A Particle tracking schemes
been investigated. All of the three idealised test cases were performed with different numerical schemes: EULER, MILSTEIN and HEUN. Even though the MILSTEIN scheme only requires a minor additional effort compared with the EULER scheme, the changes in terms of higher accuracy and faster convergence are rewarding. A two-step scheme like the HEUN scheme leads to a further improvement of the results. The set of experiments that was carried out indicates that any improvement over the EULER scheme is welcome. Even though this is not trivial, and some care needs to be taken in the choice and application of the scheme, such a scheme does not necessarily need to be complicated or expensive. As advanced as higher order Lagrangian particle transport models for dispersion in turbulent flow sometimes are, it is surprising to see how many of these models still use the EULER scheme, while minor adaptations may greatly improve the accuracy of the model. The analysis also showed, that especially the term ∇ ·K in Equation (A.3) needs special care. The effort, to improve the estimates of the gradient, results in performance gains. Further the validation of the three tracking schemes revealed that although they have by definition the same order of convergence, differences showed up.
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Acknowledgements
At the end of this 3-year journey, leading to these final pages of my thesis, it is time to take a bow and to acknowledge all the helpful people who pampered me with their kind support along the way.
First, I am indebted to my supervisor J¨org-Olaf Wolff who invited me to work with him.
He was also ensuring fair funding for the years of my study. Further, I would also like to express my gratitude for his friendly and permanent advice, guidance, the comfy working en-vironment, the possibility to travel to Australia, to take part in summer schools and finally to offer me the chance to discover parts of the ocean.
I would like to thank Joachim Ribbe for his help and to offer me the possibility to stay in Oz.
I am grateful to Emil Stanev for his kind support and to be finally my second supervisor.
I would also like to acknowledge the Wolfgang Schulenberg-Programm, the Universit¨ ats-Gesellschaft Oldenburg (UGO), the Deutsche Forschungs ats-Gesellschaft (DFG) and the Burnett Mary Regional Group, Australia, for travel grants and financial support.
I really have to express my admiration and gratitude to the developers of COHERENSand GETMfor making their code available to the scientific community. I would also like to thank the Mathworks Company for their excellent product MATLAB, the Linux community for their fine OS and Intel for their breathtaking fast compilers.
A warm “thank you” goes to all my colleagues at the ICBM especially those mates (sorry, there is no female version for mate) being members of the Theoretical Physics/Complex Systems and Theoretical Physical Oceanography working group, the numerous coffee breaks, jokes and laughing, discussions, cakes, music and motivation.
I would like to acknowledge Klemens for his selflessly care for the IT environment.
I further would like to thank Laird, Dave, Wes, Luc, and Spongebob for reminding me, that the ocean is more than a discrete grid and that a wave is much more than a bump of water.
Further, I want to thank Oliver, who showed me how to shape a surfboard, ride a wave and thus initiated an endless (summer) love story.
Special thanks goes to Pebbi and Carsten for offering me a second home in Oldenburg, Helmut for being the most astonishing landlord I ever meet, Bastian and Antje for coffee, cake and support and finally, Jens for help and motivation.
A special thanks goes to Maike, for the past, the present and the future.
Ultimately, I would like to mention my parents, but they know what I owing them.
CV
Ulf Gr¨awe
born in Stralsund, July 12, 1974 Professional life
2005-2006 Researcher at ForWind - Wind Energy Research Insti-tute/Oldenburg; modelling of the lower atmospheric boundary layer and improvement of wind power predictions
1998-2002 4 years of travelling than a rolling Carpenter/Journeyman; work-ing stays in Tunisia, Israel, Italy, Hungary, Switzerland, Austria, France, Ireland, Germany, Estonia, Netherlands
Professional training
since October 2006 PhD student at the University of Oldenburg/ICBM - physical oceanography (theory)
10/2005-08/2006 Student at the University of Oldenburg - Master of Science En-gineering Physics (Thesis “Uncertainty estimation in wind power predictions”), specialisation in turbulence, dynamical systems and oceanography
10/2002-08/2005 Student at the University of Oldenburg - Bachelor of Engineering Physics
1996-1998 Apprenticeship as carpenter, Carpentry Vifan GmbH Buschen-hagen
Schooling
1981-1991 Herder-Realschule Stralsund 1991-1994 Technical Gymnasium Stralsund
Publikationsliste
Teile der vorliegenden Arbeit wurden bereits ver¨offentlicht oder eingereicht.
Gr¨awe U, Wolff JO, Ribbe J (2009) Mixing, Hypersalinity and Gradients in Hervey Bay, Australia. Ocean Dynamics DOI: 10.1007/s10236-009-0195-4
Gr¨awe U, Wolff JO (2009) Suspended particulate matter dynamics in a particle frame-work. Environmental Fluid Mechanics DOI: 10.1007/s10652-009-9141-8
Gr¨awe U, Wolff JO, Ribbe J (2009) Impact of climate variability on an east Australian bay. Estuarine, Coastal and Shelf Science eingereicht bei: Estuarine, Coastal and Shelf Science