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E-raamat: Non-Hydrostatic Free Surface Flows

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This book provides essential information on the higher mathematical level of approximation over the gradually varied flow theory, also referred to as the Boussinesq-type theory. In this context, it presents higher order flow equations, together with their applications in a broad range of pertinent engineering and environmental problems, including open channel, groundwater, and granular material flows.

1. Introduction.- 2. Vertically integrated non-hydrostatic free surface flow equations.- 3. Inviscid channel flows.- 4. Seepage flows.- 5. Viscous channel flows.- 6. Granular flows.- 7. Concluding remarks.- Appendices.

Arvustused

Non-Hydrostatic Free Surface Flows is an exceptional book that masterfully takes the reader on a brave voyage into a universe of Free-Surface Flows that do not presume a hydrostatic pressure distribution in the vertical direction. The wealth of information amassed in this text is extraordinary. Both students and researchers will find that the quality of the presentation is outstanding, and the didactic value of the text is unparalleled. (Nikolaos D. Katopodes, Journal of Hydraulic Engineering, Vol. 147 (10), 2021) Nonhydrostatic free surface flows is an excellent book that merits having a place on the shelves of any person dedicated to any discipline in which the flow of water might be fundamental, from ecology to civil engineering. (Juan V. Giraldez, Environmental Fluid Mechanics, Vol. 19, 2019) This is the first free surface hydraulics book dedicated to Boussinesqs theory since Boussinesqs 1877 book. The book contains a clear presentation of basic theoretical aspects. It is carefully illustrated and edited. Non-hydrostatic free surface flows is a valuable addition to the literature, containing information that will be of great interest for students, researchers and professors working in open channel hydraulics. (Takashi Hosoda, Journal of Hydraulic Research, April, 2018)

1 Introduction
1(16)
1.1 Aim and Scope
2(1)
1.2 Hydrostatic and Non-hydrostatic Free Surface Flows
3(2)
1.3 Historical Background
5(7)
1.4 Non-hydrostatic Flows and Environmental Mechanics
12(1)
1.5 Methodology
13(4)
References
15(2)
2 Vertically Integrated Non-hydrostatic Free Surface Flow Equations
17(64)
2.1 Introduction
19(2)
2.2 Vertically Integrated Equations in Continuum Mechanical Description
21(8)
2.2.1 Basic Conservation Laws
21(2)
2.2.2 Depth-Integrated Continuity Equation
23(2)
2.2.3 Depth-Integrated Momentum Equations in Horizontal Plane
25(1)
2.2.4 Non-hydrostatic Stresses in z-Direction and Vertical Velocity Profile
26(3)
2.3 Shallow Flow Approximation and Depth-Averaged Equations
29(4)
2.4 Simplified Forms of Non-hydrostatic Extended Flow Equations
33(12)
2.4.1 RANS Model for River Flow
33(1)
2.4.2 One-Dimensional Water Waves Over Horizontal Topography
34(2)
2.4.3 Turbulent Uniform Flow on Steep Terrain
36(3)
2.4.4 Flows Over Curved Beds
39(2)
2.4.5 Enhanced Gravity
41(2)
2.4.6 Non-hydrostatic Model Including Friction Effects
43(2)
2.5 Sediment Transport and Movable Beds
45(12)
2.5.1 Introduction
45(4)
2.5.2 Non-hydrostatic Unsteady Free Surface Flow with Bed-Load Sediment Transport
49(8)
2.6 Numerical Methods for Boussinesq-Type Models
57(9)
2.6.1 Unsteady Flow Simulations
57(8)
2.6.2 Steady Flow Simulations
65(1)
2.7 Higher-Order Equations
66(15)
2.7.1 Fawer-Type Equations
66(4)
2.7.2 Moment Equations
70(3)
References
73(8)
3 Inviscid Channel Flows
81(236)
3.1 Introduction
84(6)
3.2 Potential Flow Theory
90(10)
3.2.1 Fundamentals
90(2)
3.2.2 Conservation Laws
92(6)
3.2.3 Flow Net
98(2)
3.3 Picard Iteration
100(8)
3.3.1 General Aspects of Iterative Solutions
100(1)
3.3.2 Second-Order Velocity Field
100(6)
3.3.3 Third-Order Velocity Field
106(2)
3.4 Approximate Treatment of Flow Net Geometry
108(10)
3.4.1 Velocity Profile
108(2)
3.4.2 Extended Equations
110(8)
3.5 Curvilinear Coordinates: Dressler's Theory
118(11)
3.5.1 Governing Equations for Potential Flow
118(1)
3.5.2 Picard Iteration in Curvilinear Coordinates
119(3)
3.5.3 Dressler's Theory
122(5)
3.5.4 Second-Order Dressier-Type Model
127(2)
3.6 Critical Flow Conditions in Curved Streamline Flows
129(17)
3.6.1 Critical Irrotational Flows
129(4)
3.6.2 Minimum Specific Energy
133(10)
3.6.3 Maximum Discharge
143(3)
3.7 2D Solution of Irrotational Flows: The x-ty Method
146(7)
3.7.1 Semi-inverse Mapping
146(3)
3.7.2 Boundary Conditions at Up- and Downstream Sections
149(1)
3.7.3 Free Surface Profile and Energy Head
149(1)
3.7.4 Solution of Laplacian Field
150(2)
3.7.5 Determination of Velocity and Pressure Distributions
152(1)
3.8 Free Overfall
153(42)
3.8.1 Picard Iteration
153(15)
3.8.2 Curvilinear Flow at the Brink Section
168(9)
3.8.3 Moment of Momentum Method
177(7)
3.8.4 Two-Dimensional Solution
184(9)
3.8.5 Flow Net
193(2)
3.9 Transition from Mild to Steep Slopes
195(17)
3.9.1 Picard Iteration
195(11)
3.9.2 Two-Dimensional Solution
206(4)
3.9.3 Flow Net
210(2)
3.10 Flow Over Round-Crested Weirs
212(14)
3.10.1 Picard Iteration
212(2)
3.10.2 Dressler's Theory
214(2)
3.10.3 Two-Dimensional Solution
216(5)
3.10.4 Flow Nets
221(5)
3.11 Sharp-Crested Weir
226(13)
3.11.1 Critical Flow
226(8)
3.11.2 Profile of High Dams
234(5)
3.12 Critical Flow Over Weir Profiles
239(15)
3.12.1 Jaeger's Theory
239(8)
3.12.2 Fawer's Theory
247(7)
3.13 Standard Sluice Gate
254(10)
3.13.1 Free Jet Flow
254(4)
3.13.2 Approach Flow
258(1)
3.13.3 Gate Pressure Distribution
259(2)
3.13.4 Bottom Pressure Distribution
261(3)
3.14 Vorticity Effects
264(11)
3.14.1 Vorticity Equation for Streamline
264(4)
3.14.2 Velocity Profile
268(3)
3.14.3 Free Overfall
271(4)
3.15 Water Waves
275(42)
3.15.1 Irrotational Water Waves
275(2)
3.15.2 Serre---Green---Naghdi Equations
277(5)
3.15.3 Small-Amplitude Waves
282(9)
3.15.4 Cnoidal and Solitary Waves
291(12)
3.15.5 Dam Break Wave
303(6)
References
309(8)
4 Seepage Flows
317(76)
4.1 Introduction
319(5)
4.2 Picard Iteration
324(3)
4.2.1 Generalized Water Table Equation
324(2)
4.2.2 Particular Cases
326(1)
4.3 Dupuit--Fawer Equations
327(5)
4.3.1 Generalized Water Table Equation
327(3)
4.3.2 Particular Cases
330(2)
4.4 Polubarinova-Kochina's Rectangular Dam Seepage Problem
332(26)
4.4.1 Picard Iteration
332(12)
4.4.2 Validity of the Dupuit--Forchheimer Theory
344(6)
4.4.3 Shallow Flow Approximation
350(3)
4.4.4 Validity of Jaeger's Theory
353(3)
4.4.5 Dupuit---Fawer Equations
356(2)
4.5 Flow Through Trapezoidal Dam
358(2)
4.6 Drainage of Recharge
360(15)
4.6.1 Horizontal Aquifer
360(13)
4.6.2 Sloping Aquifer
373(1)
4.6.3 Curved Aquifer
374(1)
4.7 Flow Over Planar Bedrock with Slope Discontinuity
375(2)
4.8 Bank Storage Problem
377(16)
4.8.1 Picard's Iteration for Anisotropic Porous Media
377(6)
4.8.2 Analytical Solution and Numerical Method
383(5)
4.8.3 Validity of Second-Order Solutions
388(2)
References
390(3)
5 Viscous Channel Flows
393(170)
5.1 Introduction
398(4)
5.2 Boundary Layer Approximation
402(37)
5.2.1 Scale Effects of Round-Crested Weir Flow
402(24)
5.2.2 Developing Flow on Steep Slopes
426(13)
5.3 Undular Hydraulic Jump
439(40)
5.3.1 Introduction
439(7)
5.3.2 Depth-Averaged RANS Equations
446(11)
5.3.3 Serre's Theory
457(6)
5.3.4 Boundary Layer Model
463(3)
5.3.5 Simulations: Plane Undular Jump
466(7)
5.3.6 Simulations: Spatial Undular Jump
473(6)
5.4 Undular Weir Flow
479(2)
5.5 Hydraulic Jump
481(4)
5.5.1 Submerged Hydraulic Jump
481(3)
5.5.2 Classical Hydraulic Jump
484(1)
5.6 Boussinesq's Original Theory for Non-hydrostatic Turbulent Open-Channel Flows
485(28)
5.6.1 Introduction
485(1)
5.6.2 Equations of Motion
485(5)
5.6.3 Turbulent Velocity Profile
490(7)
5.6.4 Differential Equation Describing Water Surface Profiles
497(3)
5.6.5 Linearized Equation Valid for Water Depths Close to the Normal Depth
500(8)
5.6.6 Classification of Free Surface Profiles
508(2)
5.6.7 Boussinesq and the Solitary Wave
510(3)
5.7 Spatially Varied Flows
513(15)
5.7.1 Hydrodynamic Equations
513(4)
5.7.2 Side-Weir Flow
517(3)
5.7.3 Bottom Outlet Flow
520(4)
5.7.4 Side-Channel Flows
524(1)
5.7.5 Test Case: Flow Over Bottom Rack
524(4)
5.8 Compound Channel Flows
528(7)
5.8.1 Introduction to Gradually Varied Flow
528(3)
5.8.2 Extended Serre Theory
531(4)
5.9 Sand Solitary Wave
535(9)
5.9.1 Existence of Sand Solitary Waves
535(1)
5.9.2 Governing Equations
536(3)
5.9.3 Analytical Solution
539(5)
5.10 Dike Breaches
544(19)
5.10.1 Extended Serre Theory
544(7)
5.10.2 Experimental Investigation
551(2)
References
553(10)
6 Granular Flows
563(22)
6.1 Introduction
564(3)
6.2 Mixture Flow Equations
567(1)
6.3 Depth-averaged Equations for Dry Granular Flows
568(5)
6.3.1 ID Savage---Hutter Theory Down an Inclined Plane
568(3)
6.3.2 Effect of Bed-Normal Velocity
571(2)
6.4 Simplified Solutions
573(6)
6.4.1 Pseudo-uniform Flow Conditions
573(1)
6.4.2 Granular Solitary Wave
574(3)
6.4.3 Granular Free Overfall
577(2)
6.5 ID Hutter---Serre Enhanced Equations Down an Inclined Plane
579(6)
References
580(5)
7 Concluding Remarks
585(4)
References
587(2)
Appendix A Pressure Distribution in Flows Over Curved Bed 589(4)
Appendix B Second Picard Iteration Cycle in Cartesian Coordinates 593(6)
Appendix C Picard Iteration in Curvilinear Coordinates 599(8)
Appendix D Derivation of the Laplace Equation for the x-psi; Transformation 607(6)
Appendix E Plane Open-Channel Flow Using Flow Net-Based Coordinates 613(8)
Appendix F Specific Energy for Flow Over Curved Bottoms 621(10)
Appendix G Viscous Boussinesq-type equations 631(8)
Appendix H Non-hydrostatic Gradually Varied Flow on Steep Slopes 639(14)
Appendix I Derivation of Vertically Integrated Equations for Non-hydrostatic Mixture Flows 653(16)
Appendix J Layer-Integrated Equations for Mixture Flows 669(12)
Author Index 681(8)
Subject Index 689
Oscar Castro-Orgaz is a Professor of Hydraulic Engineering at the University of Córdoba, Spain. He has written more than 50 papers in peer-reviewed journals of hydraulics and fluid mechanics and serves as reviewer for the main journals on these topics. He is also Associate Editor of the Journal of Hydraulic Engineering ASCE, and Editorial Board Member of Environmental Fluid Mechanics, Springer. Willi H. Hager is Professor of Hydraulics at the Swiss Federal Institute of Technology, ETHZ. He has written more than 500 papers, of which more than half in peer-reviewed journal, mainly on open channel flows, pipe flows, scour, erosion, impulse waves, wastewater hydraulics and supercritical flows. He also wrote more than 20 books in these topics. He served from 2006 to 2011 as Editor of the Journal of Hydraulic Research, and was the recipient of various international awards.
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