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1 INTRODUCTION Figure 1 shows a schematic of the crest regions of a notional sandwave. The flow separates at the crest as a salient edge. As an idealisation we picture the instantaneous shear layer rolls up into a first generation vortex with angular velocity A0 and nominal radius R 0 at a distance d 0 from the crest. The circulation r of this vortex is in reality distributed nonuniformly over its core. In common with previous models (Thomas et al, 1983, Hunt et al, 1988 and Onslow et al, 1994), we suppose as a first approximation that the distribution is uniform (ie classical Rankine vortex). The other implicit assumption here, that the vorticity is strictly two dimensional, is generally held to be an adequate approximation sufficiently close to the crest (Muller & Gyr, 1986) . In reality, the values of R 0 , A 0 and d 0 depend on upstream parameters, notably boundary layer thickness at the crest, and intensity and scale of turbulence. For stream speed U, this vortex travels downstream at speed u 0 depending on the velocity of the recirculating flow (Townsend, 1956) . It is well known (eg, Muller & Gyr 1986) that pairing occurs to form second generation vortices possessing approximately double the radius of the initial vortices. Vortex growth is characterised by entrainment due to fine scale turbulence and engulf ment as described, for example, by Ho et al (1991) following the seminal studies by Brown & Roshco (1971). Clearly, the circulation also doubles during pairing so the vorticity (circulation area density) must halve from one generation to the 6-2
next. If we now adopt the classical scaling arguments (eg Townsend 1956) that shear layer width 6 is proportional to the downstream distance x and also assume that the vortex velocity u 0 is constant throughout its translation then a useful first idealisation is to replace the stepwise changes with a steady growth rate such that radius Ri increases proportional to time: viz, R°
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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
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even flow over 0.45m width and up t
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Chapter 2 Opt 1 h(m) 0.01 Max D(m)
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Chapter 2 Part of side section Putt
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Chapter 2 Suction tank Bypass Disch
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Chapter 2 QUncorrectedflow £ Corre
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Chapter 2 60 r 501 40? 30r 20 r lOr
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1_ INTRODUCTION The main features o
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2 EXPERIMENTAL METHODS A detailed d
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the relationship is then simply ^ -
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number about 0.14. They were taken
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along the stoss slope. Figures 8 an
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3.3a) Jetting trajectories when U/V
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errors increase substantially due t
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likely distributions. 4 DISCUSSION
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Our suggestion here is akin to that
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not accommodate the differing migra
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considered by proponents of numeric
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Chapter 3 C,;: Figure 3a-j. The pla
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Q CO 23 Figure 6. Distribution of p
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Chapter 3 X(cm) 1 2 3 4 5 6 7 8 9 1
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Chapter 3 U(m/s) V(m/s) U/V M1+M2 M
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O I r+ 21 CO 2 5 8 11 14 17 20 23 >
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8 11 14 17 20 23 25 + Position Figu
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Chapter 3 U/V= B5.7 Q9.3 BlO.7^12.8
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Chapter 3 Band 1 2 3 4 U(m/s) 0.2 0
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1 INTRODUCTION In chapter 3 we cons
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velocity for a maximum of 40% of th
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layer vortices extending over the d
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2.2 Methods for measuring Coanda-fl
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Section 3.4 considers suspension fr
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This same flow structure has also b
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3.2b) Effect of varying inter-crest
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those with fall speed 0.060m/s for
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3.4 Particle capture from stoss slo
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are discussed in the context of est
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jetted grains settling to the lee s
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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
Page 191 and 192: C from figure 11 (ie 2.2) then we h
Page 193 and 194: PflRTICLE DENSITY=1000.000 Kg/n3 LI
Page 195 and 196: Chapter 5 ft) J k I Figure 4. Varyi
Page 197 and 198: Chapter 5 Relative Fall Time va Sta
Page 199 and 200: Chapter 5 Figure 7a. Trajectories o
Page 201 and 202: Chapter 5 Velocity X —Inertia X L
Page 203 and 204: Chapter 5 Velocity X —Velocity Y
Page 205 and 206: Chapter 5 Velocity Y Inertia Y Lift
Page 207 and 208: Chapter 5 DENSITY PARTICLE=2850.000
Page 209 and 210: Chapter 5 Rad = 0.006 Rad=0.003 Rad
Page 211 and 212: Chapter 5 H3 Y=0 Oy=i m Y=2 D-y=3
Page 213: CHAPTER 6: NUMERICAL SIMULATION OF
Page 217 and 218: st = (4) Where p p was the particle
Page 219 and 220: 3 RESULTS 3.1 Specified 6 and V Fig
Page 221 and 222: the blue squares to double loops an
Page 223 and 224: A0fl0 = 1.25V-0.33G-0.005 (7) and f
Page 225 and 226: Conversely, the upper line of the p
Page 227 and 228: equations. Such a discrete vortex m
Page 229 and 230: Figure 1. Schematic of the shear la
Page 231 and 232: Chapter 6 J G H K M Figure 3. Seven
Page 233 and 234: Chapter 6 1 T V=0.161 0.1 -- V41185
Page 235 and 236: Chapter 6 - DataV=0.0335, G=0.01
Page 237 and 238: CHAPTER 7: RECAPITULATION AND RECOM
Page 239 and 240: were shown to compare well with pre
Page 241 and 242: We have shown Coanda-flapping makes
Page 243 and 244: figure 5, was critically dependant
Page 245 and 246: stoss slope suspension studies of c
Page 247 and 248: Figure la-g. The seven trajectory m
Page 249 and 250: Chapter 7
Page 251 and 252: Chapter 7 0.0351 0.03 " 03 0.025 0.
Page 253 and 254: Flow 16 (1) pp 19-34. Bernal LP (19
Page 255 and 256: Mechanics of Sediment Transport. Is
Page 257 and 258: turbulence near a smooth wall in a
Page 259 and 260: moderate Reynolds number shear laye
Page 261 and 262: Spalding (1961). A single formula f
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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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