Tracking pollutants using Lagrangian Coherent Structures.
Date
2018-06
Authors
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Journal ISSN
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Publisher
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.
Description
MPhil.
Keywords
Pollutants, Lagrangian Coherent Structures