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

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CHAPTER 1. INTRODUCTION 5 Lagrangian in concept, they provide a more natural approach to model turbulent diffusion than differential transport equations. The following report is structured as follows. The second chapter gives an overview of the numerics and physics of the General Estuarine Transport Model (GETM) and the Lagrangian transport model. In chapter three, results are presented from numerical experiments carried out under idealised conditions. Chapter four shows a realistic application of the threedimensional transport model to the Wadden Sea area in order to determine the residence time of the Langeoog inter-tidal basin. The summary and an outlook can be found in chapter five. In Appendix A, the analytical solution of the tracer trajectories for the test case described in section 2.1 is derived.
Chapter 2 Theory 2.1 The physics and numerics of GETM 2.1.1 Equations of motion The General Estuarine Transport Model (GETM) is based on the threedimensional hydrostatic equations of motions with the Boussinesq approximation and the eddy viscosity assumption (Haidvogel and Beckmann [1999]). The horizontal velocity components can be written in Cartesian coordinates as (Burchard and Bolding [2002]) � ∂u ∂(uw) ∂ + − (νt + ν) ∂t ∂z ∂z ∂ ∂z u � � � 2 ∂(u ) ∂(uv) ∂ +α + − 2A ∂x ∂y ∂x M � ∂u h ∂x − ∂ � A ∂y M � �� ζ ∂u ∂v ∂b h + − fv − y ∂x ∂x dz′ � = −g ∂ζ (2.1.1) ∂x � ∂v ∂(vw) ∂ + − (νt + ν) ∂t ∂z ∂z ∂v � ∂z � ∂(vu) +α ∂x + ∂(v2 � ) ∂ − 2A ∂y ∂y M � ∂v h ∂y − ∂ � A ∂x M � �� ζ ∂u ∂v ∂b h + + fu − ∂y ∂x ∂y dz′ � = −g ∂ζ y . z z 6 (2.1.2)
Page 1 and 2: Three-dimensional Lagrangian Tracer
Page 3 and 4: Table of Contents ii 2.4.2.1 The st
Page 5 and 6: LIST OF FIGURES 2 4.2.1 Initial hor
Page 7: Chapter 1 Introduction In this stud
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 56
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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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