4 Studying the Baltic Sea Circulation with Eulerian Tracers
125
4.4.3 Hybrid Approach
In the previous two sub-sections we have discussed two applications of Eulerian
tracers for tracking oil spills, which is traditionally done with the help of Lagrangian
methods. However, a pure Lagrangian or Eulerian method is not the only choice.
Hybrid methods may sometimes have advantages. An example where Eulerian and
Lagrangian methods are combined is the oil spill model presented in Guo and Wang
(2009).
The initial oil slick was simulated with Lagrangian particles using random walk
particle tracking. When the slick thickness locally dropped below a certain threshold
the calculation continued with modelling of the slick thickness at that place with an
Eulerian-Lagrangian method on a grid.
The Eulerian-Lagrangian method combined the Eulerian and the Lagrangian approaches for the advection-diffusion equation. The equation was split into two equations, one pure advection equation and one pure diffusion equation. The advection
equation was solved with Lagrangian methods like backtracking along stream lines
and the diffusion equation with Eulerian methods. The method is known to work
well in regions that are advection dominated. In regions where the advection is not
the dominating part, like close to point sources, the method is less good. By using
a purely Lagrangian method in the initial phase and by switching to an EulerianLagrangian method when the thickness of the slick is low, the strengths of both
methods were combined.
In a similar manner, the oil that is vertically mixed within the water column
by surface waves induced turbulence, first follows with a Lagrangian method as
droplets. Those droplets that do not resurface, i.e., droplets with buoyancy which
is not dominating, are recalculated to a concentration. The evolution of the passive
tracer in time is calculated with an Eulerian-Lagrangian method.
4.5 Outlook
In this overview we introduced the Eulerian tracer approach to study the characteristics of the Baltic Sea circulation. Three examples of oil spill modelling using
Eulerian methods are presented. The method which allows the calculation of optimized fairways following (Höglund and Meier 2012) is rather idealized because the
oil dynamics is not realistically treated. However, combining the various presented
methods will result in a powerful tool which may help to prevent the pollution of
ecologically sensitive regions after accidents of oil tankers. The knowledge gained
from the idealized simulations may be used to develop more advanced management
tools taking additional processes of spreading oil slicks into account.
Acknowledgements The research presented in this study is part of the project BalticWay (The
potential of currents for environmental management of the Baltic Sea maritime industry) and has
received funding from the European Commission’s Seventh Framework Programme (FP7 2007–
2013) under Grant agreement No. 217246 made with BONUS, the joint Baltic Sea research and
development program, and from the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (Formas, Ref. No. 2008–1898).
125
4.4.3 Hybrid Approach
In the previous two sub-sections we have discussed two applications of Eulerian
tracers for tracking oil spills, which is traditionally done with the help of Lagrangian
methods. However, a pure Lagrangian or Eulerian method is not the only choice.
Hybrid methods may sometimes have advantages. An example where Eulerian and
Lagrangian methods are combined is the oil spill model presented in Guo and Wang
(2009).
The initial oil slick was simulated with Lagrangian particles using random walk
particle tracking. When the slick thickness locally dropped below a certain threshold
the calculation continued with modelling of the slick thickness at that place with an
Eulerian-Lagrangian method on a grid.
The Eulerian-Lagrangian method combined the Eulerian and the Lagrangian approaches for the advection-diffusion equation. The equation was split into two equations, one pure advection equation and one pure diffusion equation. The advection
equation was solved with Lagrangian methods like backtracking along stream lines
and the diffusion equation with Eulerian methods. The method is known to work
well in regions that are advection dominated. In regions where the advection is not
the dominating part, like close to point sources, the method is less good. By using
a purely Lagrangian method in the initial phase and by switching to an EulerianLagrangian method when the thickness of the slick is low, the strengths of both
methods were combined.
In a similar manner, the oil that is vertically mixed within the water column
by surface waves induced turbulence, first follows with a Lagrangian method as
droplets. Those droplets that do not resurface, i.e., droplets with buoyancy which
is not dominating, are recalculated to a concentration. The evolution of the passive
tracer in time is calculated with an Eulerian-Lagrangian method.
4.5 Outlook
In this overview we introduced the Eulerian tracer approach to study the characteristics of the Baltic Sea circulation. Three examples of oil spill modelling using
Eulerian methods are presented. The method which allows the calculation of optimized fairways following (Höglund and Meier 2012) is rather idealized because the
oil dynamics is not realistically treated. However, combining the various presented
methods will result in a powerful tool which may help to prevent the pollution of
ecologically sensitive regions after accidents of oil tankers. The knowledge gained
from the idealized simulations may be used to develop more advanced management
tools taking additional processes of spreading oil slicks into account.
Acknowledgements The research presented in this study is part of the project BalticWay (The
potential of currents for environmental management of the Baltic Sea maritime industry) and has
received funding from the European Commission’s Seventh Framework Programme (FP7 2007–
2013) under Grant agreement No. 217246 made with BONUS, the joint Baltic Sea research and
development program, and from the Swedish Research Council for Environment, Agricultural Sciences and Spatial Planning (Formas, Ref. No. 2008–1898).