Sensitivity of Lagrangian coherent structure identification to flow field resolution and random errors

Abstract

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 canonical flows: a two-dimensional vortex pair and a vortex ring formed by transient ejection of a jet from a tube. The flow field for the vortex pair case was steady and obtained analytically while the transient vortex ring flow was simulated using computational fluid dynamics. To evaluate resolution and random error effects, the flow fields were degraded by locally smoothing the flow and sampling it on a sparser grid to reduce spatial resolution, adding Gaussian distributed random noise to provide random errors, and/or subsampling the time series of vector fields to reduce the temporal resolution (the latter applying only for the vortex ring case). The degradation methods were meant to emulate distortions and errors introduced in common flow measurement methods such as digital particle image velocimetry. Comparing the LCS corresponding to the vortex boundary (separatrix) obtained from the degraded velocity fields with the true separatrix (obtained analytically for the vortex pair case or from high resolution, noise-free velocity fields for the vortex ring case) showed that noise levels as low as 5%-10% of the vortex velocity can cause the separatrix to significantly deviate from its true location in a random fashion, but the "mean" location still remained close to the true location. Temporal and spatial resolution degradations were found to primarily affect transient portions of the flow with strong spatial gradients. Significant deviations in the location of the separatrix were observed even for spatial resolutions as high as 2% of the jet diameter for the vortex ring case.

Lagrangian coherent structures in the California Current System – sensitivities and limitations

“…To this end, we first construct a synthetic model that captures the dynamics of the largest eddies in the CCS but can represent them with finer spatial and temporal resolution than the observations. In contrast to other studies (Olcay et al 2010, Poje et al 2010), we are not asking how small perturbations affect LCS location, since we know there are always errors in the observations and thus the LCS are inherently approximate, but how large the errors have to be before the overall topological structure of the system is obscured. That is, we are testing when LCS break down and how reliable they are in observational oceanography.…”

Vortex Ring Formation in the Left Ventricle of the Heart: Analysis by 4D Flow MRI and Lagrangian Coherent Structures

“…However, water tank experiments show that vortex rings consist of the inflowing volume plus a volume of surrounding fluid that is entrained during vortex formation 23 .…”

“…However, the effects of noise and low resolution have been studied in a computational model by reducing the spatial and temporal resolution in a computer-simulated vortex ring 23 . Lowered temporal and spatial resolution gave an underestimation of vortex volume between 1% and 20%.…”

Refining finite-time Lyapunov exponent ridges and the challenges of classifying them

“…2,10,25 One particular study systematically subsampled turbulent ocean models to study the impact of spatial and temporal on the FTLE calculation. 13 Another study has investigated the impact of noise and discretization on a FTLE field calculated via finite-difference on a uniform field; 21 here, we focus on the relative impacts of both on the different FTLE calculation methods. Our goal is to study the impact of varying spatial resolution and the presence of noise on the finite-difference based FTLE calculation relative to the analytically calculated values.…”