing properties in geophysical fluids cannot ignore the analysis of Lagrangian trajectories. The primary reason for considering this aspect as highly relevant is related to the existence of Lagrangian chaos, which refers to the exponential separation of trajectories with arbitrarily close initial conditions. For trajectories to separate chaotically, it is not necessary for the flow regime to be turbulent; it suffices that the fluid velocity field is nonlinear and periodic in time. The non-trivial fact that Lagrangian chaos can coexist with a regular Eulerian field suggests that the transport and diffusion properties of trajectories cannot be directly inferred from the characteristics of the velocity field.

Modern techniques used to characterize Lagrangian dispersion in geophysical fluid dynamics derive from dynamical systems theory, specifically the concept of the (maximum) Lyapunov exponent, which measures the rate of growth over time of the infinitesimal error on the initial condition of a trajectory. An extension of this concept is the Finite Scale Lyapunov Exponent (FSLE), which represents the relative dispersion rate of trajectories as a function of their separation. The great advantage of this technique is that the FSLE measure is not constrained by the assumption of infinitesimal separations between trajectories, thus allowing the analysis of various dispersion regimes present across all observable scales (chaos, turbulence, diffusion...).

The project aims to study and understand the dispersion properties in geophysical fluids using numerical Lagrangian analysis techniques, observational data from satellites and in situ, and the production of experimental trajectories in the laboratory. The program is structured as follows:

• Characterization of dispersion regimes dependent on the scale of motion

• Study of local mixing properties

• Analysis of the impact of direct transport of biological, biogeochemical, and/or sedimentary tracers.

• Production of trajectories in the laboratory.

Numerical simulations of Lagrangian trajectories in the open sea generated from large-scale velocity fields, that can be used, to measure the transport and dispersion properties of ocean surface currents across a wide range of scales. The effective technique of Lagrangian sub-grid kinematic models is used to restore sub-grid unresolved motions.

Significant reference observations come from numerous data acquired from surface Lagrangian drifters released into the ocean, often complemented by satellite observations, providing a synoptic view of the tracers. Lagrangian trajectories can also be reconstructed from laboratory experiments for detailed studies of particular circulation systems (zonal currents, vortex lattices...).