Tracking pollutants using Lagrangian Coherent Structures.

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2018-06

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University of Ghana

Abstract

In steady flows, the notion of boundaries separating dynamically distinct regions is not ambiguous. This is because the invariant manifolds of time-independent flows and the critical points of time-periodic flows provide adequate information to determine the behaviour of the solutions of these systems. However, for time dependent systems, it is strenuous to determine the nature of their solutions due to their dependence on time. Nevertheless, it was observed that just like steady flows, most time-dependent systems have boundaries that prevent cross-mixing of dynamically distinct regions. They are known as Lagrangian Coherent Structures(LCSs) and they are embedded in time-dependent flows as robust structures that determine the flow pattern of fluid particles. This project investigates LCSs and also employs a numerical method to compute the Finite Time Lyapunov Exponent to detect these structures. Initially, the coherent structures are defined as hyperbolic material lines that separate dynamically distinct regions in an unsteady flow. Then, the LCSs are classified into attracting and repelling structures based on their in_uence on the time-dependent flow. Subsequently, the LCSs are also defined as a second derivative ridges of the FTLE fields. This defi- nition is perceptible from the numerical computations of the double-gyre model where the coherent structures are extracted as ridges of the computed FTLE fields. Furthermore, we employ the Finite time Lyapunov Exponent model to carry out numerical simulations on satellite observed surface velocities along the coast of Ghana. The aim of this realistic application is to determine the Lagrangian Coherent Structures that are formed in geophysical flows. Finally, based on these results, we hypothesize the implications of a crude oil spill along the coast of Ghana. It was realized that in the event of a spill, the oil is likely to be confined to the coast temporarily due to the concentration of repelling LCSs. Also, for a longer time interval the oil spill is likely to be advected from the coastline.

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MPhil.

Keywords

Pollutants, Lagrangian Coherent Structures

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