Lagrangian coherent structures are distinguished surfaces of trajectories in a dynamical system that exert a major influence on nearby trajectories over a time interval of interest. The type of this i
Figure 1: An invariant manifold in the extended phase space, formed by an evolving material surface.
Figure 2a: Hyperbolic LCS (attracting in red and repelling in blue) and elliptic LCS (boundaries of green regions) in a two-dimensional turbulence simulation. (Image: Mohammad Farazmand)
Figure 3: Instantaneous streamlines and the evolution of trajectories starting from the interior of one of them in a linear solution of the Navier–Stokes equation. This dynamical system is classified as elliptic by a number of frame-dependent coherence diagnostics, such as the Okubo–Weiss criterion. (Image: Francisco Beron-Vera)
Figure 4. Attracting and repelling LCSs in the extended phase space of a two-dimensional dynamical system.
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In the mathematical field of dynamical systems, an attractor is a set of states toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get c
Lagrangian coherent structure
…to M ( t 1 ) . In classical dynamical systems theory, invariant manifolds satisfying such an attraction property over infinite times are called attractors. They are not only special, but even locally unique in the phase space: no continuous family of attractors may exist. In contrast, in dynamical systems…
Visual representation of a strange attractor. Another visualization of the same 3D attractor is this video. Code capable of rendering this is available.