9 Statistics of Lagrangian Transport Reveals Hidden Features of Velocity Fields
293
a prime test whether it would be possible to choose specific areas for potential accidents (or to impose specific travel routes) that minimize the environmental risk.
A feasible way to tackle this issue is to rely on the analysis of a large pool of numerically simulated transport patterns for shorter time intervals of varying length. Doing
so eventually allows identifying the presence and basic features of semi-persistent
current patterns that may later be used for practical purposes.
For the search of such patterns, we develop a technique that will be used in
Chaps. 10 and 11 for approximately solving the inverse problem of current-driven
transport. The starting point is a 3D circulation model that provides surface velocity fields for a longer time interval at fixed points. These velocities reflect the
so-called Eulerian specification of the flow field for each fixed location in space as
time passes. In marine conditions one has to use fixed moorings (e.g., at offshore
structures) in order to properly measure the Eulerian velocities. As it is much easier
to model the flow in the Eulerian sense, this framework is mostly used in circulation
modelling. An average of such fields (Fig. 9.3) gives some idea about how the water
particles might move.
A large part of the complexity of the reproduction of the actual drift of water or
pollution particles, or current-driven transport, stems from its Lagrangian 6 nature.
In this specification of the motion the observer follows an individual water particle
as it moves through space and time. The Lagrangian velocity and transport can be
directly measured using drifting buoys as described in Chap. 8. This transport is
usually reconstructed by first calculating the Eulerian velocities for a certain grid
and then constructing Lagrangian trajectories (pathways) for single water particles
(Fig. 9.6). Finally, the patterns of transport are evaluated and highlighted by considering large ensembles of Lagrangian pathways of various lengths. The aim of this
analysis is the identification and visualization of several properties of surface that
cannot be extracted directly from the current fields.
The number of studies concerning Lagrangian propagation and trajectories of
various substances in the marine environment is rapidly increasing. They frequently
address natural constituents such as propagation pathways of different water masses
(Meier 2007), suspended matter (Gräwe and Wolff 2010), fish eggs and larvae (Mariani et al. 2010) or turtle hatchlings (Monzon-Argullo et al. 2010). Another major
class of studies of Lagrangian propagations relates to different adverse impacts such
as oil (Korotenko et al. 2004), microorganisms (Korajkic et al. 2009) or marine litter
(Yoon et al. 2010).
The technique of Lagrangian transport is commonly used to determine which
environment would be most seriously damaged so that it may receive priority protection (see Abascal et al. 2010 and references therein). The majority of the relevant
research efforts address the direct problem of current-induced propagation of passive tracers, with the aim to make clear where an object, particle or substance will
be transported if the initial fields of velocities, forcing and boundary conditions (or,
6 A deeper treatment of the Eulerian and Lagrangian specifications of the flow is presented in
Chap. 7. For further information we recommend classical sources such as Batchelor (1973), Lamb
(1994).
293
a prime test whether it would be possible to choose specific areas for potential accidents (or to impose specific travel routes) that minimize the environmental risk.
A feasible way to tackle this issue is to rely on the analysis of a large pool of numerically simulated transport patterns for shorter time intervals of varying length. Doing
so eventually allows identifying the presence and basic features of semi-persistent
current patterns that may later be used for practical purposes.
For the search of such patterns, we develop a technique that will be used in
Chaps. 10 and 11 for approximately solving the inverse problem of current-driven
transport. The starting point is a 3D circulation model that provides surface velocity fields for a longer time interval at fixed points. These velocities reflect the
so-called Eulerian specification of the flow field for each fixed location in space as
time passes. In marine conditions one has to use fixed moorings (e.g., at offshore
structures) in order to properly measure the Eulerian velocities. As it is much easier
to model the flow in the Eulerian sense, this framework is mostly used in circulation
modelling. An average of such fields (Fig. 9.3) gives some idea about how the water
particles might move.
A large part of the complexity of the reproduction of the actual drift of water or
pollution particles, or current-driven transport, stems from its Lagrangian 6 nature.
In this specification of the motion the observer follows an individual water particle
as it moves through space and time. The Lagrangian velocity and transport can be
directly measured using drifting buoys as described in Chap. 8. This transport is
usually reconstructed by first calculating the Eulerian velocities for a certain grid
and then constructing Lagrangian trajectories (pathways) for single water particles
(Fig. 9.6). Finally, the patterns of transport are evaluated and highlighted by considering large ensembles of Lagrangian pathways of various lengths. The aim of this
analysis is the identification and visualization of several properties of surface that
cannot be extracted directly from the current fields.
The number of studies concerning Lagrangian propagation and trajectories of
various substances in the marine environment is rapidly increasing. They frequently
address natural constituents such as propagation pathways of different water masses
(Meier 2007), suspended matter (Gräwe and Wolff 2010), fish eggs and larvae (Mariani et al. 2010) or turtle hatchlings (Monzon-Argullo et al. 2010). Another major
class of studies of Lagrangian propagations relates to different adverse impacts such
as oil (Korotenko et al. 2004), microorganisms (Korajkic et al. 2009) or marine litter
(Yoon et al. 2010).
The technique of Lagrangian transport is commonly used to determine which
environment would be most seriously damaged so that it may receive priority protection (see Abascal et al. 2010 and references therein). The majority of the relevant
research efforts address the direct problem of current-induced propagation of passive tracers, with the aim to make clear where an object, particle or substance will
be transported if the initial fields of velocities, forcing and boundary conditions (or,
6 A deeper treatment of the Eulerian and Lagrangian specifications of the flow is presented in
Chap. 7. For further information we recommend classical sources such as Batchelor (1973), Lamb
(1994).