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CONTENTS PART I FLUID MOTIONS Chapter 1 INTRODUCTION 2 The nature of fluids 2 Pressure 3 Viscosity 10 Diffusion 15 Viscosity as a diffusion coefficient 17 Chapter 2 FLOW PAST A SPHERE I: DIMENSIONAL; ANALYSIS, REYNOLDS NUMBERS, AND FROUDE NUMBERS 19 Introduction 19 Which variables are important? 20 Some dimensional reasoning, and its consequences 21 How to construct dimensionless variables 25 What if you choose the wrong variables? 25 “Dimensional analysis” 31 Significance of Reynolds numbers and Froude numbers 32 Conclusion 34 Chapter 3 FLOW PAST A SPHERE II: STOKES’ LAW, THE BERNOULLI EQUATION, TURBULENCE, BOUNDARY LAYERS, FLOW SEPARATION 35 Introduction 35 The Navier–Stokes equation 35 Flow past a sphere at low Reynolds numbers 36 Inviscid flow 40 The Bernoulli equation 43 Turbulence 48 Boundary layers 58 Flow separation 65 Flow past a sphere at high Reynolds numbers 70 Settling of spheres 74 Chapter 4 FLOW IN PIPES AND CHANNELS 83 Introduction 83 Laminar flow down an inclined plane 84 Turbulent flow in pipes and channels: initial material 91 Turbulent shear stress 93 The turbulence closure problem 98 Structure of turbulent boundary layers 99 Flow resistance 103 Velocity profiles 115 Coherent structures in turbulent shear flow 149 Chapter 5 OPEN-CHANNEL FLOW 157 Introduction 157 Two practical problems 159 Uniform flow 160 Energy in open-channel flow 164The hydraulic jump 172 Hydraulic regimes of open-channel flow 176 Gradually varied flow 178 Chapter 6 OSCILLATORY FLOW 184 Introduction 184 The nature of waves 184 Water motions due to waves 187 Wave boundary layers 190 Combined flow (waves plus current 194 Chapter 7 FLOW IN ROTATING ENVIRONMENTS 201 Introduction 201 Playing on a rotating table 201 The Coriolis effect on the Earth’s surface 205 The Rossby number 212 Inertia currents 213 The Ekman spiral 215 Geostrophic motion 220 Ekman layers 227 Planetary boundary layers 230 PART II SEDIMENT TRANSPORT Chapter 8 SEDIMENTS, VARIABLES, FLUMES 237 Introduction 237 Sediment 238 Hydrodynamic perspective 241 Particle motions vs. turbulence 242 Observing sediment transport 245 Variables 246 Flumes 254 Chapter 9 THRESHOLD OF MOVEMENT 260 Introduction 260 Forces on bed particles 260 Balance of forces 265 Dimensional analysis 267 How is the threshold for movement identified? 269 Representations of the movement threshold 272 Recasting the Shields diagram 275 The Hjulstrøm diagram 278 Chapter 10 MOVEMENT OF SEDIMENT BY WATER FLOWS 285 Introduction 285 The bed, the flow, and the load 286 Transport mode vs. flow intensity 289 Bed load 294 Suspension in a shear flow: the diffusional theory of suspension 307 The effect of acceleration of gravity 314 Chapter 11 MOVEMENT OF SEDIMENT BY THE WIND 320Introduction 320 Saltation 321 Chapter 12 BED CONFIGURATIONS 350 Introduction 350 Unidirectional-flow bed configurations 352 Oscillatory-flow and combined-flow bed configurations 419 Wind ripples 431 Eolian dunes 432 Chapter 13 THE SEDIMENT TRANSPORT RATE 445 Introduction 445 The sediment load and the sediment transport rate 445 Predicting the sediment transport rate 450 Chapter 14 MIXED-SIZE SEDIMENTS 457 Introduction 457 A useful thought experiment 458 The bed-surface size distribution 458 Fractional transport rates 459 Gradation independence versus equal mobility 460 A thought experiment gradation independence versus equal mobility 462 Real data on fractional transport rates, from the flume and from the field 467 Movement threshold in mixed-size sediments 471 Deviations from the condition of equal mobility 477 More on sediment-discharge formulas 479 PART III CURRENT-GENERATED SEDIMENTARY STRUCTURES Chapter 15 DEPOSITION 483 Introduction 483 Modes of deposition 483 Why deposition or erosion? 491 A note on degradation 496 Chapter 16 CROSS STRATIFICATION 497 Stratification and cross stratification 497 The nature of cross stratification 498 Some general points about interpretation 499 The basic idea behind climbing-bed-form cross stratification 503 Important kinds of climbing-bed-form cross stratification 508 Cross stratification not produced by climbing bed forms 526 Chapter 17 PLANAR STRATIFICATION 531 Introduction 531 Features of planar lamination 533 The origin of planar lamination in sands and sandstones 533 Planar lamination in fine sediments 533 INDEX PARTIAL LIST OF


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MIT 12 090 - FLUID MOTIONS

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