Geomorphological Fluid Mechanics (Lecture Notes in Physics, 582)

✍ Scribed by N.J. Balmforth (editor), A. Provenzale (editor)

• Publisher: Springer
• Year: 2001
• Tongue: English
• Leaves: 568
• Edition: 2001
• Category: Library

✦ Synopsis

Geomorphology deals with some of the most striking patterns of nature. From mountain ranges and mid-ocean ridges to river networks and sand dunes, there is a whole family of forms, structures, and shapes that demand rationalization as well as mathematical description. In the various chapters of this volume, many of these patterns are explored and discussed, and attempts are made to both unravel the reasons for their very existence and to describe their dynamics in quantitative terms. Particular focus is placed on lava and mud flows, ice and snow dynamics, river and coastal morphodynamics and landscape formation. Combining a pedagogical approach with up-to-date reviews of forefront research, this volume will serve both postgraduate students and lecturers in search of advanced textbook material, and experienced researchers wishing to get acquainted with the various physical and mathematical approaches in a range of closely related research fields.

✦ Table of Contents

Chapter 1
1.1 Introduction
1.2 Convection
1.2.1 Mathematical Formulation
1.2.2 Convective Instability
1.2.3 Weakly Nonlinear Convective Rolls
1.2.4 Extended Systems
1.3 Asymptotics, Galerkin Approximation and Conceptual Models
1.4 Solitary Waves in Conduits
1.5 Blown by Wind
1.5.1 Saltation and Reptation
1.5.2 A Minimal Model
1.6 Morals
Acknowledgements
References
Chapter 2
2.1 Introduction
2.2 Microstructure and Macroscopic Fluid Phenomena
2.3 Governing Equations
2.4 Constitutive Models
2.5 Generalized Newtonian Models
2.5.2 Variants and Deviants
2.5.3 Temperature Dependence
2.5.4 Concentration Dependence
2.5.5 Hysteresis
2.6 Viscoelasticity
2.7 Concluding Remarks
Acknowledgements
References
Chapter 3
3.1 Introduction
3.2 Rheometry
3.2.1 Standard viscometers
3.2.2 What Can Be Done Without a Rheometer?
3.3 The Contribution of Continuum Mechanics
3.4 Rheophysics
3.4.1 Definition of the Bulk Stress Tensor and Selected Applications
3.4.2 Approximate Models
3.4.3 Contribution of Dimensional Analysis
References
Chapter 4
4.1 Introduction
4.1.1 Some Distinctive Features of Granular Materials
4.1.2 Particle Size Segregation
4.1.3 Structure of Theories
4.2 Single-Phase Theories
4.2.1 Molecular Dynamics
4.2.2 Statistical Mechanics
4.2.3 Continuum Mechanical Models without Additional Balance Laws
4.2.4 Constitutive Theories with Additional Balance Laws
4.3 Other Models Based on Additional Balance Laws – Discussion
4.4 Concluding Remarks
Acknowledgement
References
Chapter 5
5.1 Introduction
5.2 Some Basic Assumptions and Deductions
5.2.1 The Rheology of the Mantle
5.2.2 Thermal Forcing and the Inevitability of Convection in the Mantle
5.2.3 Boundary Layersin Convection at High Rayleigh Numbers
5.3 Upwelling Thermals and Plumes
5.3.1 The Initiation of Convection at the Base of the Mantle
5.3.2 Isolated "Thermals"
5.3.3 Starting Plumes
5.3.4 Long-lived Plumes
5.3.5 Surface Uplift
5.4 Mantle Plumes and Surface Topography
5.4.1 Plume Fluxesfrom Hotspot Tracks
5.4.2 New Plumesand Flood Basalts
5.5 The Upper Boundary Layer
5.6 Synopsis
References
Chapter 6
6.1 Introduction
6.2 Viscous Fingering Instabilities
6.3 Dissolution Instability and Channelised Flow in Permeable Media
6.4 The Shapes of Free-Surface Yield-Strength Flows on a Slope
6.5 Instabilities of Solidifying Free-Surface Gravity Currents
6.6 Freezing Flows down a Slope
6.7 Conclusions
References
Chapter 7
7.1 Introduction
7.2 Mathematical Formulation
7.2.1 Governing Equations in Axisymmetrical Geometry
7.2.2 Boundary Conditions for Cooling, Expanding Domes
7.2.3 Thin-layer Theory
7.3 Isothermal Domes
7.3.1 Shallow Isothermal Domes
7.3.2 Restoring the Dimensions
7.3.3 Experiments
7.4 Flows on Inclined Planes
7.4.1 Shallow Flow Dynamics
7.4.2 Inclined Domes
7.4.3 Streams and Hulme’s Solution
7.5 Concluding Remarks
Acknowledgements
References
Chapter 8
8.1 Introduction
8.2 Ascent of Magma to the Surface
8.3 Eruption Column Models
8.4 Ash Flows
8.5 Analogue Laboratory Models
8.6 CO_2-Charged Lake Eruptions
8.7 Discussion
Acknowledgements
References
Chapter 9
9.1 Ice: Land, Sea and Air
9.2 Ice Flow: As Clear as Mud
9.3 Drumlins, Glaciers, Icebergs and Avalanches
Acknowledgements
References
Chapter 10
10.1 Introduction
10.2 Glacial Inventories
10.3 Glacial Campaigns
10.4 Mass Balances
10.5 Morphologic Variations Associated with the Regression
10.6 Conclusions
References
Chapter 11
11.1 Introduction
11.1.1 Motivation
11.1.2 A Descriptive View of Ice Sheet and Ice Shelf Flows
11.2 Fundamental Equations for Cold Ice Masses
11.3 Scale Analysis and Perturbation Scheme
11.3.1 Scaled Equations
11.3.2 Perturbation Scheme
11.3.3 Second Order Stress Formulas
11.4 Second Order Shallow Ice Approximation (SOSIA)
11.4.1 Velocity and Stress Deviator Fields
11.4.2 Updating the Geometry and T mperature Field
11.5 Some Results
11.6 Scale Analysis and Perturbation Scheme
11.6.1 Non-Dimensionalized Ice Shelf Equations
11.6.2 Zeroth Order Ice Shelf Equations
11.6.3 First Order Mechanical Ice Shelf Equations
11.7 First Order Shallow Shelf Approximation (FOSSA)
11.7.1 General Procedure
11.7.2 Determination of the T mperature Field
11.8 Closure
Acknowledgement
Appendix A1:Sliding and energy jump conditions at the basal surface
Appendix A2:SIA corrections to the sliding law
Appendix A3:Detailed equations for the FOSSA
References
Chapter 12
12.1 Introduction
12.1.1 The Link Between Iceberg Deterioration and Drift
12.1.2 Outline of the Chapter
12.2 Terminology – Classification of Shape and Size
12.2.1 Shape
12.2.2 Size Classifications of Tabular and Non-tabular Icebergs
12.2.3 Iceberg Geometry for Use in Drift and Deterioration Calculations
12.3 Iceberg Deterioration Mechanisms
12.3.1 Relative Importance of Various Mechanisms
12.3.2 Equations to Predict Deterioration Mechanisms
12.3.3 Validation of Deterioration Equations
12.4 Melt Deterioration of Bergy Bits and Growlers
12.4.1 Determination of Constants in Heat Flux Equation
12.5 Iceberg Life Expectancies
12.5.1 Computations Based on Deterioration Model
12.5.2 Empirical Model for Iceberg Life Expectancy
12.6 Ice Piece Size Distributions
12.6.1 Size Distributions of Newly Calved Ice Pieces
12.6.2 Evolution of Initial Calved Piece Size Distribution
12.6.3 Dispersion of Calved Small Ice Pieces from Parent Iceberg
12.7 Iceberg Dynamics and Drift
12.7.1 Introduction
12.7.2 Equations of Motion, Various Force Contributions
12.7.3 Comments Concerning Possible Errors and Uncertainties
12.7.4 Numerical Integration Schemes
12.8 Concluding Remarks
Acknowledgements
References
Chapter 13
13.1 Introduction
13.1.1 A Physical Picture of Avalanches
13.1.2 Avalanche Release
13.1.3 Avalanche Motion
13.2 Modelling Avalanches
13.2.1 Statistical Methods
13.2.2 Deterministic Approach (Avalanche-dynamics Models)
13.2.3 Small-scale Models
References
Chapter 14
14.1 Introduction
14.2 The Granular Avalanche Model of Savage & Hutter
14.2.1 Governing Equations in Conservative Form
14.2.2 Curvilinear Coordinate System
14.2.3 Depth Integration
14.2.4 Non-Dimensionalization and Ordering
14.2.5 Earth Pressure Coefficients
14.2.6 Model Equations in Conservative Form
14.3 Numerical Integration of the Savage–Hutter Equations
14.3.1 Standard Form of the Differential Equations and Characteristic Speeds
14.3.2 Remarks on Numerical Integration
14.4 Examples
14.4.1 Similarity Solutions
14.4.2 Motion of a Granular Avalanche on an Inclined Plane Chute into the Horizontal Run-Out Zone
14.4.3 Motion of a Granular Avalanche in a Convex and Concave Curved Chute
14.4.4 Granular Avalanche over Complex Basal Topography
14.5 Concluding Remarks
Acknowledgement
References
Chapter 15
15.1 Introduction
15.2 Bedform Phenomenology
15.3 Moving a Sandy Bottom
15.3.1 Initiation of Sediment Motion
15.3.2 Sediment Transport
15.4 A Shallow World
15.5 Rolling Shallowly Downhill
15.6 Sediment Instabilities in Shallow Water
15.7 Lagging Behind
15.8 Landscaping
15.8.1 Two-dimensional Instabilities
15.8.2 Channelization
15.9 Conclusion
Acknowledgements
References
Chapter 16
16.1 Formulation
16.2 Mass Conservation of the Solid Phase
16.3 Evolution Equation of the Bed Interface
16.4 Motion of the Solid Phase
16.4.1 Incipient Transport
16.4.2 Bedload Transport
16.4.3 Transport in Suspension
16.5 Conclusive Remarks
Acknowledgments
References
Chapter 17
17.1 Introduction
17.2 Wind Power
17.3 Classification of Sand Dunes
17.4 Dunes Accumulated and Controlled by Topographic Barriers
17.5 Self-accumulated Dunes
17.5.1 The Steady-state Dune Profile
17.5.2 Transverse and Barchan Dunes
17.5.3 Linear Seif Dunes
17.5.4 Hybrid Dunes
17.5.5 Star Dunes
17.6 Vegetated Dunes
17.6.1 Vegetated-linear Dunes
17.6.2 Parabolic Dunes
17.6.3 Foredunes
References
Chapter 18
18.1 Introduction
18.1.1 Dunes
18.1.2 Drumlins
18.2 Dunes
18.2.1 St. Venant Equations
18.2.2 Instability
18.2.3 The Orr–Sommerfeld Model
18.2.4 Orr–Sommerfeld–Exner–St. Venant Model
18.2.5 Well-posedness
18.2.6 The Canonical Dune Equation
18.2.7 Caveats
18.3 Drumlins
18.3.1 The Hindmarsh Model
18.3.2 Till Rheology and Flow
18.3.3 Fourier Integral Solution
18.3.4 Linear Stability
18.3.5 A Nonlinear Model
18.4 Discussion
Acknowledgements
References
Chapter 19
19.1 Introduction
19.2 Large-Scale Tidal Patterns
19.2.1 Estuaries
19.2.2 Wetlands
19.3 Mesoscale Patterns
19.3.1 Bars
19.3.2 Free Bars
19.3.3 Forced Bars
19.4 Small-Scale Patterns
19.5 Morphodynamic Equilibrium
19.5.1 Equilibrium of Tidal Channels
19.5.2 Equilibrium of Tidal Inlets
19.6 Morphodynamic Stability
19.6.1 The Formation of Tidal Free Bars
19.6.2 The Formation of Dunes in Tidal Channels
19.7 Morphodynamic Evolution
19.7.1 Evolution of Tidal Channels
19.7.2 Evolution of Tidal Flats and Salt Marshes
Acknowledgments
References
Chapter 20
20.1 Introduction
20.2 Linear Bragg Resonance by Rigid Bars
20.2.1 No Reflection from x > L
20.2.2 Finite Reflection from x_1 > L
20.3 Long Waves Generated by Short Waves Scattered by Bars
20.4 Sand-Bar Formation Dominated by Bedload
20.5 Laws of Bedload Transport
20.6 Fluid Flow
20.6.1 The Potential Core
20.6.2 The Boundary Layer
20.7 Properties of Bar Evolution Equation
20.8 Numerical Simulation of a Laboratory Experiment
20.9 Further Remarks on Sand Bars
20.9.1 On Scaling in Laboratory Experiments
20.9.2 Future Challenges on Sand-bar Theories
Acknowledgements
References
Chapter 21
Introduction
21.2 A Typology of Torrential Flows
21.2.1 The Watershed as a Complex Physical System
21.2.2 Types of Transport
21.3 Initiation, Motion, Effects of Debris Flow
21.3.1 Initiation
21.3.2 Motion
21.3.3 Deposition and Effects
21.4 Debris Flow Classiffcation
21.5 Modelling Debris Flows
21.5.1 Statistical Approach
21.5.2 Deterministic Approach
References
Chapter 22
22.1 Introduction
22.2 One-Dimensional Slow Flows
22.2.1 The Lubrication Approximation
22.2.2 Profiles of Final Deposit
22.2.3 Stationary Waves
22.2.4 Transient Collapse of Finite Mass
22.3 Two-Dimensional Slow Flow in a Wide Channel
22.3.1 The Lubrication Approximation
22.3.2 Steady Uniform Flow
22.3.3 Transient Spreading After Dam Collapse
22.4 Surges in High-Speed Flows
22.4.1 Boundary Layer Approximation and Depth-averaging
22.4.2 Linearized Instability of Uniform Flow
22.4.3 Roll Waves by Numerical Computation
22.5 Other Related Works
22.6 Future Challenges
Acknowledgements
References