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flow just separated from the convex surface. Bradbury found that vorticity-induced entrainment of the confined fluid caused jet deflection towards the flap for all angles less than some unspecified critical value. For larger angles, there was a different stable pattern in which the jet detached from the convex surface and the confined recirculating flow was directed everywhere upstream towards the convex surface. Kiya & Sasaki (1983) studied the separation bubble on the front edge of a thick rectangular plate. They found that large vortices were shed at a mean frequency of 0.6U/L where U here is the free stream velocity and L is the time-mean bubble separation length. These vortices appeared in the free shear layer separating from the salient leading edge and grew by entrainment until restricted by the proximity of the plate. A second oscillation was superimposed at a lower frequency of 0.2U/L, associated with large scale flapping of the shear layer during partial shedding of the separation bubble. Kiya & Sasaki do not give a detailed interpretation of this second phenomenon but we believe that boundary restriction of the entrainment flows played an important role. Soulsby & Bettess (1991) found the time averaged flow velocity over the trough of estuarine sandwaves showed no mean flow reversal at any height above the trough, which they explained as lack of permanent separation at the crest. Further measurements of the fluctuating velocity at 0.1, 0.2, 0.4 and 0.8m above the trough (where the crest height was about 0.8m) showed negative 4-3
velocity for a maximum of 40% of the time, which occurred during the decelerating phase of the tide after the crest had been sharpened by the accelerating phase. We ascribe this to the low lee slope angle of 15 degrees, which would probably promote reattachment further up the lee slope by the Coanda effect. Although there is no definitive evidence of sediment transport by Coanda-flapping, it seems likely that the phenomenon played a role in the sediment transport events reported by Soulsby (1989). Indeed the existence of such interactions between the free shear layer and adjoining bedform was postulated as background context for our project. The intermittent ejection of sediment from the vicinity of the crest might be attributed to any of at least four possible mechanisms as follows: firstly, surface or internal waves; secondly, feedback from downstream shear layer/bed interaction (only feasible in very shallow water); thirdly, by upstream events and fourthly, by boundary layer bursting events. In order to assess the relative importance of these possible mechanisms we performed a series of experiments on flow transport over the first of two crests and compared the results with those for transport over the middle crest in a set of three. We have also studied particle capture by steady shear layer entrainment flows for which, again, there is little published literature explicitly. Some indication as to the relative significance of stoss and lee slope erosion can be found from observations that antidunes form for supercritical Froude numbers 4-4
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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
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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 and 138: Chapter 3 Band 1 2 3 4 U(m/s) 0.2 0
Page 139: 1 INTRODUCTION In chapter 3 we cons
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
Page 189 and 190: 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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