Instability in Geophysical Flows

Instability in Geophysical Flows

Instabilities are present in all natural fluids from rivers to atmospheres. This book considers the physical processes that generate instability. Part I describes the normal mode instabilities most important in geophysical applications, including convection, shear instability and baroclinic instabil...

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Detalles Bibliográficos
Otros Autores: Smyth, William D., 1955- author (author), Carpenter, Jeffrey R., 1979- author
Formato: Libro electrónico
Idioma:Inglés
Publicado: Cambridge, England : Cambridge University Press [2019]
Edición:First edition
Colección:Physical Sciences
Materias:
Geodynamics.
Geophysics.
Marine geophysics.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009645337806719
Tabla de Contenidos:
  • Cover
  • Half-title page
  • Title page
  • Copyright page
  • Contents
  • Preface
  • Acknowledgments
  • Part I Normal Mode Instabilities
  • 1 Preliminaries
  • 1.1 What Is Instability?
  • 1.2 Goals
  • 1.3 Tools
  • 1.4 Numerical Solution of a Boundary Value Problem
  • 1.5 The Equations of Motion
  • 1.6 Further Reading
  • 1.7 Appendix: A Closer Look at Perturbation Theory
  • 2 Convective Instability
  • 2.1 The Perturbation Equations
  • 2.2 Simple Case: Inviscid, Nondiffusive, Unbounded Fluid
  • 2.3 Viscous and Diffusive Effects
  • 2.4 Boundary Effects: the Rayleigh-Benard Problem
  • 2.5 Nonlinear Effects
  • 2.6 Summary
  • 2.7 Appendix: Waves and Convection in a Compressible Fluid
  • 3 Instabilities of a Parallel Shear Flow
  • 3.1 The Perturbation Equations
  • 3.2 Rayleigh's Equation
  • 3.3 Analytical Example: the Piecewise-Linear Shear Layer
  • 3.4 Solution Types for Rayleigh's Equation
  • 3.5 Numerical Solution of Rayleigh's Equation
  • 3.6 Shear Scaling
  • 3.7 Oblique Modes and Squire Transformations
  • 3.8 Rules of Thumb for a General Shear Instability
  • 3.9 Numerical Examples
  • 3.10 Perturbation Energetics
  • 3.11 Necessary Conditions for Instability
  • 3.12 The Wave Resonance Mechanism of Shear Instability
  • 3.13 Quantitative Analysis of Wave Resonance
  • 3.14 Summary
  • 3.15 Appendix: Classical Proof of the Rayleigh and Fjørtoft Theorems
  • 3.16 Further Reading
  • 4 Parallel Shear Flow: the Effects of Stratification
  • 4.1 The Richardson Number
  • 4.2 Equilibria and Perturbations
  • 4.3 Oblique Modes
  • 4.4 The Taylor-Goldstein Equation
  • 4.5 Application to Internal Wave Phenomena
  • 4.6 Analytical Examples of Instability in Stratified Shear Flows
  • 4.7 The Miles-Howard Theorem
  • 4.8 Howard's Semicircle Theorem
  • 4.9 Energetics
  • 4.10 Summary
  • 4.11 Further Reading
  • 4.12 Appendix: Veering Flows
  • 4.13 Appendix: Spatial Growth.
  • 5 Parallel Shear Flow: the Effects of Viscosity
  • 5.1 Conditions for Equilibrium
  • 5.2 Conditions for Quasi-Equilibrium: the Frozen Flow Approximation
  • 5.3 The Orr-Sommerfeld Equation
  • 5.4 Boundary Conditions for Viscous Fluid
  • 5.5 Numerical Solution of the Orr-Sommerfeld Equation
  • 5.6 Oblique Modes
  • 5.7 Shear Scaling and the Reynolds Number
  • 5.8 Numerical Examples
  • 5.9 Perturbation Energetics in Viscous Flow
  • 5.10 Summary
  • 6 Synthesis: Viscous, Diffusive, Inhomogeneous, Parallel Shear Flow
  • 6.1 Expanding the Basic Equations
  • 6.2 Numerical Solution
  • 6.3 2D and Oblique Modes: Squire Transformations
  • 6.4 Shear and Diffusion Scalings
  • 6.5 Application: Instabilities of a Stably Stratified Shear Layer
  • 6.6 Application: Analysis of Observational Data
  • 6.7 Summary
  • 6.8 Further Reading
  • 7 Nonparallel Flow: Instabilities of a Cylindrical Vortex
  • 7.1 Cyclostrophic Equilibrium
  • 7.2 The Perturbation Equations
  • 7.3 Barotropic Modes (m = 0)
  • 7.4 Axisymmetric Modes (l = 0)
  • 7.5 Analytical Example: the Rankine Vortex
  • 7.6 Numerical Example: a Continuous Vortex
  • 7.7 Wave Interactions in Barotropic Vortices
  • 7.8 Mechanisms of Centrifugal and Convective Instabilities
  • 7.9 Swirling Flows
  • 7.10 Summary
  • 7.11 Further Reading
  • 8 Instability in a Rotating Environment
  • 8.1 Frontal Zones
  • 8.2 Geostrophic Equilibrium and the Thermal Wind Balance
  • 8.3 The Perturbation Equations
  • 8.4 Energetics
  • 8.5 The Vertical Vorticity Equation
  • 8.6 Analytical Solution #1: Inertial and Symmetric Instabilities
  • 8.7 Analytical Solution #2: Baroclinic Instability
  • 8.8 Numerical Solution Method
  • 8.9 Instability in the Ageostrophic Regime
  • 8.10 Summary
  • 8.11 Further Reading
  • 9 Convective Instability in Complex Fluids
  • 9.1 Conditional Instability in a Moist Atmosphere or a Freezing Ocean.
  • 9.2 Double Diffusive Instabilities
  • 9.3 Bioconvection
  • 9.4 CO[sub(2)] Sequestration
  • 10 Summary
  • 10.1 Equilibrium States
  • 10.2 Instabilities
  • Part II The View Ahead
  • 11 Beyond Normal Modes
  • 11.1 Instability as an Initial Value Problem
  • 11.2 Transient Growth in Simple Linear Systems
  • 11.3 Computing the Optimal Initial Condition
  • 11.4 Optimizing Growth at t = 0[sup(+)]
  • 11.5 Growth at Short and Long Times: a Simple Example
  • 11.6 Example: The Piecewise Shear Layer
  • 11.7 Mechanics of Transient Growth in a Shear Layer
  • 11.8 Generalizing the Inner Product
  • 11.9 Summary
  • 11.10 Appendix: Singular Value Decomposition
  • 11.11 Further Reading
  • 12 Instability and Turbulence
  • 12.1 Secondary Instabilities and the Transition to Turbulence
  • 12.2 Turbulence-Driven Instabilities
  • 12.3 Cyclic Instability
  • 12.4 Further Reading
  • 13 Refining the Numerical Methods
  • 13.1 Higher-Order Finite Differences
  • 13.2 Finite Differences on an Adaptive Grid
  • 13.3 Galerkin Methods
  • 13.4 The Shooting Method
  • 13.5 Generalizations
  • 13.6 Further Reading
  • Appendix A Homework Exercises
  • Appendix B Projects
  • References
  • Index.

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