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The Effects of Small Density Differences at Large Confluences

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The Effects of Small Density Differences at Large Confluences The effects of small density differences at large confluences Erik van Rooijen i The effects of small density differences at large confluences by Erik van Rooijen 15 November 2016 Graduation Committee: Prof. dr. ir. W.S.J. (Wim) Uijttewaal Delft University of Technology (chairman) Dr. ir. C.J. (Kees) Sloff Delft University of Technology, Deltares (daily supervisor) Dr. ir. E. (Erik) Mosselman Delft University of Technology, Deltares (second reviewer) Dr. Yuan, J. (Jing) National University of Singapore (supervisor) Dr. Chua, V.P. (Vivian) National University of Singapore (examiner) Dr. Ooi, S. (Seng Keat) National University of Singapore (examiner) ii Contents List of symbols ....................................................................................................................................... vii Preface .................................................................................................................................................... 1 Abstract ................................................................................................................................................... 2 1. Introduction .................................................................................................................................... 3 2. Theory and literature ...................................................................................................................... 4 2.1 Main characteristics of confluences .............................................................................................. 4 2.2 Confluences and meanders ........................................................................................................... 4 2.3 Discordant beds ............................................................................................................................. 5 2.4 Mixing & shear layer ..................................................................................................................... 5 2.5 Density differences ........................................................................................................................ 6 2.6 The two-layer model ..................................................................................................................... 8 2.7 Density differences in confluences ................................................................................................ 8 2.8 Boils ............................................................................................................................................... 9 3. Methods ........................................................................................................................................ 11 3.1 Numerical modelling ................................................................................................................... 11 3.2 Validation of the software used .................................................................................................. 11 3.3 Model runs used .......................................................................................................................... 11 3.4 Aerial photographs ..................................................................................................................... 12 3.5 The confluence of the Rio Negro and Solimões rivers ................................................................. 13 4. Results and discussion .................................................................................................................. 16 4.1 Validation of the software used .................................................................................................. 16 4.2 Effects on the large-scale flow pattern ....................................................................................... 17 4.3 Effect on the mixing layer ........................................................................................................... 28 4.4 Aerial photographs ..................................................................................................................... 31 4.5 The Rio Negro – Solimões confluence ......................................................................................... 34 5. Conclusions ................................................................................................................................... 42 6. Recommendations ........................................................................................................................ 43 7. References .................................................................................................................................... 44 A. Overview of model runs used .......................................................................................................... I A.1 Validation of software ................................................................................................................... I A.2 General schematized model .......................................................................................................... I B. Analysis of LANDSAT imagery ........................................................................................................ III C. Formula for the calculation of water density .............................................................................. VIII iii D. Boils in stratified water column ..................................................................................................... IX D.1 Introduction ................................................................................................................................. IX D.2 How to set-up the research ......................................................................................................... IX iv List of figures and tables Figure 1 Overview of the flow at a confluence, after Best [1987] .......................................................... 4 Figure 2 Plan view of stream lines at the bed for a confluence with discordant beds, after Biron et al. [1996] ...................................................................................................................................................... 5 Figure 3 Water pressures on a small partition of water with width Δx under influence of density differences and resulting pressures. A. Differing densities over the entire water column. On the right side is the low density water and on the left side the high density fluid. Water level differences are exaggerated. As a result in reality the small part at the top of the resulting pressures profile where the pressure is linearly increasing with depth will be so small it can be neglected. B. Stratified situation. C. Head of a density current. .................................................................................................. 7 Figure 4 A lock release with heavy (dark) and light (light) water. The dashed line indicates Benjamin’s [1968] potential flow solution for the shape at the fronts, joined by a horizontal line. After Shin et al. [2004]. ..................................................................................................................................................... 7 Figure 5 Overview of the used parameters in the two-layer model. ...................................................... 8 Figure 6 Hairpin vortices downstream of a dune, from Best [2005], originally from Nezu & Nakagawa ................................................................................................................................................................ 9 Figure 7 Definitions of several of the used parameters. Shown is a cross-section downstream of the confluence with heavy water right and light water left. The dashed line is the mean location and the dash-point line is the depth averaged location of the shear layer. ...................................................... 12 Figure 8 Schematic map of the confluence area of the Rio Negro and Solimões rivers. The arrows indicate the flow direction. The city of Manaus is located in the top left corner of the figure. .......... 13 Figure 9 Discharges at the confluence, Solimões (blue) and Rio Negro (black), data from the National Water Agency [ANA 2016], the circles denote measurements from Filizola et al. [2009]. .................. 14 Figure 10 The numerical grid used on top of the bed levels used for the Rio Negro – Solimões model. The three cyan lines are the locations of the cross-sections of Figure 36. ........................................... 14 Figure 11 A top view of the model used to assess the characteristics of the mixing layer in Delft3D, showing clear Kelvin-Helmholtz instabilities. The colours indicate the amount of a tracer added to the lower tributary. ............................................................................................................................... 16 Figure 12 Width of the mixing layer as function of downstream distance. Blue: from model. Black: from theory. .......................................................................................................................................... 16 Figure 13 Densities in the same cross section for hydrostatic computation with σ-layers (left), hydrostatic computation with z-layers (middle) and non-hydrostatic computation (right) ................ 17 Figure 14 Densities (kg/m3) in the top layer (flow from left to right) and 4 cross-sections equally far apart (denoted by the black lines in the top figure). The
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