Unsteady Flow in Open Channels 1st Edition by Jurjen Battjes, Robert Jan Labeur ISBN 9781316984215 1316984214

Unsteady Flow in Open Channels 1st Edition by Jurjen Battjes, Robert Jan Labeur  – Ebook PDF Instant Download/Delivery: 9781316984215 ,1316984214
Full download Unsteady Flow in Open Channels 1st Edition after payment

Product details:
ISBN 10: 1316984214
ISBN 13: 9781316984215
Author: Jurjen Battjes, Robert Jan Labeur

Unsteady Flow in Open Channels 1st Edition Table of contents:

1 Basic Equations for Long Waves

1.1 Approach

1.2 Schematization of the Cross Section

1.3 Mass Balance

1.4 Equations of Motion

1.4.1 Euler Equations

1.4.2 Flow Resistance

1.4.3 Momentum Balance

1.5 Summary of the Long-Wave Equations

Problems

2 Classification and Analysis of Long Waves

2.1 Types of Long Waves

2.1.1 Translatory Waves

2.1.2 Tsunamis

2.1.3 Seiches

2.1.4 Tides

2.1.5 Flood Waves in Rivers

2.2 A Condition for the Long-Wave Approximation

2.3 Estimation of Terms

2.3.1 Advective Acceleration Term

2.3.2 Resistance Term

2.4 Solution Methods

2.4.1 Complete Equations

2.4.2 Simplified Equations

Problems

3 Elementary Wave Equation

3.1 Simple Wave

3.1.1 Propagation

3.1.2 Balance Equations

Volume Balance

Momentum Balance

3.2 Elementary Wave Equation

3.2.1 Derivation

3.2.2 General Solution

3.2.3 Total Derivative

3.3 Relation between Discharge and Free-Surface Elevation in a Progressive Wave

3.4 Solution for Arbitrary Initial Conditions

3.5 Boundary Conditions

3.6 Periodic Progressive and Standing Waves

3.6.1 Infinitely Long Canal

3.6.2 Semi-Infinitely Long Canal with a Closed End

3.6.3 Closed Basin

3.6.4 Semi-Closed Basin Connected to a Reservoir or Tideless Sea

3.6.5 Semi-Closed Basin Connected to a Tidal Sea

Problems

4 Translatory Waves

4.1 Introduction

4.2 Low Translatory Waves in Uniform Channels

4.3 Propagation in Non-Uniform Canals

4.3.1 Rapidly Varying Cross Section

4.3.2 Gradually Varying Cross Section

4.4 Damping of Translatory Waves

4.5 High Translatory Waves

4.5.1 Wave Deformation

4.5.2 Tidal Bores

4.5.3 Bore Propagation

4.6 Field Observations

4.6.1 Observations in the Twenthekanaal

Layout

Primary Wave

Propagation and Reflection

Damping

4.6.2 Observations in the Approach Canal to the Lanaye Lock

Problems

5 Method of Characteristics

5.1 Introduction

5.2 Mathematical Formulation

5.3 Principle of Application

5.3.1 General Procedure

5.3.2 Characteristics

5.3.3 Boundary Conditions

Subcritical Flow

Supercritical Flow

Transcritical Flow

5.3.4 External Forces

5.4 Graphical Solution Procedure

5.4.1 Initial Value Problem

5.4.2 Inclusion of the Boundary Conditions

Boundary Types

Absorbing Boundaries

5.5 Simple Wave

5.5.1 General Solution

5.5.2 Expansion Wave

5.5.3 Compression Wave

Problems

6 Tidal Basins

6.1 Introduction

6.2 Mathematical Formulation

6.2.1 Motion in the Basin

6.2.2 Motion in the Channel

Rigid Column Approximation

Momentum Equation

6.2.3 Coupled System

6.3 Linearization of the Quadratic Resistance

6.4 System with Discrete Storage and Resistance

6.4.1 Governing Equation

6.4.2 Nonhomogeneous Solution

6.4.3 Explicit Solution

6.5 System with Discrete Storage, Resistance and Inertia

6.6 Solution through Complex Algebra

6.6.1 Complex Representation

6.6.2 Solution

Problems

7 Harmonic Wave Propagation

7.1 Introduction

7.2 Complex Representation of Damped Progressive Harmonic Waves

7.3 Formulation and General Solution

7.3.1 Formulation

7.3.2 General Solution

7.3.3 Solution of the Dispersion Equation

7.3.4 Solution for the Discharge

7.4 Unidirectional Propagation

7.4.1 Physical Interpretation

7.4.2 Propagation in Compound Channels

7.5 Bi-directional Wave Propagation

7.5.1 Relation between the Complex Amplitudes at the Ends of a Prismatic Section

7.5.2 Response Function of a Semi-Closed Prismatic Basin

7.6 Propagation in Non-Uniform Channels

7.6.1 Abrupt Channel Transition

7.6.2 Exponentially Varying Cross Section

Dispersion Equation

Unidirectional Wave Propagation

Morphological Equilibrium

7.7 Propagation in Networks

7.8 Nonlinear Effects

7.8.1 Tidal Wave Deformation

7.8.2 Mean Slope of the Free Surface

Problems

8 Flood Waves in Rivers

8.1 Introduction

8.2 Quasi-Steady Approximation

8.3 Quasi-Uniform Approximation

8.3.1 Formulation and General Solution

8.3.2 The High-Water Wave Speed

8.3.3 Kinematic Wave Behaviour

8.4 Influence of Variable Free-Surface Slope

8.4.1 Diffusion Model for Flood Waves

8.4.2 Elementary Solution

8.4.3 Observations

8.5 Discussion

Problems

9 Steady Flow

9.1 Rapidly Varying Flow

9.1.1 Scaling Analysis

9.1.2 Flow Patterns

Inflow Section

Minimal Cross Section

Outflow Section

9.1.3 Bernoulli Equation

9.1.4 Relations between Water Level and Discharge

Flow under a Gate

Broad-Crested Weir

Sharp-Crested Weir

9.1.5 Hydraulic Jump

9.2 Gradually Varying Flow

9.2.1 Governing Differential Equation

9.2.2 Integral Curves

9.2.3 Classification of Backwater Curves

9.2.4 Boundary Conditions

9.2.5 Explicit Representation

9.3 Uniform Flow

9.3.1 Equilibrium Relations

9.3.2 Resistance Relations

The Log Law

Chézy

Manning

Strickler

9.3.3 The Overall Resistance of a Channel

9.3.4 Applicability to Unsteady Flow

Problems

10 Transport Processes

10.1 Introduction

10.2 Generic Balance Equation

10.3 Molecular Diffusion

10.3.1 Fick’s Law of Diffusion

10.3.2 One-Dimensional Diffusion

Solution in an Infinite Domain

Solution in a Semi-Infinite Domain

Solution in a Finite Domain

10.3.3 The Random Walk Model

10.3.4 Two-Dimensional Diffusion

10.4 Advection and Molecular Diffusion

10.5 Turbulent Diffusion

10.5.1 Reynolds Averaging

10.5.2 Closure Hypothesis

10.6 Vertical Diffusion in Free-Surface Flows

10.6.1 Turbulence Diffusivity

10.6.2 Vertical Distribution of Horizontal Velocity

10.7 Horizontal Transport in Free-Surface Flows

10.7.1 Introduction

10.7.2 Two-Dimensional Horizontal Transport

Longitudinal Transport

Lateral Transport

Two-Dimensional Advection–Diffusion Equation

Case 1: Instantaneous Release at a Point

Case 2: Continuous Release at a Point

10.7.3 One-Dimensional Horizontal Transport

Case 3: Instantaneous Release in a Cross Section

Problems

11 Numerical Computation of Solutions

11.1 Introduction

11.2 Canal-Basin System

11.2.1 Model Equations

11.2.2 Discretization

11.2.3 Semi-implicit Method

Continuity Equation

Momentum Equation

11.2.4 Some Other Solution Methods

11.2.5 Properties of the Semi-implicit Method

Accuracy

Stability

Convergence

11.2.6 Python Implementation

Input and Initialization

Time Stepping

Output of Results

11.2.7 Verification

11.3 Semi-Implicit Method for Long Waves

11.3.1 Model Equations

11.3.2 Discretization

Spatial Domain

Time Domain

11.3.3 Semi-Implicit Method

Continuity Equation

Boundary Conditions

Momentum Equation

Inclusion of Momentum Advection

11.3.4 Some Other Solution Methods

Leapfrog Method

Implicit θ-Method

Preissmann Method

Finite Element Method

11.3.5 Properties of the Semi-Implicit Method

Accuracy and Consistency

Stability

Convergence

11.3.6 Python Implementation

Input and Initialization

Time Stepping

Output of Results

11.3.7 Verification

11.4 Characteristics-Based Methods

11.4.1 Characteristic Equations

11.4.2 Space–Time Discretization

11.4.3 Forward Time Backward Space Method

Interpolation

Boundary Conditions

Forcing Terms

Supercritical Flow

11.4.4 Some Other Characteristics-Based Methods

Higher-Order Interpolation

Implicit Interpolation

Flux Difference Splitting

11.4.5 Properties

Accuracy

Monotonicity and Stability

Convergence

11.4.6 Python Implementation

Initialization

Time Stepping

11.4.7 Verification

Problems

Appendix A Pressurized Flow in Closed Conduits

A.1 Introduction

A.2 Governing Equations

A.2.1 Constitutive Equations

Liquid Compressibility

Pipe Elasticity

A.2.2 Conservation of Mass

A.2.3 Conservation of Momentum

A.3 Pressure Waves in Pipelines

A.3.1 Characteristic Equations

A.3.2 Physical Behaviour

A.4 Closure Procedures

A.4.1 Abrupt Closure

A.4.2 Gradual Closure

A.4.3 Influence of Exit Losses and/or Wall Friction

A.4.4 Influence of Time Scales

Problems

Appendix B Summary of Formulas

One-Dimensional Shallow Water Equations

Elementary Wave Equation

Translatory Waves

Characteristic Method

Linearized Channel-Basin System

Harmonic Method

Flood Wave

Steady Flow

Transport

Pressurized Pipe Flow

References

Author Index

Subject Index

People also search for Unsteady Flow in Open Channels 1st Edition:

unsteady flow in open channels pdf

in open channels gradually varied flow is caused’

types of open channel flow

uniform flow in an open channel

Tags:

Jurjen Battjes,Robert Jan Labeur,Unsteady Flow,Open Channels