Non-Hydrostatic Free Surface Flows:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cham
Springer
[2017]
|
| Series: | Advances in Geophysical and Environmental Mechanics and Mathematics
|
| Subjects: | |
| Online Access: | BTU01 FFW01 TUM01 UBG01 UBT01 UPA01 Volltext Inhaltsverzeichnis |
| Physical Description: | 1 Online-Ressource (XVI, 696 p. 230 illus., 17 illus. in color) |
| ISBN: | 9783319479712 |
| DOI: | 10.1007/978-3-319-47971-2 |
Staff View
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Record in the Search Index
| _version_ | 1804177431106420736 |
|---|---|
| adam_text | 4 Contents
I
1 Introduction 1
1 1 Aim and Scope 2
1 2 Hydrostatic and Non-hydrostatic Free Surface Flows 3
1 3 Historical Background 5
1 4 Non-hydrostatic Flows and Environmental Mechanics 12
1 5 Methodology 13
References 15
2 Vertically Integrated Non-hydrostatic Free Surface Flow
Equations 17
2 1 Introduction 19
2 2 Vertically Integrated Equations in Continuum Mechanical
Description 21
221 Basic Conservation Laws 21
222 Depth-Integrated Continuity Equation 23
223 Depth-Integrated Momentum Equations in Horizontal
Plane 25
224 Non-hydrostatic Stresses in z-Direction and Vertical
Velocity Profile 26
2 3 Shallow Flow Approximation and Depth-Averaged
Equations 29
2 4 Simplified Forms of Non-hydrostatic Extended
Flow Equations 33
241 RANS Model for River Flow 33
242 One-Dimensional Water Waves Over Horizontal
Topography 34
243 Turbulent Uniform Flow on Steep Terrain 36
244 Flows Over Curved Beds 39
245 Enhanced Gravity 41
246 Non-hydrostatic Model Including Friction Effects 43
xi
Contents
xii
2 5 Sediment Transport and Movable Beds 45
251 Introduction 45
252 Non-hydrostatic Unsteady Free Surface Flow
with Bed-Load Sediment Transport 49
2 6 Numerical Methods for Boussinesq-Type Models 57
261 Unsteady Flow Simulations 57
262 Steady Flow Simulations 65
2 7 Higher-Order Equations 66
271 Fawer-Type Equations 66
272 Moment Equations 70
References 73
3 Inviscid Channel Flows 81
3 1 Introduction 84
3 2 Potential Flow Theory 90
321 Fundamentals 90
322 Conservation Laws 92
323 Flow Net 98
3 3 Picard Iteration 100
331 General Aspects of Iterative Solutions 100
332 Second-Order Velocity Field 100
333 Third-Order Velocity Field 106
3 4 Approximate Treatment of Flow Net Geometry 108
341 Velocity Profile 108
342 Extended Equations 110
3 5 Curvilinear Coordinates: Dressler’s Theory 118
351 Governing Equations for Potential Flow 118
352 Picard Iteration in Curvilinear Coordinates 119
353 Dressler’s Theory 122
354 Second-Order Dressier-Type Model 127
3 6 Critical Flow Conditions in Curved Streamline Flows 129
361 Critical Irrotational Flows 129
362 Minimum Specific Energy 133
363 Maximum Discharge 143
3 7 2D Solution of Irrotational Flows: The x-i}/ Method 146
371 Semi-inverse Mapping 146
372 Boundary Conditions at Up- and Downstream
Sections 149
373 Free Surface Profile and Energy Head 149
374 Solution of Laplacian Field 150
375 Determination of Velocity and Pressure
Distributions 152
3 8 Free Overfall 153
381 Picard Iteration 153
382 Curvilinear Flow at the Brink Section 168
Contents
3 9
3 10
3 11
383 Moment of Momentum Method
384 Two-Dimensional Solution
385 Row Net
Transition from Mild to Steep Slopes
391 Picard Iteration
392 Two-Dimensional Solution
393 Row Net
Flow Over Round-Crested Weirs
3 10 1 Picard Iteration
3 10 2 Dressler’s Theory
3 10 3 Two-Dimensional Solution
3 10 4 Row Nets
Sharp-Crested Weir
3 11 1 Critical Row
3 11 2 Profile of High Dams
4
3 12 Critical Flow Over Weir Profiles
3 12 1 Jaeger’s Theory
3 12 2 Fawer’s Theory
3 13 Standard Sluice Gate
3 13 1 Free Jet Flow
3 13 2 Approach Flow
3 13 3 Gate Pressure Distribution
3 13 4 Bottom Pressure Distribution
3 14 Vorticity Effects
3 14 1 Vorticity Equation for Streamline
3 14 2 Velocity Profile
3 14 3 Free Overfall
3 15 Water Waves
3 15 1 Irrotational Water Waves
3 15 2 Serre-Green-Naghdi Equations
3 15 3 Small-Amplitude Waves
3 15 4 Cnoidal and Solitary Waves
3 15 5 Dam Break Wave
References
Seepage Flows
4 1 Introduction
4 2 Picard Iteration
421 Generalized Water Table Equation
422 Particular Cases
4 3 Dupuit-Fawer Equations
431 Generalized Water Table Equation
432 Particular Cases
xiii
177
184
193
195
195
206
210
212
212
214
216
221
226
226
234
239
239
247
254
254
258
259
261
264
264
268
271
275
275
277
282
291
303
309
317
319
324
324
326
327
327
330
Contents
xiv
4 4 Polubarinova-Kochina’s Rectangular Dam Seepage Problem 332
441 Picard Iteration 332
442 Validity of the Dupuit-Forchheimer Theory 344
443 Shallow Flow Approximation 350
444 Validity of Jaeger’s Theory 353
445 Dupuit-Fawer Equations 356
4 5 Flow Through Trapezoidal Dam 358
4 6 Drainage of Recharge 360
461 Horizontal Aquifer 360
462 Sloping Aquifer 373
463 Curved Aquifer 374
4 7 Flow Over Planar Bedrock with Slope Discontinuity 375
4 8 Bank Storage Problem 377
481 Picard’s Iteration for Anisotropic Porous Media 377
482 Analytical Solution and Numerical Method 383
483 Validity of Second-Order Solutions 388
References 390
5 Viscous Channel Flows 393
5 1 Introduction 398
5 2 Boundary Layer Approximation 402
521 Scale Effects of Round-Crested Weir Flow 402
522 Developing Flow on Steep Slopes 426
5 3 Undular Hydraulic Jump 439
531 Introduction 439
532 Depth-Averaged RANS Equations 446
533 Serre’s Theory 457
534 Boundary Layer Model 463
535 Simulations: Plane Undular Jump 466
536 Simulations: Spatial Undular Jump 473
5 4 Undular Weir Flow 479
5 5 Hydraulic Jump 481
551 Submerged Hydraulic Jump 481
552 Classical Hydraulic Jump 484
5 6 Boussinesq’s Original Theory for Non-hydrostatic Turbulent
Open-Channel Flows 485
561 Introduction 485
562 Equations of Motion 485
563 Turbulent Velocity Profile 490
564 Differential Equation Describing Water Surface
Profiles 497
565 Linearized Equation Valid for Water Depths Close
to the Normal Depth 500
566 Classification of Free Surface Profiles 508
567 Boussinesq and the Solitary Wave 510
Contents
xv
5 7 Spatially Varied Flows 513
571 Hydrodynamic Equations 513
572 Side-Weir Flow 517
573 Bottom Outlet Flow 520
574 Side-Channel Flows 524
575 Test Case: Flow Over Bottom Rack 524
5 8 Compound Channel Flows 528
581 Introduction to Gradually Varied Flow 528
582 Extended Serre Theory 531
5 9 Sand Solitary Wave 535
591 Existence of Sand Solitary Waves 535
592 Governing Equations 536
593 Analytical Solution 539
5 10 Dike Breaches 544
5 10 1 Extended Serre Theory 544
5 10 2 Experimental Investigation 551
References 553
6 Granular Flows 563
6 1 Introduction 564
6 2 Mixture Flow Equations 567
6 3 Depth-averaged Equations for Dry Granular Flows 568
631 ID Savage-Hutter Theory Down an Inclined Plane 568
632 Effect of Bed-Normal Velocity 571
6 4 Simplified Solutions 573
641 Pseudo-uniform Flow Conditions 573
642 Granular Solitary Wave 574
643 Granular Free Overfall 577
6 5 ID Hutter-Serre Enhanced Equations Down
an Inclined Plane 579
References 580
7 Concluding Remarks 585
References 587
Appendix A: Pressure Distribution in Flows Over Curved Bed 589
Appendix B: Second Picard Iteration Cycle in Cartesian
Coordinates 593
Appendix C: Picard Iteration in Curvilinear Coordinates 599
Appendix D: Derivation of the Laplace Equation
for the Transformation 607
Appendix E: Plane Open-Channel Flow Using Flow Net-Based
Coordinates 613
XVI
Contents
Appendix F: Specific Energy for Flow Over Curved Bottoms 621
Appendix G: Viscous Boussinesq-type equations 631
Appendix H: Non-hydrostatic Gradually Varied Flow
on Steep Slopes 639
Appendix I: Derivation of Vertically Integrated Equations
for Non-hydrostatic Mixture Flows 653
Appendix J: Layer-Integrated Equations for Mixture Flows 669
Author Index 681
|
| any_adam_object | 1 |
| author | Castro-Orgaz, Oscar Hager, Willi H. 1951- |
| author_GND | (DE-588)121396657 |
| author_facet | Castro-Orgaz, Oscar Hager, Willi H. 1951- |
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| dewey-sort | 3624.151 |
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| discipline | Geowissenschaften Bauingenieurwesen Umwelt |
| doi_str_mv | 10.1007/978-3-319-47971-2 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:47:57Z |
| institution | BVB |
| isbn | 9783319479712 |
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| spelling | Castro-Orgaz, Oscar Verfasser aut Non-Hydrostatic Free Surface Flows Oscar Castro-Orgaz, Willi H. Hager Cham Springer [2017] © 2017 1 Online-Ressource (XVI, 696 p. 230 illus., 17 illus. in color) txt rdacontent c rdamedia cr rdacarrier Advances in Geophysical and Environmental Mechanics and Mathematics Earth sciences Hydrology Hydrogeology Geotechnical engineering Fluid mechanics Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrology/Water Resources Engineering Fluid Dynamics Geowissenschaften Hager, Willi H. 1951- Verfasser (DE-588)121396657 aut Erscheint auch als Druck-Ausgabe 978-3-319-47969-9 https://doi.org/10.1007/978-3-319-47971-2 Verlag URL des Erstveröffentlichers Volltext HEBIS Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029662315&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Castro-Orgaz, Oscar Hager, Willi H. 1951- Non-Hydrostatic Free Surface Flows Earth sciences Hydrology Hydrogeology Geotechnical engineering Fluid mechanics Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrology/Water Resources Engineering Fluid Dynamics Geowissenschaften |
| title | Non-Hydrostatic Free Surface Flows |
| title_auth | Non-Hydrostatic Free Surface Flows |
| title_exact_search | Non-Hydrostatic Free Surface Flows |
| title_full | Non-Hydrostatic Free Surface Flows Oscar Castro-Orgaz, Willi H. Hager |
| title_fullStr | Non-Hydrostatic Free Surface Flows Oscar Castro-Orgaz, Willi H. Hager |
| title_full_unstemmed | Non-Hydrostatic Free Surface Flows Oscar Castro-Orgaz, Willi H. Hager |
| title_short | Non-Hydrostatic Free Surface Flows |
| title_sort | non hydrostatic free surface flows |
| topic | Earth sciences Hydrology Hydrogeology Geotechnical engineering Fluid mechanics Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrology/Water Resources Engineering Fluid Dynamics Geowissenschaften |
| topic_facet | Earth sciences Hydrology Hydrogeology Geotechnical engineering Fluid mechanics Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrology/Water Resources Engineering Fluid Dynamics Geowissenschaften |
| url | https://doi.org/10.1007/978-3-319-47971-2 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029662315&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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