Related papers: Finite-time Lyapunov exponents in the instantaneou…
The identification and visualization of Lagrangian structures in flows plays a crucial role in the study of dynamic systems and fluid dynamics. The Finite Time Lyapunov Exponent (FTLE) has been widely used for this purpose; however, it only…
We propose a new Eulerian numerical approach for constructing the forward flow maps in continuous dynamical systems. The new algorithm improves the original formulation developed in [23, 24] so that the associated partial differential…
This paper compares the advantages, limitations, and computational considerations of using Finite-Time Lyapunov Exponents (FTLEs) and Lagrangian Descriptors (LDs) as tools for identifying barriers and mechanisms of fluid transport in…
Finite-time Lyapunov exponents (FTLEs) provide a powerful approach to compute time-varying analogs of invariant manifolds in unsteady fluid flow fields. These manifolds are useful to visualize the transport mechanisms of passive tracers…
We review and discuss some different techniques for describing local dispersion properties in fluids. A recent Lagrangian diagnostics, based on the Finite Scale Lyapunov Exponent (FSLE), is presented and compared to the Finite Time Lyapunov…
Objective Eulerian Coherent Structures (OECSs) and instantaneous Lyapunov exponents (iLEs) govern short-term material transport in fluid flows as Lagrangian Coherent Structures and the Finite-Time Lyapunov Exponent do over longer times.…
FTLE (Finite Time Lyapunov Exponent) computation is one of the standard approaches to Lagrangian flow analysis. The main features of interest in FTLE fields are ridges that represent hyperbolic Lagrangian Coherent Structures. FTLE ridges…
We consider issues associated with the Lagrangian characterisation of flow structures arising in aperiodically time-dependent vector fields that are only known on a finite time interval. A major motivation for the consideration of this…
To facilitate the understanding and to quantitatively assess the material transport in fluids, a modern characterisation method has emerged in fluid dynamics in the last decades footed in dynamical systems theory. It allows to examine the…
While more rigorous and sophisticated methods for identifying Lagrangian based coherent structures exist, the finite-time Lyapunov exponent (FTLE) field remains a straightforward and popular method for gaining some insight into transport by…
This work provides an experimental method for simultaneously measuring finite time Lyapunov exponent fields for multiple particle groups, including non-flow tracers, in three-dimensional multiphase flows. From sequences of particle images,…
In this paper we use the finite size Lyapunov Exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3d) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are…
It is a wide-spread convention to identify repelling Lagrangian Coherent Structures (LCSs) with ridges of the forward finite-time Lyapunov exponent (FTLE) field, and attracting LCSs with ridges of the backward FTLE. We show that in…
The dynamics of inertial particles in fluid flows have been the focus of extensive research due to their relevance in a wide range of industrial and environmental processes. Earlier studies have examined the dynamics of aerosols and bubbles…
In the context of the analysis of the chaotic properties of homogeneous and isotropic turbulence, direct numerical simulations are used to study the fluctuations of the finite time Lyapunov exponent (FTLE) and its relation to Reynolds…
We investigate finite-time Lyapunov exponents (FTLEs), a measure for exponential separation of input perturbations, of deep neural networks within the framework of continuous-depth neural ODEs. We demonstrate that FTLEs are powerful…
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their…
Ridges of the Finite-Size Lyapunov Exponent (FSLE) field have been used as indicators of hyperbolic Lagrangian Coherent Structures (LCSs). A rigorous mathematical link between the FSLE and LCSs, however, has been missing. Here we prove that…
We use finite-time Lyapunov exponent (FTLE) distributions to probe transition mechanisms in high-dimensional reservoir maps trained on low-dimensional chaotic dynamics across multiple regimes. While trained reservoirs accurately predict…
Lagrangian coherent structures (LCS) in fluid flows appear as co-dimension one ridges of the finite time Lyapunov exponent (FTLE) field. In three- dimensions this means two-dimensional ridges. A fast algorithm is presented here to locate…