Geophysical Fluid Dynamics - Understanding (Almost) Everything with Rotating Shallow Water Models
The book explains the key notions and fundamental processes in the dynamics of the fluid envelopes of the Earth (transposable to other planets), and methods of their analysis, from the unifying viewpoint of rotating shallow-water model (RSW). The model, in its one- or two-layer versions, plays a dis...
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| Language: | English |
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Oxford
Oxford University Press
2018
Oxford University Press, Incorporated |
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| ISBN: | 0198804334, 9780198804338 |
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| Abstract | The book explains the key notions and fundamental processes in the dynamics of the fluid envelopes of the Earth (transposable to other planets), and methods of their analysis, from the unifying viewpoint of rotating shallow-water model (RSW). The model, in its one- or two-layer versions, plays a distinguished role in geophysical fluid dynamics, having been used for around a century for conceptual understanding of various phenomena, for elaboration of approaches and methods, to be applied later in more complete models, for development and testing of numerical codes and schemes of data assimilations, and many other purposes. Principles of modelling of large-scale atmospheric and oceanic flows, and corresponding approximations, are explained and it is shown how single- and multi-layer versions of RSW arise from the primitive equations by vertical averaging, and how further time-averaging produces celebrated quasi-geostrophic reductions of the model. Key concepts of geophysical fluid dynamics are exposed and interpreted in RSW terms, and fundamentals of vortex and wave dynamics are explained in Part 1 of the book, which is supplied with exercises and can be used as a textbook. |
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| AbstractList | The book explains the key notions and fundamental processes in the dynamics of the fluid envelopes of the Earth (transposable to other planets), and methods of their analysis, from the unifying viewpoint of rotating shallow-water model (RSW). The model, in its one- or two-layer versions, plays a distinguished role in geophysical fluid dynamics, having been used for around a century for conceptual understanding of various phenomena, for elaboration of approaches and methods, to be applied later in more complete models, for development and testing of numerical codes and schemes of data assimilations, and many other purposes. Principles of modelling of large-scale atmospheric and oceanic flows, and corresponding approximations, are explained and it is shown how single- and multi-layer versions of RSW arise from the primitive equations by vertical averaging, and how further time-averaging produces celebrated quasi-geostrophic reductions of the model. Key concepts of geophysical fluid dynamics are exposed and interpreted in RSW terms, and fundamentals of vortex and wave dynamics are explained in Part 1 of the book, which is supplied with exercises and can be used as a textbook. Solutions of the problems are available at Editorial Office by request. In-depth treatment of dynamical processes, with special accent on the primordial process of geostrophic adjustment, on instabilities in geophysical flows, vortex and wave turbulence and on nonlinear wave interactions follows in Part 2. Recently arisen new approaches in, and applications of RSW, including moist-convective processes constitute Part 3. Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This book explains key notions and fundamental processes of the dynamics of large- and medium-scale atmospheric and oceanic motions from the unifying viewpoint of the rotating shallow water model. The model plays a distinguished role in geophysical fluid dynamics. It has been used for about a century for conceptualunderstanding of various phenomena, for elaboration of approaches and methods to be used later in more complete models, for development and testing of numerical codes, and for many other purposes. In spite of its simplicity, the model grasps essential features of the complete "primitive equations"models, being their vertically averaged version, and gives an intuitive representation and clear vision of principal dynamical processes. This book is a combination of a course on geophysical fluid dynamics (Part 1), with explanations and illustrations of fundamentals, and problems, as well as a more advanced treatise of a range of principal dynamical phenomena (Part 2), including recently arisen approaches and applications (Part 3). Mathematics and physics underlying dynamical phenomena are explained, with necessary demonstrations. Yet, an important goal of the book is to develop the reader's physical intuition and qualitativeinsights. For the dynamics of large and medium scale motions in the oceans and the atmosphere, a simplified rotating shallow water model, obtained by vertical averaging, is used throughout the book in order to explain the fundamentals, and to give in-depth treatment of important dynamical processes. The book explains the key notions and fundamental processes in the dynamics of the fluid envelopes of the Earth (transposable to other planets), and methods of their analysis, from the unifying viewpoint of rotating shallow-water model (RSW). The model, in its one- or two-layer versions, plays a distinguished role in geophysical fluid dynamics, having been used for around a century for conceptual understanding of various phenomena, for elaboration of approaches and methods, to be applied later in more complete models, for development and testing of numerical codes and schemes of data assimilations, and many other purposes. Principles of modelling of large-scale atmospheric and oceanic flows, and corresponding approximations, are explained and it is shown how single- and multi-layer versions of RSW arise from the primitive equations by vertical averaging, and how further time-averaging produces celebrated quasi-geostrophic reductions of the model. Key concepts of geophysical fluid dynamics are exposed and interpreted in RSW terms, and fundamentals of vortex and wave dynamics are explained in Part 1 of the book, which is supplied with exercises and can be used as a textbook. |
| Author | Zeitlin, Vladimir |
| Author_xml | – sequence: 1 fullname: Zeitlin, Vladimir |
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| Keywords | atmospheric and oceanic vortices instabilities in geophysical flows geophysical fluid dynamics rotating shallow water turbulence atmospheric and oceanic modelling oceanic and atmospheric waves |
| LCCN | 2017959942 |
| Language | English |
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| Notes | Includes bibliographical references and index |
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| Snippet | The book explains the key notions and fundamental processes in the dynamics of the fluid envelopes of the Earth (transposable to other planets), and methods of... For the dynamics of large and medium scale motions in the oceans and the atmosphere, a simplified rotating shallow water model, obtained by vertical averaging,... Geophysical fluid dynamics examines the dynamics of stratified and turbulent motion of fluids in the ocean and outer core, and of gases in the atmosphere. This... |
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| SubjectTerms | Earth Sciences Earth Sciences and Geography Fluid dynamics Geophysics Geophysics, Geodesy & Seismology |
| TableOfContents | Title Page
Preface
Table of Contents
1. Introduction
2. Primitive Equations Model
3. Simplifying Primitive Equations: Rotating Shallow-Water Models and Their Properties
4. Wave Motions in Rotating Shallow Water with Boundaries, Topography, at the Equator, and in Laboratory
5. Getting Rid of Fast Waves: Slow Dynamics
6. Vortex Dynamics on the f and Beta Plane and Wave Radiation by Vortices
7. Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods
8. Geostrophic Adjustment and Wave-Vortex (Non) Interaction
9. RSW Modons and Their Surprising Properties: RSW Turbulence
10. Instabilities of Jets and Fronts and Their Nonlinear Evolution
11. Instabilities in Cylindrical Geometry: Vortices and Laboratory Flows
12. Resonant Wave Interactions and Resonant Excitation of Wave-Guide Modes
13. Wave Turbulence
14. Rotating Shallow-Water Model with Horizontal Density and/or Temperature Gradients
15. Rotating Shallow-Water Models with Moist Convection
16. Rotating Shallow-Water Models with Full Coriolis Force
References
Index 6.1.4 Contour dynamics -- 6.1.5 Structure (Casimir)-preserving discretisations of vorticity equation in Fourier space -- 6.2 Quasi-geostrophic modons in the β- and f-plane approximations -- 6.2.1 Influence of the beta effect upon a monopolar vortex -- 6.2.2 Constructing QG modon solutions: one-layer case -- 6.2.3 Constructing QG modon solutions: two-layer case -- 6.3 A crash course in 2D turbulence -- 6.3.1 Reminder on statistical description of turbulence -- 6.3.2 Developed turbulence: energy and enstrophy cascades -- 6.4 When vortices emit waves: Lighthill radiation -- 6.4.1 2D hydrodynamics and vortex-pair solution in complex notation -- 6.4.2 Gravity waves in cylindrical geometry -- 6.4.3 Lighthill radiation -- 6.4.4 Back-reaction of wave radiation -- 6.4.5 Lighthill radiation in the presence of rotation -- 6.5 Summary, comments, and bibliographic remarks -- 6.6 Problems -- 7 Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods -- 7.1 One-layer model -- 7.1.1 1.5-dimensional one-layer RSW model -- 7.1.2 Lagrangian approach to the 1.5-dimensional model -- 7.1.3 Quasilinear and hyperbolic systems -- 7.1.4 Wave breaking in non-rotating and rotating one-layer RSW -- 7.1.5 Hydraulic theory applied to rotating shallow water -- 7.1.6 A brief description of finite-volume numerical methods for one-layer RSW -- 7.1.7 Illustration: breaking of equatorial waves -- 7.2 Two-layer model -- 7.2.1 1.5 dimensional two-layer RSW -- 7.2.2 Characteristic equation and loss of hyperbolicity -- 7.2.3 Rankine-Hugoniot conditions -- 7.2.4 A finite-volume numerical method for two-layer RSW -- 7.3 Summary, comments, and bibliographic remarks -- 7.4 Problems -- Part II Understanding Fundamental Dynamical Phenomena with Rotating Shallow-Water Models -- 8 Geostrophic Adjustment and Wave-Vortex (Non)Interaction 8.1 Geostrophic adjustment in the barotropic (one-layer) model -- 8.1.1 Quasi-geostrophic regime -- 8.1.2 Frontal geostrophic regime -- 8.2 Geostrophic adjustment in the baroclinic (two-layer) model -- 8.2.1 Quasi-geostrophic regime -- 8.2.2 Frontal geostrophic regime -- 8.3 Geostrophic adjustment in one dimension and the first idea of frontogenesis -- 8.3.1 Theoretical considerations -- 8.3.2 Numerical simulations: Rossby adjustment -- 8.4 Geostrophic adjustment in the presence of boundaries, topography, and at the equator -- 8.4.1 Geostrophic adjustment with a lateral boundary -- 8.4.2 Geostrophic adjustment over escarpment -- 8.4.3 Geostrophic adjustment in the equatorial beta plane -- 8.5 Summary, comments, and bibliographic remarks -- 9 RSW Modons and their Surprising Properties: RSW Turbulence -- 9.1 QG vs RSW modons: one-layer model -- 9.1.1 General properties of steady solutions -- 9.1.2 `Ageostrophic adjustment' of QG modons -- 9.1.3 Properties of RSW modons -- 9.2 QG vs RSW modons: two-layer model -- 9.2.1 Adjustment of barotropic QG modons -- 9.2.2 Adjustment of baroclinic QG modons -- 9.2.3 Adjustment of essentially ageostrophic modons -- 9.3 Shock modons -- 9.4 Interactions of RSW modons -- 9.4.1 2 modons → 2 modons collision -- 9.4.2 2 → 2 `loose' modon collision -- 9.4.3 2 modons → tripole collisions -- 9.4.4 2 modons → tripole + monopole collisions -- 9.4.5 Collisions of shock modons -- 9.5 2D vs RSW turbulence -- 9.5.1 Set-up and initialisations -- 9.5.2 General features of the evolution of the vortex system -- 9.5.3 Non-universality of RSW turbulence -- 9.6 Summary, comments, and bibliographic remarks -- 10 Instabilities of Jets and Fronts and their Nonlinear Evolution -- 10.1 Instabilities: general notions and techniques -- 10.1.1 Definitions and general concepts -- 10.1.2 (In)stability criteria for plane-parallel flows 4.2 Waves over topography/bathymetry far from lateral boundaries -- 4.2.1 Topographic waves -- 4.2.2 Mountain (lee) waves in RSW -- 4.3 Waves in outcropping flows -- 4.4 Equatorial waves -- 4.4.1 Equatorial waves in one-layer model -- 4.4.2 Waves in two-layer RSW with a rigid lid on the equatorial beta plane -- 4.5 Waves in rotating annulus -- 4.5.1 RSW in cylindrical geometry -- 4.5.2 Analytic solution of the eigenvalue problem -- 4.6 Summary, comments, and bibliographic remarks -- 4.7 Problems -- 5 Getting Rid of Fast Waves: Slow Dynamics -- 5.1 General properties of the horizontal motion. Geostrophic equilibrium -- 5.2 Slow dynamics in a one-layer model -- 5.2.1 Derivation of the QG equations -- 5.2.2 Rossby waves and vortex dynamics: β plane vs f plane -- 5.2.3 QG dynamics in the presence of topography. Mountain Rossby waves -- 5.2.4 Frontal geostrophic dynamics -- 5.3 Slow dynamics in the two-layer model with a rigid lid -- 5.3.1 Derivation of the QG equations -- 5.3.2 Rossby waves in the two-layer QG model -- 5.3.3 Baroclinic instability: first acquaintance -- 5.3.4 Frontal geostrophic regimes -- 5.4 Slow dynamics in two-layer model with a free surface -- 5.4.1 Equations of motion, parameters, and scaling -- 5.4.2 QG equations -- 5.5 Large-scale slow dynamics in the presence of wave guides -- 5.5.1 A reminder on multi-scale asymptotic expansions -- 5.5.2 Slow motions in the presence of a lateral boundary -- 5.5.3 Slow motions over escarpment -- 5.5.4 Slow motions at the equator -- 5.6 Summary, comments, and bibliographic remarks -- 5.7 Problems -- 6 Vortex Dynamics on the f and beta Plane and Wave Radiation by Vortices -- 6.1 Two-dimensional vortex dynamics -- 6.1.1 2D Euler equations in stream-function-vorticity variables -- 6.1.2 Lagrangian formulation of 2D hydrodynamics of a perfect fluid -- 6.1.3 Dynamics of point vortices 10.9 Summary, comments, and bibliographic remarks 10.1.3 Direct approach to linear stability analysis of plane-parallel and circular flows -- 10.2 Geostrophic barotropic and baroclinic instabilities of jets -- 10.2.1 Barotropic instability of a Bickley jet on the f plane -- 10.2.2 Baroclinic instability of a Bickley jet in the f plane -- 10.3 Ageostrophic instabilities in the Phillips model: Rossby-Kelvin and shear instabilities -- 10.4 Ageostrophic instabilities of jets and their nonlinear evolution -- 10.4.1 Linear stability -- 10.4.2 Nonlinear saturation of essentially ageostrophic instabilities -- 10.4.3 A brief summary of the results on essentially ageostrophic instabilities of mid-latitude jets -- 10.5 Understanding the nature of inertial instability -- 10.6 Instabilities of jets at the equator and their nonlinear evolution, with emphasis on inertial instability -- 10.6.1 Linear stability and nonlinear saturation of instabilities in one-layer RSW model at the equator -- 10.6.2 Linear stability and nonlinear saturation of instabilities in two-layer RSW model at the equator -- 10.6.3 A brief summary of the results on instabilities of equatorial jets -- 10.7 Instabilities of coastal currents and their nonlinear evolution -- 10.7.1 Passive lower layer: results of the linear stability analysis -- 10.7.2 Passive lower layer: nonlinear evolution of the instability -- 10.7.3 Active lower layer: results of linear stability analysis -- 10.7.4 Active lower layer: nonlinear saturation of instabilities -- 10.7.5 A brief summary of the results on instabilities of coastal currents -- 10.8 Instabilities of double-density fronts and the role of topography -- 10.8.1 Set-up, scaling, parameters, and boundary conditions -- 10.8.2 Linear stability analysis -- 10.8.3 Nonlinear saturation of the instabilities -- 10.8.4 A brief summary of the results on instabilities of double fronts over topography Intro -- Part I Modelling Large-scale Oceanic and Atmospheric Flows: From Primitive to Rotating Shallow-Water Equations and Beyond -- 1 Introduction -- 2 Primitive Equations Model -- 2.1 Preliminaries -- 2.2 A crash course in fluid dynamics -- 2.2.1 The perfect fluid -- 2.2.2 Real fluids: incorporating molecular transport -- 2.3 Rotation, sphericity, and tangent plane approximation -- 2.3.1 Hydrodynamics in the rotating frame with gravity -- 2.3.2 Hydrodynamics in spherical coordinates and the `traditional' approximation in GFD -- 2.3.3 The tangent plane approximation -- 2.4 Primitive equations in the oceanic and atmospheric context -- 2.4.1 Oceanic context -- 2.4.2 Atmospheric context -- 2.4.3 Remarkable properties of the PE dynamics -- 2.4.4 What do we lose by assuming hydrostatics? -- 2.5 Summary, comments, and bibliographic remarks -- 2.6 Problems -- 3 Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties -- 3.1 Vertical averaging of horizontal momentum and mass conservation equations -- 3.2 Archetype models -- 3.2.1 One-layer RSW model -- 3.2.2 Two-layer RSW model with a rigid lid -- 3.2.3 Two-layer RSW model with a free upper surface -- 3.2.4 RSW model on the sphere -- 3.3 Vortices and waves in rotating shallow-water models -- 3.3.1 One-layer RSW model -- 3.3.2 Two-layer RSW model -- 3.4 Lagrangian approach and variational principles for shallow-water models -- 3.4.1 Lagrangian formulation of one-layer RSW -- 3.4.2 Lagrangian formulation of two-layer RSW -- 3.5 Summary, comments, and bibliographic remarks -- 3.6 Problems -- 4 Wave Motions in Rotating Shallow Water with Boundaries, Topography, at the Equator, and in Laboratory -- 4.1 Introducing lateral boundaries and shelf -- 4.1.1 Kelvin waves in RSW with an idealised coast -- 4.1.2 Waves in RSW with idealised coast and a shelf |
| Title | Geophysical Fluid Dynamics - Understanding (Almost) Everything with Rotating Shallow Water Models |
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