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A perturbation-theoretic approach to Lagrangian flow networks
Naoya Fujiwara1, Kathrin Kirchen2, Jonathan F Donges3
1Center for Spatial Information Science, The University of Tokyo, 5-1-5 Kashiwanoha, Kahshiwa-shi, Chiba 277-8568, Japan.
Chaos (Woodbury, N.Y.)
|April 3, 2017
Summary
This study models geophysical flows using Lagrangian flow networks and Markov chains. Analytical solutions predict how transport changes affect contaminant spread in oceans and atmospheres.
Area of Science:
- Geophysics
- Complex Systems Analysis
- Fluid Dynamics
Background:
- Complex network approaches are effective for studying transport in diverse systems.
- Geophysical flows like ocean currents and atmospheric winds present complex transport dynamics.
Purpose of the Study:
- To develop a generic framework for analyzing geophysical flow dynamics using Lagrangian flow networks.
- To investigate the impact of transport process modifications on particle advection and contaminant spread.
Main Methods:
- Transforming passive particle advection into a Markov chain based on transition probabilities.
- Utilizing perturbation-theoretic methods to analyze three problem classes: absorption, constant input, and steady-state shifts.
- Expressing changes in the steady-state solution analytically using the flow's eigensystem and perturbations.
Main Results:
- Demonstrated analytical expressions for steady-state changes under various transport modifications.
- Validated the framework's applicability to efficient absorption, particle input, and background flow perturbations.
- Showcased the link between flow perturbations and contaminant distribution shifts.
Conclusions:
- The Lagrangian flow network approach provides analytical insights into geophysical transport dynamics.
- Results offer a basis for developing improved strategies to manage environmental contamination in fluid and gaseous media.
- The findings are relevant for mitigating impacts of oil spills, radioactive substances, and volcanic aerosols.