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CHAPTER 4: LEE AND STOSS SUSPENSION EXPERIMENTS SUMMARY Sediment transport over representative fixed bedforms is investigated to elucidate main mechanisms contributing to sediment motion over mobile sandwaves. This idealisation is satisfactory since the bedform migration velocity is much less than particle transport velocity. We focus on the suspended sediment budget contributed by sediment suspended from the lee and stoss slopes downstream of the crest. The fixed bedform comprises only three crests against the more usual five for 'equilibrium' velocity profiles. This was done so that the coupling between two shear layers could be analysed without effects from the relics of shear layers further upstream. Main finding is that shear layer flapping (ie cyclic separation and reattachment) makes a large contribution to total sediment scour from the lee slope. We term this behaviour ' Coanda-flapping' because of the similarity between the periodically reattached free shear layer here and the Coanda effect where a free shear layer is sucked onto a nearby surface by restriction of the local entrainment flows. Although fractional flow depth at the crest and flow Froude number are recognised as important parameters, the frequency of this flapping nevertheless correlates well with the passage of free-shear vortices generated by the upstream crest. Concentration distributions for particles captured from the lee slope indicate a possible mechanism for sandwave washout, as discussed in chapter 1. 4-1
1 INTRODUCTION In chapter 3 we considered the fate of particles jetting from the crest of a fixed bedform. Our attention is now directed at sediment transport from the lee and stoss slopes downstream of the crest, again modelled using fixed bedforms and model particles. We focus on three main mechanisms as follows: capture by the recirculating flows on the lee slope; capture by motions induced by shear layer flapping and capture by interaction between the shear layer vorticity impinging on the downstream stoss slope. Recirculating fluid in the separation bubble below the shear layer is usually also unstable at a lower frequency which corresponds to the flapping of the shear layer. We term this phenomenon 'Coanda-flapping' because it is akin to the Coanda effect. The latter is the phenomenon where a separated flow moves towards a fixed surface due to the sub-pressure caused by the vorticity within the shear layer which would entrain fluid into the shear zone in the absence of the fixed surface. The Coanda-flapping phenomenon has a marked effect on sediment transport, though it appears not to have been cited in the open literature as a sediment capture mechanism. Wille & Fernholz's (1965) review of a colloquium on the Coanda effect reported Bradbury's study of an air jet blown over a convex surface with trailing flap; see figure 1. The angle subtended between the flap and the jet was increased until the 4-2
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FLUID-PARTICLE TRANSPORT DYNAMICS O
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SYNOPSIS The local dynamics of sand
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TABLE OF CONTENTS LIST OF FIGURES C
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CHAPTER 3: JETTING EXPERIMENTS Summ
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2 Numerical scheme 6-5 3 Results 6-
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LIST OF FIGURES Chapter 1 Figure 1.
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U=830mm/s. Figure 16. Thomas et al
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in the boundary layer. a) The forma
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Chapter 3 Figure 1. After Alien (19
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at various values of U/V from 2.7 t
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y Coanda-flapping of the free shear
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of a sandwave crest in the estuary
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Figure 7h-i. The temporal fluctuati
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inclined downwards whereas the time
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starting position (X,Y) at zero ini
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d Sand grain diameter (m) Fi Number
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G Vortex core growth rate (tn/s) ki
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1 INTRODUCTION Sand forms the botto
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where U is the depth-averaged veloc
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The wavelengths of dunes primarily
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detached and then confined within a
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The vortex radius rn and apparent w
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Recent work by Nezu & Nakagawa (199
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found in the outer streaks. 4 MODEL
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(1987), for example, modelled gas-s
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Profiles of shear stress and turbul
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6ft v "' ' Re In the limit of large
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that the particle radius was much s
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and travels downstream at speed }*U
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capture by transient large eddies s
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Chapter 1 Figure 3. Alien (1984). L
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Chapter 1 10 8 e 4 I 08 •- 02 Yal
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Chapter 1 bw speed fluid Figure 11.
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Chapter 1 Figure 16. Thomas et al (
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Chapter 1 StCMl STRESS SCALE « K /
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Chapter 1 Haiht Vdodty Figure 22. S
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Chapter 1 Time = 1.2 2.4 ' ' :•
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1 INTRODUCTION AND DESIGN CONSIDERA
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Initial costing for a flume of the
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flanges and a maximum flow rate of
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could be wound above or below the l
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4 EXPERIMENTAL SETUP AND METHODS He
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4.2 Flow visualisation and model pa
Page 87 and 88: any divergence from the beam and to
Page 89 and 90: even flow over 0.45m width and up t
Page 91 and 92: Chapter 2 Opt 1 h(m) 0.01 Max D(m)
Page 93 and 94: Chapter 2 Part of side section Putt
Page 95 and 96: Chapter 2 Suction tank Bypass Disch
Page 97 and 98: Chapter 2 QUncorrectedflow £ Corre
Page 99 and 100: Chapter 2 60 r 501 40? 30r 20 r lOr
Page 101 and 102: 1_ INTRODUCTION The main features o
Page 103 and 104: 2 EXPERIMENTAL METHODS A detailed d
Page 105 and 106: the relationship is then simply ^ -
Page 107 and 108: number about 0.14. They were taken
Page 109 and 110: along the stoss slope. Figures 8 an
Page 111 and 112: 3.3a) Jetting trajectories when U/V
Page 113 and 114: errors increase substantially due t
Page 115 and 116: likely distributions. 4 DISCUSSION
Page 117 and 118: Our suggestion here is akin to that
Page 119 and 120: not accommodate the differing migra
Page 121 and 122: considered by proponents of numeric
Page 123 and 124: Chapter 3 C,;: Figure 3a-j. The pla
Page 125 and 126: Q CO 23 Figure 6. Distribution of p
Page 127 and 128: Chapter 3 X(cm) 1 2 3 4 5 6 7 8 9 1
Page 129 and 130: Chapter 3 U(m/s) V(m/s) U/V M1+M2 M
Page 131 and 132: O I r+ 21 CO 2 5 8 11 14 17 20 23 >
Page 133 and 134: 8 11 14 17 20 23 25 + Position Figu
Page 135 and 136: Chapter 3 U/V= B5.7 Q9.3 BlO.7^12.8
Page 137: Chapter 3 Band 1 2 3 4 U(m/s) 0.2 0
Page 141 and 142: velocity for a maximum of 40% of th
Page 143 and 144: layer vortices extending over the d
Page 145 and 146: 2.2 Methods for measuring Coanda-fl
Page 147 and 148: Section 3.4 considers suspension fr
Page 149 and 150: This same flow structure has also b
Page 151 and 152: 3.2b) Effect of varying inter-crest
Page 153 and 154: those with fall speed 0.060m/s for
Page 155 and 156: 3.4 Particle capture from stoss slo
Page 157 and 158: are discussed in the context of est
Page 159 and 160: jetted grains settling to the lee s
Page 161 and 162: Chapter 4 ENTRAINED FLOW Figure 1.
Page 163 and 164: Figure 3a-j. The plates show partic
Page 165 and 166: Chapter 4 Percentage occurrence •
Page 167 and 168: Chapter 4 Interval (s) 60 80 100 12
Page 169 and 170: Chapter 4 0.024m Conc=8% Figure 12.
Page 171 and 172: Chapter 4 Figure 16. A cloud of par
Page 173 and 174: 1 INTRODUCTION We use a Rankine vor
Page 175 and 176: effective particle fall speed in th
Page 177 and 178: particle velocity Vx=0. The initial
Page 179 and 180: the vortex axis. Vortex circulation
Page 181 and 182: dimensional fall times T^ for diffe
Page 183 and 184: horizontal component lift force (fi
Page 185 and 186: corresponds to the trajectory trave
Page 187 and 188: stepping the calculation in VT . Do
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averaged exclusion of the coherent
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C from figure 11 (ie 2.2) then we h
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PflRTICLE DENSITY=1000.000 Kg/n3 LI
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Chapter 5 ft) J k I Figure 4. Varyi
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Chapter 5 Relative Fall Time va Sta
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Chapter 5 Figure 7a. Trajectories o
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Chapter 5 Velocity X —Inertia X L
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Chapter 5 Velocity X —Velocity Y
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Chapter 5 Velocity Y Inertia Y Lift
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Chapter 5 DENSITY PARTICLE=2850.000
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Chapter 5 Rad = 0.006 Rad=0.003 Rad
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Chapter 5 H3 Y=0 Oy=i m Y=2 D-y=3
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CHAPTER 6: NUMERICAL SIMULATION OF
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next. If we now adopt the classical
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st = (4) Where p p was the particle
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3 RESULTS 3.1 Specified 6 and V Fig
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the blue squares to double loops an
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A0fl0 = 1.25V-0.33G-0.005 (7) and f
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Conversely, the upper line of the p
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equations. Such a discrete vortex m
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Figure 1. Schematic of the shear la
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Chapter 6 J G H K M Figure 3. Seven
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Chapter 6 1 T V=0.161 0.1 -- V41185
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Chapter 6 - DataV=0.0335, G=0.01
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CHAPTER 7: RECAPITULATION AND RECOM
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were shown to compare well with pre
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We have shown Coanda-flapping makes
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figure 5, was critically dependant
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stoss slope suspension studies of c
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Figure la-g. The seven trajectory m
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Chapter 7
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Chapter 7 0.0351 0.03 " 03 0.025 0.
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Flow 16 (1) pp 19-34. Bernal LP (19
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Mechanics of Sediment Transport. Is
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turbulence near a smooth wall in a
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moderate Reynolds number shear laye
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Spalding (1961). A single formula f
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USA. 1-12
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APPENDIX 1: BOUNDARY LAYER STUDIES
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(1967) used hydrogen bubble visuali
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The burst-sweep dynamics study of U
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Horseshoe vortex Vortex filament Ho
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APPENDIX 2: FAST9003.HR(RW)/NHT - P
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of the vorticity shed into the near
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transport dynamics of multiphase fl
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APPENDIX 3: FUNDAMENTAL NAVIER-STOK
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APPENDIX 4: CLOSURE METHODS 1 ZERO
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where cr k and CD are empirical con
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K = CDe^ 2 p 2 \U2 -U1 \=e 1e 2 c (
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APPENDIX 6: K-e MODEL OF JOHNS ET A
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They then defined a hydrodynamic co
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with respect to the rest of the vor
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The vorticity equation can be split
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around the crest and the motion of
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micrometers, with mean of 80 microm
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i——COMPARISON WITH PREVIOUS WOR
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width speed (metres) ^(cm/s) 11 Fig
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U (33) = 1.16ms-' Depth = 2.65 m Fi
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APPENDIX 9 : DERIVATION OF FORCES O
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APPENDIX 10 : MODEL CODE FOR CALCUL
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APPENDIX 11: MODEL CODE FOR GROWING
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105 if (scancode .eq. 57) stop GOTO
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