Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction

Abstract

Abstract-This paper presents a method for filtered ridge extraction based on adaptive mesh refinement. It is applicable in situations where the underlying scalar field can be refined during ridge extraction. This requirement is met by the concept of Lagrangian coherent structures which is based on trajectories started at arbitrary sampling grids that are independent of the underlying vector field. The Lagrangian coherent structures are extracted as ridges in finite Lyapunov exponent fields computed from these grids of trajectories. The method is applied to several variants of finite Lyapunov exponents, one of which is newly introduced. High computation time due to the high number of required trajectories is a main drawback when computing Lyapunov exponents of 3-dimensional vector fields. The presented method allows a substantial speed-up by avoiding the seeding of trajectories in regions where no ridges are present or do not satisfy the prescribed filter criteria such as a minimum finite Lyapunov exponent.

Barriers in the transition to global chaos in collisionless magnetic reconnection. I. Ridges of the finite time Lyapunov exponent field

“…15 when ridges are computed using the Hessian of the scalar field, noise amplification can become an issue, especially when chaotic "velocity fields" are taken into account, as in the case of the magnetic fields we considered in this paper. A large collection of criteria addressing ridge filtering is available in technical literature.…”

“…A large collection of criteria addressing ridge filtering is available in technical literature. 15 Here, in order to remove weak features caused by noise, we have chosen a natural, easy to implement, criterion which prescribes a minimum height of the ridge s ! s min .…”

Influence of finite-time Lyapunov exponents on winter precipitation over the Iberian Peninsula

“…In order to characterize the atmospheric transport, we introduce the finite-time Lyapunov exponents (FTLE), which measure, at a given location, the maximum stretching rate of starting at r(t 0 ; t 0 , r 0 ) = r 0 and ending at r(t 0 + τ ; t 0 , r 0 ) (Shadden et al, 2005;Sadlo and Peikert, 2007). The integration time τ must be predefined and it has to be long enough to allow trajectories to explore the coherent structures present in the flow.…”

Path-integrated Lagrangian measures from the velocity gradient tensor

“…Here we compute LCS in terms of second-derivative ridges of the FTLE field σ or the Okubo-Weiss Q P , at each time t (Sadlo and Peikert, 2007). In order to filter spurious ridges or weak LCS, a minimum threshold for both fields was used.…”