We consider Lagrangian coherent structures (LCSs) as the boundaries of material subsets
whose advective evolution is metastable under weak diffusion. For their detection, we first …

This paper develops the theory and computation of Lagrangian Coherent Structures (LCS),
which are defined as ridges of Finite-Time Lyapunov Exponent (FTLE) fields. These ridges …

We develop a general theory of transport barriers for three-dimensional unsteady flows with
arbitrary time-dependence. The barriers are obtained as two-dimensional Lagrangian …

One aspect of the coexistence of regular structures and chaos in many dynamical systems is
the emergence of coherent sets: If we place a large number of passive tracers in a coherent …

We develop a mathematical theory that clarifies the relationship between observable
Lagrangian Coherent Structures (LCSs) and invariants of the Cauchy–Green strain tensor …

Mixing under laminar flow conditions is key to a wide variety of industrial fluid systems of
size extending from micrometres to metres. Profound insight into three-dimensional laminar …

The effect of spatial and temporal resolutions and random errors on identification of
Lagrangian coherent structures (LCSs) from Eulerian velocity fields is evaluated using two …

Turbulence pervades our world, from weather patterns to the air entering our lungs. This
book describes methods that reveal its structures and dynamics. Building on the existence of …

Short-term variability in material structures is often seen as significant in unsteady flows.
Such variability is of prime interest in many fields ranging from flow control to environmental …

For two-dimensional velocity fields defined on finite time intervals, we derive an analytic
condition that can be used to determine numerically the location of uniformly hyperbolic …