Environmental Fluid Mechanics

Hillel Rubin9780824787813, 0824787811

Doubling as a reference and a text, this book covers basic fluid principles and the application of these principles in various circumstances. It describes the use of physical and numerical models and computational approaches to analyze environmental processes, especially fluid motion on the earths surface, underground, and in the ocean. Rubin teaches at Technion-Israel Institute of Technology. Atkinson teaches at the State University of New York at Buffalo.

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Table of contents :
Environmental Fluid Mechanics……Page 1
Preface……Page 4
Contents……Page 7
1.1.1 Historical Perspective……Page 12
Contents……Page 0
1.1.2 Objectives And Scope……Page 14
1.2.1 General……Page 15
1.2.3 Review Of Fluid Properties……Page 16
Contravariant Vectors And Tensors, Invariants……Page 19
Covariant Vectors And Tensors, Mixed Tensors……Page 20
Addition, Multiplication, And Contraction Of Tensors……Page 21
The Metric Tensor And The Line Element……Page 22
The Conjugate Tensor; Lowering And Raising Suffixes……Page 23
Geodesics And Christoffel Symbols……Page 24
Derivatives Of Tensors……Page 25
Cartesian Tensors……Page 26
Physical Components Of Tensors……Page 27
Complex Numbers……Page 30
1.3.3 Partial Differential Equations……Page 34
1.4.1 Uses Of Dimensional Analysis……Page 38
Buckingham Theorem……Page 40
Solved Problems……Page 43
Unsolved Problems……Page 50
Supplemental Reading……Page 54
2.2 Fluid Velocity, Pathlines, Streamlines, And Streaklines……Page 55
2.3 Rate Of Strain, Vorticity, And Circulation……Page 58
2.4.1 General Presentation Of The Approaches……Page 62
2.4.3 Reynolds Transport Theorem……Page 64
2.5.2 The Differential Approach……Page 66
2.5.3 The Stream Function……Page 67
2.5.4 Stratified Flow……Page 69
2.6 Conservation Of Momentum……Page 70
2.7 The Equations Of Motion And Constitutive Equations……Page 75
2.8 Conservation Of Energy……Page 81
2.9 Scaling Analyses For Governing Equations……Page 85
2.9.1 Mass Conservation……Page 86
2.9.2 Momentum Conservation……Page 88
2.9.3 Thermal Energy Equation……Page 95
Solved Problems……Page 97
Unsolved Problems……Page 114
Supplemental Reading……Page 133
3.1 Various Forms Of The Equations Of Motion……Page 134
3.2 One-directional Flows……Page 137
3.2.1 Domains Described By Cartesian Coordinates — Steady-state Conditions……Page 138
3.2.2 Domains Described By Cylindrical Coordinates — Steady-state Conditions……Page 140
3.3 Creeping Flows……Page 143
3.4.1 Quasi-steady-state Oscillations Of A Flat Plate……Page 146
3.4.2 Unsteady Motion Of A Flat Plate……Page 147
3.5 Numerical Simulation Considerations……Page 148
3.5.1 Basic Presentation……Page 149
3.5.2 Presentation With The Stream Function……Page 150
Solved Problems……Page 152
Unsolved Problems……Page 159
Supplemental Reading……Page 171
4.1 Introduction……Page 172
4.2.1 General Considerations……Page 173
4.2.2 Uniform Flow……Page 177
4.2.3 Flow At A Corner……Page 178
4.2.4 Source Flow……Page 179
4.2.5 Simple Vortex……Page 180
4.2.6 Doublet……Page 182
4.2.7 The Image Method……Page 184
4.3 Flow Through Porous Media……Page 188
4.3.1 Darcy’s Law……Page 189
4.3.3 Anisotropic Porous Medium……Page 190
4.3.4 Flow-nets……Page 191
4.4.1 Force On A Cylinder……Page 194
4.4.2 Steady Flow Around A Circular Cylinder Without Circulation……Page 195
4.4.3 Steady Flow Around A Circular Cylinder With Circulation……Page 197
4.4.4 The Theorem Of Blasius……Page 199
4.4.5 The Lift Theorem Of Kutta–zhukovski……Page 200
4.5 Numerical Simulation Considerations……Page 201
Solved Problems……Page 209
Unsolved Problems……Page 212
Supplemental Reading……Page 218
5.1 Introduction……Page 219
5.2 Definitions……Page 220
5.3 Frequency Analysis……Page 228
5.4 Stability Analysis……Page 234
5.4.1 Stability Of Plane Laminar Flows……Page 237
5.5.1 Reynolds Averaging……Page 240
5.5.2 Turbulent Kinetic Energy Equation……Page 245
5.5.3 Reynolds Stress Equations……Page 247
5.5.4 Dissipation Equation……Page 249
5.6 Scales Of Turbulent Motion……Page 250
Solved Problems……Page 253
Unsolved Problems……Page 255
Supplemental Reading……Page 258
6.1 Introduction……Page 259
6.2 The Equations Of Motion For Boundary Layers……Page 260
6.3 The Integral Approach Of Von Karman……Page 266
6.4 Laminar Boundary Layers……Page 270
6.5 Turbulent Boundary Layers……Page 272
6.6 Application Of The Boundary Layer Concept To Heat And Mass Transfer……Page 274
Solved Problems……Page 277
Unsolved Problems……Page 281
Supplemental Reading……Page 282
7.2.1 Basic Geometric Parameters Of The Channel Cross Section……Page 284
7.2.2 Parameters Of Open Channel Flow……Page 286
7.2.3 The Longitudinal Cross Section Of Open Channel Flow……Page 287
7.2.4 The Equation Of Open Channel Flow……Page 288
7.2.5 Uniform Flow In Open Channels……Page 291
7.2.6 The Concept Of Specific Energy And Critical Depth……Page 292
7.2.7 The Concept Of The Momentum Function……Page 294
7.3 Application Of The Energy Conservation Principle……Page 296
Contraction — Expansion Of The Channel Cross Section……Page 297
Elevation Of The Channel Bottom……Page 299
7.3.2 Lateral Outflow From The Channel……Page 301
7.4.1 Forces Acting On A Channel Constriction……Page 303
7.4.2 Lateral Flow Into An Open Channel……Page 305
7.5.1 Use Of Navier–stokes Equations For Unidirectional Turbulent Flow……Page 306
7.5.2 Turbulent Flow In A Smooth Channel……Page 308
7.5.3 Transition And Rough Turbulent Flow In Open Channels……Page 311
7.6.2 The Differential Equations Of Gradually Varied Flow……Page 313
7.6.4 Various Types Of Hydraulic Profiles……Page 316
7.6.5 St. Venant Equations……Page 321
7.6.6 Numerical Calculation Of The Hydraulic Profiles For Prismatic Channels……Page 324
7.6.7 Numerical Calculation Of The Hydraulic Profiles For Nonprismatic Channels……Page 325
7.7.1 Introduction……Page 326
7.7.2 Horizontally Averaged Model For Temperature Distribution……Page 328
7.7.3 Barotropic Models……Page 331
7.7.4 Three-dimensional Models……Page 334
Solved Problems……Page 335
Unsolved Problems……Page 358
Supplemental Reading……Page 366
8.1 Introduction……Page 368
8.2 The Wave Equation……Page 369
8.3 Gravity Surface Waves……Page 371
8.4.1 The General Wave Propagation Equation……Page 373
8.4.2 The Potential Function For Deep Water Waves……Page 374
8.4.3 Pathlines Of The Fluid Particles……Page 375
8.4.5 The Wave Energy……Page 377
8.5.1 The Potential Function Of Shallow Water Waves……Page 379
8.5.2 The Wave Velocity Of Propagation……Page 380
8.5.3 Pathlines Of The Fluid Particles……Page 383
8.6 The Group Velocity……Page 385
8.7.1 General Aspects……Page 389
8.7.2 The Simple Negative Wave Problem……Page 395
8.7.3 Positive Waves And Surge Formation……Page 397
8.7.4 The Kinematic Wave……Page 399
8.8 Numerical Aspects……Page 400
8.8.1 The Method Of Characteristics……Page 401
Solved Problems……Page 402
Unsolved Problems……Page 406
Supplemental Reading……Page 407
9.1 Introduction……Page 408
9.2.1 Geostrophic Balance……Page 409
9.2.2 Potential Vorticity……Page 414
9.3 The Taylor–proudman Theorem……Page 416
9.4 Wind-driven Currents (ekman Layer)……Page 418
9.5 Vertically Integrated Equations Of Motion……Page 422
Solved Problems……Page 424
Unsolved Problems……Page 425
Supplemental Reading……Page 428
10.1.1 Water, Heat, And Solute Transport……Page 429
10.2 Basic Definitions, Advective Transport……Page 432
10.3.1 Molecular Diffusion, Fick’s Law……Page 433
10.3.2 Turbulent Diffusion……Page 435
10.3.3 Statistical Theory Of Diffusion……Page 436
10.4 The Advection–diffusion Equation……Page 437
10.4.1 Source And Sink Reaction Terms……Page 440
10.4.2 Boundary And Initial Conditions……Page 441
10.5 Dispersion……Page 444
10.5.1 Taylor Analysis……Page 445
10.5.2 Longitudinal Dispersion In Rivers……Page 448
10.6 Dispersion In Porous Media……Page 452
10.7 Analytical Solutions To The Advection–diffusion Equation……Page 457
Instantaneous Point Source……Page 458
Continuous Point Source……Page 460
Instantaneous Line Source……Page 462
Instantaneous Plane Source……Page 464
Continuous Plane Source……Page 466
10.7.4 Instantaneous Volume Source……Page 468
10.7.5 Effect Of Finite Domain……Page 469
10.8 Numerical Solutions To The Advection–diffusion Equation……Page 472
10.8.1 Numerical Dispersion……Page 476
Solved Problems……Page 479
Unsolved Problems……Page 483
Supplemental Reading……Page 494
11.1 Introduction……Page 495
11.2 The Approximation Of Dupuit……Page 496
11.3.2 Basic Equation Of Contaminant Transport……Page 502
11.3.3 Various Issues Of Interest……Page 504
11.3.4 Application Of The Boundary Layer Approximations……Page 508
11.4.1 The Sharp Interface Approximation……Page 512
11.4.2 Salinity Transport……Page 515
11.5 Non-aqueous Phase Liquid (napl) In Groundwater……Page 517
11.6.1 The Equations Of Flow……Page 521
11.6.2 The Equation Of Contaminant Transport……Page 526
Solved Problems……Page 528
Unsolved Problems……Page 536
Supplemental Reading……Page 538
12.2 Momentum Transport……Page 539
12.2.1 Seiches……Page 543
12.3.1 Temperature Equation……Page 545
12.3.2 Solar Radiation Absorption……Page 548
12.3.3 Surface Heat Exchange……Page 550
12.4 Exchange Of Gases……Page 558
12.4.1 Dissolved Oxygen In Open Channel Flow……Page 564
12.5 Measurement Of Gas Mass Transfer Coefficients……Page 570
12.5.1 Exchange Of Volatile Organic Chemicals……Page 572
Solved Problem……Page 574
Unsolved Problems……Page 576
Supplemental Reading……Page 579
13.1 Buoyancy And Stability Considerations……Page 581
13.1.1 Equation Of State……Page 582
13.1.2 Gravitational Stability……Page 584
13.2 Internal Waves……Page 587
13.2.1 Lowest Mode Solutions……Page 590
13.2.2 Small-scale Internal Waves……Page 596
13.3.1 Linear Stability Theory……Page 597
13.3.2 Convection……Page 604
Rayleigh–benard Convection……Page 606
13.4 Double-diffusive Convection……Page 609
Stability Analysis……Page 611
13.5.1 Introduction……Page 615
13.5.2 Analysis……Page 616
Unsolved Problems……Page 623
Supplemental Reading……Page 624
14.1 Jets And Plumes……Page 626
14.1.1 Jets……Page 628
14.1.2 Plumes……Page 633
14.1.3 Turbulent Buoyant Jets……Page 635
14.2 Submerged Discharges And Multiport Diffuser Design……Page 636
14.3 Surface Buoyant Discharges……Page 640
14.3.1 Arrested Wedge Analysis……Page 641
14.3.2 Flow On The Slope……Page 647
Unsolved Problems……Page 650
Supplemental Reading……Page 651
15.1 Introduction……Page 652
15.2 Hydraulic Properties Of Sediments……Page 654
15.3.1 Duboys’ Analysis……Page 658
15.3.2 Other Bed Load Formulas……Page 661
15.4 Suspended Sediment Calculations……Page 664
15.4.1 Boundary Conditions……Page 667
15.4.2 Lake And Reservoir Modeling — Benthic Nepheloid Layer……Page 671
15.5.1 Size Distribution……Page 673
15.5.2 Particle Aggregation — Smoluchowski Model……Page 675
Collision Frequency……Page 680
15.6 Particle-associated Contaminant Transport……Page 681
Kinetic Approach……Page 684
Solved Problems……Page 687
Unsolved Problems……Page 689
Supplemental Reading……Page 692
16.1 Introduction……Page 696
16.2.1 General Aspects……Page 697
16.2.2 Containment Of The Contaminated Site……Page 698
16.2.3 Pump-and-treat Of Contaminated Groundwater……Page 701
16.2.4 In-situ Remediation……Page 705
16.3.1 Basic Concepts And Definitions……Page 706
16.3.2 Kinetics Of Biodegradation……Page 707
16.3.3 Modeling Of Biodegradation……Page 710
16.3.4 The Biofilm Model……Page 712
16.3.5 Microcolony Modeling……Page 713
16.4 Remediation Of Surface Waters……Page 714
Solved Problems……Page 718
Unsolved Problems……Page 722
Supplementary Reading……Page 724