Three-dimensional Lagrangian Tracer Modelling in Wadden Sea ...

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List of Tables 3.2.1 The Rouse profile: sediment concentrations computed by three different models. . . . . . . . . . . . . . . . . . . . . . 45 4.1.1 Volumes, areas, mean depths and tidal prism under spring tide conditions for the Langeoog inter-tidal basin. . . . . . . 51 4.2.1 Initial conditions for the simulations caried out to estimate the residence time of the Langeoog inter-tidal basin. . . . . 60 3
Chapter 1 Introduction In this study, a three-dimensional baroclinic turbulence model especially developed for the simulation of currents and transports in shallow water sea areas (such as the North Frisian Wadden Sea) is extended to include the advective and diffusive transport of passive Lagrangian tracers. In physical oceanography, a tracer is a substance such as a dye or a radioactive isotope that can be traced as it is transported with the mean flow field. The measurement of anthropogenic and natural tracers in the ocean provided the first estimate about the time scales of the ventilation of the deep ocean. Since the 1970s, tracer methods have made significant contributions to the understanding of the ocean circulation, internal water mass structures and time scales of the ventilation. Furthermore, numerical simulations of tracer transport are a valuable tool to estimate the dispersion of pollutants such as oil or sewage disposals in the ocean for the research of the long-term effects and the development of effective counter-active measures. Advective processes play a key role in the transport of tracer particles, therefore a particle tracking model should resolve these processes as accurate as possible. In this thesis, the analytical solution of the Lagrangian advection equation (Duwe [1988]) is used to implement a Lagrangian tracer model. In addition to advection, transport occurs due to turbulent motions in the water column. Turbulent mixing is included in the particle tracking model by means of a stochastic model. The first stochastic model to describe natural phenomena was introduced by Einstein as he studied the random motion of microscopic particles suspended in a fluid (Einstein [1905]). Since that time stochastic or random walk models of particle motions have proved to be a successful and flexible tool in the investigation of the dispersion of passive tracers in high Reynolds-number turbulence (Maier-Reimer and Sündermann [1982], Dimou and Adams [1993], Hunter et al. [1993]). Being 4
Page 1 and 2: Three-dimensional Lagrangian Tracer
Page 3 and 4: Table of Contents ii 2.4.2.1 The st
Page 5: LIST OF FIGURES 2 4.2.1 Initial hor
Page 9 and 10: Chapter 2 Theory 2.1 The physics an
Page 11 and 12: CHAPTER 2. THEORY 8 2.1.2 Boundary
Page 13 and 14: CHAPTER 2. THEORY 10 2.1.4 Transpor
Page 15 and 16: CHAPTER 2. THEORY 12 restructured i
Page 17 and 18: CHAPTER 2. THEORY 14 = ∆x n n x x
Page 19 and 20: CHAPTER 2. THEORY 16 Substituting E
Page 21 and 22: CHAPTER 2. THEORY 18 where ¯ denot
Page 23 and 24: CHAPTER 2. THEORY 20 Now, let us as
Page 25 and 26: CHAPTER 2. THEORY 22 2. In particle
Page 27 and 28: CHAPTER 2. THEORY 24 To determine t
Page 29 and 30: CHAPTER 2. THEORY 26 2.4.1.3 Interp
Page 31 and 32: CHAPTER 2. THEORY 28 can be describ
Page 33 and 34: CHAPTER 2. THEORY 30 Properties of
Page 35 and 36: CHAPTER 2. THEORY 32 where p(x, t|x
Page 37 and 38: CHAPTER 2. THEORY 34 [1997] showed
Page 39 and 40: CHAPTER 2. THEORY 36 to the discret
Page 41 and 42: CHAPTER 3. IDEALISED TESTCASES 38 A
Page 43 and 44: CHAPTER 3. IDEALISED TESTCASES 40 o
Page 45 and 46: CHAPTER 3. IDEALISED TESTCASES 42 3
Page 47 and 48: CHAPTER 3. IDEALISED TESTCASES 44 5
Page 49 and 50: CHAPTER 3. IDEALISED TESTCASES 46 z
Page 51 and 52: CHAPTER 3. IDEALISED TESTCASES 48 z
Page 53 and 54: Chapter 4 Realistic application 4.1
Page 55 and 56: CHAPTER 4. REALISTIC APPLICATION 52
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CHAPTER 4. REALISTIC APPLICATION 54
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CHAPTER 5. SUMMARY AND OUTLOOK 70 t
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APPENDIX A. APPENDIX TO SECTION 3.1
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APPENDIX A. APPENDIX TO SECTION 3.1
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APPENDIX B. APPENDIX TO SECTION 2.4
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REFERENCES 78 Dimou, K. N., and E.
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REFERENCES 80 Stanev, E., J.-O. Wol
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Three-dimensional Lagrangian Tracer Modelling in Wadden Sea ...

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