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4 Discussion 4-19 4.1 Relative importance of sediment transport mechanisms 4-20 4.2 Bedform shape and migration 4-21 5 Conclusion 4-23 Figures CHAPTER 5: NUMERICAL SIMULATIONS WITH FIXED VORTEX CORES Summary 5 _1 1 Introduction 5_2 2 Computational procedure 5-4 2.1 Iteration interval 5-5 2.2 Initial conditions 5-5 3 Results 5-6 3.1 Varying VT at fixed R and A 5-6 3.2 Forces on particles starting below the vortex 5-7 3.3 Forces on particles initially above the vortex 5-9 a) Reference trajectory and first time-peak trajectory 5-10 b) First time-trough and second time-peak trajectories 5-10 c) Second time-trough and third time-peak trajectories 5-12 d) Core-entry limiting trajectory and cusp point 5-13 3.4 Vortex-particle interaction criterion 5-14 4 Discussion 5-16 4.1 Forces acting on a particle in shear flows 5-16 4.2 Effective particle fall speed 5-18 4.3 Comparison of criterion C with published data 5-19 5 Conclusions 5-20 Figures CHAPTER 6: NUMERICAL SIMULATION OF PARTICLE TRAJECTORIES IN GROWING VORTICES Summary 6-1 1 introduction 6-2
2 Numerical scheme 6-5 3 Results 6-7 3.1 Specified G and V 6-7 a) General points on parameter space 6-7 b) Detail of inner region of parameter space 6-8 3.2 Different values of V and G 6-9 a) Varying particle fall speed 6-9 b) Varying shear layer growth rate 6-10 c) Functions fitting parameter space boundaries 6-10 4 Discussion 6-11 4.1 Forces dominating the parameter space 6-12 4.2 Implications for practical modelling of sandwaves 6-13 5 Conclusions 6-15 Figures CHAPTER 7: RECAPITULATION AND RECOMMENDATIONS 1 Status of sandwave modelling 7-1 2 Project methods and results 7-2 2.1 Experimental studies 7-2 a) Concentration peak at crest height 7-3 b) Modal trajectories 7-3 c) Coanda-flapping 7-4 d) Stoss slope particle capture 7-5 2.2 Numerical studies 7-5 a) Fixed vortex modelling 7-5 b) Shear layer modelling 7-6 3 Recommendations 7-7 3.1 Experimental techniques 7-7 3.2 Numerical modelling techniques 7-9 Figures CHAPTER 8: REFERENCES 8-1
Page 1 and 2: FLUID-PARTICLE TRANSPORT DYNAMICS O
Page 3 and 4: SYNOPSIS The local dynamics of sand
Page 5 and 6: TABLE OF CONTENTS LIST OF FIGURES C
Page 7: CHAPTER 3: JETTING EXPERIMENTS Summ
Page 11 and 12: LIST OF FIGURES Chapter 1 Figure 1.
Page 13 and 14: U=830mm/s. Figure 16. Thomas et al
Page 15 and 16: in the boundary layer. a) The forma
Page 17 and 18: Chapter 3 Figure 1. After Alien (19
Page 19 and 20: at various values of U/V from 2.7 t
Page 21 and 22: y Coanda-flapping of the free shear
Page 23 and 24: of a sandwave crest in the estuary
Page 25 and 26: Figure 7h-i. The temporal fluctuati
Page 27 and 28: inclined downwards whereas the time
Page 29 and 30: starting position (X,Y) at zero ini
Page 31 and 32: d Sand grain diameter (m) Fi Number
Page 33 and 34: G Vortex core growth rate (tn/s) ki
Page 35 and 36: 1 INTRODUCTION Sand forms the botto
Page 37 and 38: where U is the depth-averaged veloc
Page 39 and 40: The wavelengths of dunes primarily
Page 41 and 42: detached and then confined within a
Page 43 and 44: The vortex radius rn and apparent w
Page 45 and 46: Recent work by Nezu & Nakagawa (199
Page 47 and 48: found in the outer streaks. 4 MODEL
Page 49 and 50: (1987), for example, modelled gas-s
Page 51 and 52: Profiles of shear stress and turbul
Page 53 and 54: 6ft v "' ' Re In the limit of large
Page 55 and 56: that the particle radius was much s
Page 57 and 58: 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.
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Figure 3a-j. The plates show partic
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Chapter 4 Percentage occurrence •
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Chapter 4 Interval (s) 60 80 100 12
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Chapter 4 0.024m Conc=8% Figure 12.
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Chapter 4 Figure 16. A cloud of par
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1 INTRODUCTION We use a Rankine vor
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effective particle fall speed in th
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particle velocity Vx=0. The initial
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the vortex axis. Vortex circulation
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dimensional fall times T^ for diffe
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horizontal component lift force (fi
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corresponds to the trajectory trave
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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
Page 309 and 310:
APPENDIX 11: MODEL CODE FOR GROWING
Page 311:
105 if (scancode .eq. 57) stop GOTO
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