Theory Of Lagrangian Coherent Structures Research Articles

Multiple Lagrangian Jet‐Core Structures in the Malvinas Current

AbstractThe Malvinas Current (MC) in the Southwestern Atlantic is characterized as a system of multiple Lagrangian jets. This is done by applying geodesic theory of Lagrangian Coherent Structures (LCSs) on altimetry‐derived velocity. The number and spatial disposition of jet‐cores organizing the MC are found to vary in time influenced by topographic waves propagating along the current. The Lagrangian analysis reveals that permanent jet‐cores tend to approach one another upstream, yet do not merge into a single jet as the Eulerian analysis of the data suggests. Independent support for the existence of multiple jets is provided by trajectories of surface drifters from a deployment of unparalleled dimensions for the region and ocean color images. The drifters develop the characteristic boomerang‐shaped patterns into which passive tracers straddling jet‐cores deform and exhibit Lagrangian metrics that are largely consistent with those derived from altimetry data. Ocean color imagery reveals similar “chevrons” and suggest upwelling along the jets, which is consistent with a new solution of arrested topographic wave dynamics. This observation and the finding that the MC jet system is influenced by propagating waves suggests that the MC variability may have major implications in the modulation of primary productivity on synoptic timescales. Drifters flowing into the open ocean, exhibit organizing patterns that are largely shaped by mesoscale circulation and essentially differ from those observed along the MC. Evidence of this observation is provided on the basis of LCS analysis and the calculation of a quasi‐objective Lagrangian metric derived directly from drifter trajectories.

Lagrangian coherent structures and entrainment near the turbulent/non-turbulent interface of a gravity current

In this paper, we employ the theory of Lagrangian coherent structures for three-dimensional vortex eduction and investigate the effect of large-scale vortical structures on the turbulent/non-turbulent interface (TNTI) and entrainment of a gravity current. The gravity current is realized experimentally and different levels of stratification are examined. For flow measurements, we use a multivolume three-dimensional particle tracking velocimetry technique. To identify vortical Lagrangian coherent structures (VLCSs), a fully automated three-dimensional extraction algorithm for multiple flow structures based on the so-called Lagrangian-averaged vorticity deviation method is implemented. The size, the orientation and the shape of the VLCSs are analysed and the results show that these characteristics depend only weakly on the strength of the stratification. Through conditional analysis, we provide evidence that VLCSs modulate the average TNTI height, consequently affecting the entrainment process. Furthermore, VLCSs influence the local entrainment velocity and organize the flow field on both the turbulent and non-turbulent sides of the gravity current boundary.

Surface mixing and biological activity in the North-West African upwelling.

Near-shore water along the North-West African margin is one of the world's major upwelling regions. It is associated with physical structures of oceanic fronts which influence the biological productivity. The study of these coherent structures in connection with chlorophyll concentration data is of fundamental importance for understanding the spatial distributions of the plankton. In this work, we study the horizontal stirring and mixing in different upwelling areas using Lagrangian coherent structures (LCSs). These LCSs are calculated using the recent geodesic theory of LCSs. We use these LCSs to study the link between the chlorophyll fronts concentrations and surface mixing, based on 10 years of satellite data. These LCSs move with the flow as material lines, thus the horizontal mixing is calculated from the intersection of these LCSs with the finite time Lyapunov exponent maps. We compare our results with those of a recent study conducted over the same area, but based on finite size Lyapunov exponents (FSLEs), whose output is a plot of scalar distributions. We discuss the differences between FSLE and geodesic theory of LCS. The latter yields analytical solutions of LCSs, while FSLEs can only provide LCSs for sharp enough ridges of nearly constant height.

A variational theory of hyperbolic Lagrangian Coherent Structures

We develop a mathematical theory that clarifies the relationship between observable Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy–Green strain tensor field. Motivated by physical observations of trajectory patterns, we define hyperbolic LCSs as material surfaces (i.e., codimension-one invariant manifolds in the extended phase space) that extremize an appropriate finite-time normal repulsion or attraction measure over all nearby material surfaces. We also define weak LCSs (WLCSs) as stationary solutions of the above variational problem. Solving these variational problems, we obtain computable sufficient and necessary criteria for WLCSs and LCSs that link them rigorously to the Cauchy–Green strain tensor field. We also prove a condition for the robustness of an LCS under perturbations such as numerical errors or data imperfection. On several examples, we show how these results resolve earlier inconsistencies in the theory of LCS. Finally, we introduce the notion of a Constrained LCS (CLCS) that extremizes normal repulsion or attraction under constraints. This construct allows for the extraction of a unique observed LCS from linear systems, and for the identification of the most influential weak unstable manifold of an unstable node.