Pollution Transport Patterns Obtained Through Generalized Lagrangian Coherent Structures

Abstract

Identifying atmospheric transport pathways is important to understand the effects of pollutants on weather, climate, and human health. The atmospheric wind field is variable in space and time and contains complex patterns due to turbulent mixing. In such a highly unsteady flow field, it can be challenging to predict material transport over a finite-time interval. Particle trajectories are often used to study how pollutants evolve in the atmosphere. Nevertheless, individual trajectories are sensitive to their initial conditions. Lagrangian Coherent Structures (LCSs) have been shown to form the template of fluid parcel motion in a fluid flow. LCSs can be characterized by special material surfaces that organize the parcel motion into ordered patterns. These key material surfaces form the core of fluid deformation patterns, such as saddle points, tangles, filaments, barriers, and pathways. Traditionally, the study of LCSs has looked at coherent structures derived from integrating the wind velocity field. It has been assumed that particles in the atmosphere will generally evolve with the wind. Recent work has begun to look at the motion of chemical species, such as water vapor, within atmospheric flows. By calculating the flux associated with each species, a new effective flux-based velocity field can be obtained for each species. This work analyzes generalized species-weighted coherent structures associated with various chemical species to find their patterns and pathways in the atmosphere, providing a new tool and language for the assessment of pollutant transport and patterns.

Rigid Sets and Coherent Sets in Realistic Ocean Flows

“…Future works include utilizing methods that efficiently transfer the uncertainty of the flow fields to the LCS and the rigid and coherent sets (Lermusiaux and Lekien (2005); Lermusiaux et al (2006); Lermusiaux (2006); Feppon and Lermusiaux (2018b)), leading to probabilistic rigid and coherent sets. Extracting the three-dimensional in space rigid and coherent sets (Kulkarni et al (2018)) would also be useful in realistic ocean and atmospheric applications (Bettencourt et al (2012); Schmale III and Ross (2015); Nolan et al (2020)). The use of tight control on the numerical diffusion using flow map composition (Kulkarni and Lermusiaux (2019)) should also be investigated.…”

“…The terminology was born from direct observations of realistic flows and refers to the persistence of distinguished material sub-domains over time (Farazmand and Haller (2012); Haller and Beron-Vera (2012); Haller (2015); Balasuriya et al (2018); Andrade-Canto et al (2020)). Extracting LCS is expected to allow for improved Lagrangian hazard predictions; typical ocean applications include pollution tracking (Lekien et al (2005); Coulliette et al (2007); Lermusiaux et al (2019); Nolan et al (2020)), search and rescue (Serra et al (2020)), or ecosystem characterizations (Scales et al (2018); Doshi et al (2019); Paris et al (2020)). Various useful definitions of LCS have been proposed (Farazmand and Haller (2012); Froyland et al (2007); Haller (2015); Karrasch (2015); Onu et al (2014); Peacock and Haller (2013); Shadden et al (2005); Tang et al (2010); Allshouse and Thiffeault (2012)), and there are as many computational methodologies to extract them from time-dependent (non-autonomous) velocity fields v(t, x).…”

In the wind: Invasive species travel along predictable atmospheric pathways

“…To estimate the locations of LCS in a spatiotemporally varying velocity field, v ( x ,t), we calculated the ridges of the Finite‐Time Lyapunov Exponent (FTLE) field (Nolan et al, 2020), where λ max is the maximum eigenvalue of the right Cauchy‐Green deformation tensor.…”

“…To estimate the locations of LCS in a spatiotemporally varying velocity field, v(x,t), we calculated the ridges of the Finite-Time Lyapunov Exponent (FTLE) field (Nolan et al, 2020),…”

Learning and Leveraging Features in Flow-Like Environments to Improve Situational Awareness

“…Aerial vehicles are affected by coherent features during takeoff and landing [5]. Robots used for environmental monitoring may be interested in atmospheric and oceanic transport pathways that play a role in the movement of pollutants [6]. Marine vehicles can plan energy efficient trajectories in the ocean by leveraging coherent structures [7]- [9] and maintaining sensors in their desired monitoring regions [10], [11].…”