Muutke küpsiste eelistusi

Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water models [Kõva köide]

(Professor Emeritus, Sorbonne University)
  • Formaat: Hardback, 512 pages, kõrgus x laius x paksus: 249x177x30 mm, kaal: 1116 g, Over 230 illustrations
  • Ilmumisaeg: 15-Feb-2018
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198804334
  • ISBN-13: 9780198804338
Teised raamatud teemal:
Geophysical Fluid Dynamics: Understanding (almost) everything with rotating shallow water modelsSuurem pilt
  • Formaat: Hardback, 512 pages, kõrgus x laius x paksus: 249x177x30 mm, kaal: 1116 g, Over 230 illustrations
  • Ilmumisaeg: 15-Feb-2018
  • Kirjastus: Oxford University Press
  • ISBN-10: 0198804334
  • ISBN-13: 9780198804338
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780198804338.html
Märksõnad:
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 conceptual understanding 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 qualitative insights.
Part I: Modelling Large-scale Oceanic and Atmospheric Flows: From Primitive to Rotating Shallow-Water Equations and Beyond
1 Introduction
3(3)
2 Primitive Equations Model
6(23)
2.1 Preliminaries
6(1)
2.2 A crash course in fluid dynamics
6(8)
2.2.1 The perfect fluid
6(7)
2.2.2 Real fluids: incorporating molecular transport
13(1)
2.3 Rotation, sphericity, and tangent plane approximation
14(3)
2.3.1 Hydrodynamics in the rotating frame with gravity
14(1)
2.3.2 Hydrodynamics in spherical coordinates and the 'traditional' approximation in GFD
15(2)
2.3.3 The tangent plane approximation
17(1)
2.4 Primitive equations in the oceanic and atmospheric context
17(10)
2.4.1 Oceanic context
18(1)
2.4.2 Atmospheric context
19(3)
2.4.3 Remarkable properties of the PE dynamics
22(4)
2.4.4 What do we lose by assuming hydrostatics?
26(1)
2.5 Summary, comments, and bibliographic remarks
27(1)
2.6 Problems
28(1)
3 Simplifying Primitive Equations: Rotating Shallow-Water Models and their Properties
29(20)
3.1 Vertical averaging of horizontal momentum and mass conservation equations
29(4)
3.2 Archetype models
33(3)
3.2.1 One-layer RSW model
33(1)
3.2.2 Two-layer RSW model with a rigid lid
34(1)
3.2.3 Two-layer RSW model with a free upper surface
34(2)
3.2.4 RSW model on the sphere
36(1)
3.3 Vortices and waves in rotating shallow-water models
36(6)
3.3.1 One-layer RSW model
36(4)
3.3.2 Two-layer RSW model
40(2)
3.4 Lagrangian approach and variational principles for shallow-water models
42(5)
3.4.1 Lagrangian formulation of one-layer RSW
42(4)
3.4.2 Lagrangian formulation of two-layer RSW
46(1)
3.5 Summary, comments, and bibliographic remarks
47(1)
3.6 Problems
48(1)
4 Wave Motions in Rotating Shallow Water with Boundaries, Topography, at the Equator, and in Laboratory
49(37)
4.1 Introducing lateral boundaries and shelf
49(8)
4.1.1 Kelvin waves in RSW with an idealised coast
49(3)
4.1.2 Waves in RSW with idealised coast and a shelf
52(5)
4.2 Waves over topography/bathymetry far from lateral boundaries
57(5)
4.2.1 Topographic waves
57(2)
4.2.2 Mountain (lee) waves in RSW
59(3)
4.3 Waves in outcropping flows
62(5)
4.4 Equatorial waves
67(10)
4.4.1 Equatorial waves in one-layer model
67(8)
4.4.2 Waves in two-layer RSW with a rigid lid on the equatorial beta plane
75(2)
4.5 Waves in rotating annulus
77(6)
4.5.1 RSW in cylindrical geometry
77(2)
4.5.2 Analytic solution of the eigenvalue problem
79(4)
4.6 Summary, comments, and bibliographic remarks
83(2)
4.7 Problems
85(1)
5 Getting Rid of Fast Waves: Slow Dynamics
86(31)
5.1 General properties of the horizontal motion. Geostrophic equilibrium
86(2)
5.2 Slow dynamics in a one-layer model
88(8)
5.2.1 Derivation of the QG equations
88(2)
5.2.2 Rossby waves and vortex dynamics: beta plane vs f plane
90(1)
5.2.3 QG dynamics in the presence of topography. Mountain Rossby waves
91(4)
5.2.4 Frontal geostrophic dynamics
95(1)
5.3 Slow dynamics in the two-layer model with a rigid lid
96(5)
5.3.1 Derivation of the QG equations
96(2)
5.3.2 Rossby waves in the two-layer QG model
98(1)
5.3.3 Baroclinic instability: first acquaintance
98(2)
5.3.4 Frontal geostrophic regimes
100(1)
5.4 Slow dynamics in two-layer model with a free surface
101(1)
5.4.1 Equations of motion, parameters, and scaling
101(1)
5.4.2 QG equations
102(1)
5.5 Large-scale slow dynamics in the presence of wave guides
102(12)
5.5.1 A reminder on multi-scale asymptotic expansions
102(1)
5.5.2 Slow motions in the presence of a lateral boundary
103(3)
5.5.3 Slow motions over escarpment
106(2)
5.5.4 Slow motions at the equator
108(6)
5.6 Summary, comments, and bibliographic remarks
114(2)
5.7 Problems
116(1)
6 Vortex Dynamics on the f and beta Plane and Wave Radiation by Vortices
117(27)
6.1 Two-dimensional vortex dynamics
117(7)
6.1.1 2D Euler equations in stream-function-vorticity variables
117(2)
6.1.2 Lagrangian formulation of 2D hydrodynamics of a perfect fluid
119(1)
6.1.3 Dynamics of point vortices
120(1)
6.1.4 Contour dynamics
121(1)
6.1.5 Structure (Casimir)-preserving discretisations of vorticity equation in Fourier space
122(2)
6.2 Quasi-geostrophic modons in the 0-and f-plane approximations
124(10)
6.2.1 Influence of the beta effect upon a monopolar vortex
124(1)
6.2.2 Constructing QG modon solutions: one-layer case
125(2)
6.2.3 Constructing QG modon solutions: two-layer case
127(7)
6.3 A crash course in 2D turbulence
134(3)
6.3.1 Reminder on statistical description of turbulence
134(2)
6.3.2 Developed turbulence: energy and enstrophy cascades
136(1)
6.4 When vortices emit waves: Lighthill radiation
137(5)
6.4.1 2D hydrodynamics and vortex-pair solution in complex notation
138(1)
6.4.2 Gravity waves in cylindrical geometry
138(1)
6.4.3 Lighthill radiation
139(1)
6.4.4 Back-reaction of wave radiation
140(1)
6.4.5 Lighthill radiation in the presence of rotation
141(1)
6.5 Summary, comments, and bibliographic remarks
142(1)
6.6 Problems
143(1)
7 Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods
144(25)
7.1 One-layer model
145(14)
7.1.1 1.5-dimensional one-layer RSW model
145(1)
7.1.2 Lagrangian approach to the 1.5-dimensional model
145(2)
7.1.3 Quasilinear and hyperbolic systems
147(1)
7.1.4 Wave breaking in non-rotating and rotating one-layer RSW
148(2)
7.1.5 Hydraulic theory applied to rotating shallow water
150(3)
7.1.6 A brief description of finite-volume numerical methods for one-layer RSW
153(5)
7.1.7 Illustration: breaking of equatorial waves
158(1)
7.2 Two-layer model
159(5)
7.2.1 1.5 dimensional two-layer RSW
159(1)
7.2.2 Characteristic equation and loss of hyperbolicity
160(2)
7.2.3 Rankine-Hugoniot conditions
162(1)
7.2.4 A finite-volume numerical method for two-layer RSW
163(1)
7.3 Summary, comments, and bibliographic remarks
164(2)
7.4 Problems
166(3)
Part II: Understanding Fundamental Dynamical Phenomena with Rotating Shallow-Water Models
8 Geostrophic Adjustment and Wave-Vortex (Non)Interaction
169(28)
8.1 Geostrophic adjustment in the barotropic (one-layer) model
169(11)
8.1.1 Quasi-geostrophic regime
169(6)
8.1.2 Frontal geostrophic regime
175(5)
8.2 Geostrophic adjustment in the baroclinic (two-layer) model
180(3)
8.2.1 Quasi-geostrophic regime
180(1)
8.2.2 Frontal geostrophic regime
181(2)
8.3 Geostrophic adjustment in one dimension and the first idea of frontogenesis
183(8)
8.3.1 Theoretical considerations
183(6)
8.3.2 Numerical simulations: Rossby adjustment
189(2)
8.4 Geostrophic adjustment in the presence of boundaries, topography, and at the equator
191(3)
8.4.1 Geostrophic adjustment with a lateral boundary
191(1)
8.4.2 Geostrophic adjustment over escarpment
191(1)
8.4.3 Geostrophic adjustment in the equatorial beta plane
192(2)
8.5 Summary, comments, and bibliographic remarks
194(3)
9 RSW Modons and their Surprising Properties: RSW Turbulence
197(24)
9.1 QG vs RSW modons: one-layer model
197(6)
9.1.1 General properties of steady solutions
197(1)
9.1.2 'Ageostrophic adjustment' of QG modons
198(3)
9.1.3 Properties of RSW modons
201(2)
9.2 QG vs RSW modons: two-layer model
203(3)
9.2.1 Adjustment of barotropic QG modons
203(1)
9.2.2 Adjustment of baroclinic QG modons
204(1)
9.2.3 Adjustment of essentially ageostrophic modons
204(2)
9.3 Shock modons
206(2)
9.4 Interactions of RSW modons
208(5)
9.4.1 2 modons --> 2 modons collision
209(1)
9.4.2 2 --> 2 'loose' modon collision
209(1)
9.4.3 2 modons --> tripole collisions
210(1)
9.4.4 2 modons --> tripole + monopole collisions
210(3)
9.4.5 Collisions of shock modons
213(1)
9.5 2D vs RSW turbulence
213(6)
9.5.1 Set-up and initialisations
214(1)
9.5.2 General features of the evolution of the vortex system
215(3)
9.5.3 Non-universality of RSW turbulence
218(1)
9.6 Summary, comments, and bibliographic remarks
219(2)
10 Instabilities of Jets and Fronts and their Nonlinear Evolution
221(68)
10.1 Instabilities: general notions and techniques
221(5)
10.1.1 Definitions and general concepts
221(2)
10.1.2 (In)stability criteria for plane-parallel flows
223(2)
10.1.3 Direct approach to linear stability analysis of plane-parallel and circular flows
225(1)
10.2 Geostrophic barotropic and baroclinic instabilities of jets
226(6)
10.2.1 Barotropic instability of a Bickley jet on the f plane
226(2)
10.2.2 Baroclinic instability of a Bickley jet in the f plane
228(4)
10.3 Ageostrophic instabilities in the Phillips model: Rossby-Kelvin and shear instabilities
232(3)
10.4 Ageostrophic instabilities of jets and their nonlinear evolution
235(9)
10.4.1 Linear stability
235(6)
10.4.2 Nonlinear saturation of essentially ageostrophic instabilities
241(3)
10.4.3 A brief summary of the results on essentially ageostrophic instabilities of mid-latitude jets
244(1)
10.5 Understanding the nature of inertial instability
244(4)
10.6 Instabilities of jets at the equator and their nonlinear evolution, with emphasis on inertial instability
248(13)
10.6.1 Linear stability and nonlinear saturation of instabilities in one-layer RSW model at the equator
248(6)
10.6.2 Linear stability and nonlinear saturation of instabilities in two-layer RSW model at the equator
254(6)
10.6.3 A brief summary of the results on instabilities of equatorial jets
260(1)
10.7 Instabilities of coastal currents and their nonlinear evolution
261(14)
10.7.1 Passive lower layer: results of the linear stability analysis
261(1)
10.7.2 Passive lower layer: nonlinear evolution of the instability
262(4)
10.7.3 Active lower layer: results of linear stability analysis
266(3)
10.7.4 Active lower layer: nonlinear saturation of instabilities
269(4)
10.7.5 A brief summary of the results on instabilities of coastal currents
273(2)
10.8 Instabilities of double-density fronts and the role of topography
275(9)
10.8.1 Set-up, scaling, parameters, and boundary conditions
275(2)
10.8.2 Linear stability analysis
277(3)
10.8.3 Nonlinear saturation of the instabilities
280(3)
10.8.4 A brief summary of the results on instabilities of double fronts over topography
283(1)
10.9 Summary, comments, and bibliographic remarks
284(5)
11 Instabilities in Cylindrical Geometry: Vortices and Laboratory Flows
289(49)
11.1 Axisymmetric vortex solutions in rotating shallow water
290(2)
11.1.1 One-layer model
290(1)
11.1.2 Two-layer model
291(1)
11.2 Instabilities of isolated quasi-geostrophic vortices and their nonlinear evolution
292(7)
11.2.1 One-layer configuration, barotropic vortices
292(3)
11.2.2 Two-layer configuration, baroclinic upper-layer vortex
295(4)
11.3 Instabilities of ageostrophic vortices and their nonlinear evolution
299(11)
11.3.1 General considerations
299(1)
11.3.2 Results of the linear stability analysis
300(5)
11.3.3 Nonlinear saturation of the instabilities
305(5)
11.4 Instabilities of intense hurricane-like vortices and their nonlinear evolution
310(7)
11.4.1 Idealised rotating shallow-water hurricane
311(2)
11.4.2 Results of the linear stability analysis
313(1)
11.4.3 Nonlinear saturation of the hurricane's instability
314(3)
11.4.4 A brief summary of the results on instabilities of idealised hurricanes
317(1)
11.5 Instabilities of laboratory flows in rotating annuli
317(19)
11.5.1 Stability of two-layer flows under the rigid lid
317(8)
11.5.2 Stability of flows in rotating annulus with outcropping and topography
325(10)
11.5.3 A brief summary of the results of analysis of instabilities in the rotating annulus
335(1)
11.6 Summary, comments, and bibliographic remarks
336(2)
12 Resonant Wave Interactions and Resonant Excitation of Wave-guide Modes
338(41)
12.1 Resonant wave triads: first acquaintance
338(3)
12.1.1 Perturbation theory for Rossby waves
338(2)
12.1.2 Wave resonances and wave modulation
340(1)
12.2 Resonant excitation of trapped coastal waves by free inertia-gravity waves
341(23)
12.2.1 Resonant excitation of wave-guide modes: general philosophy
341(1)
12.2.2 Resonant excitation of Kelvin waves by free inertia-gravity waves at abrupt shelf: barotropic model
342(5)
12.2.3 Resonant excitation of Kelvin waves by free inertia-gravity waves at abrupt shelf: baroclinic model
347(8)
12.2.4 Resonant excitation of coastal waves by free inertia-gravity waves at the shelf with gentle slope
355(9)
12.3 Resonant excitation of baroclinic Rossby and Yanai waves in the equatorial wave guide
364(12)
12.3.1 Reminder on two-layer equatorial RSW and general conditions of removal of resonances
364(1)
12.3.2 Wave-wave resonances
365(7)
12.3.3 Wave mean current resonances
372(4)
12.4 Summary, comments, and bibliographic remarks
376(3)
13 Wave Turbulence
379(30)
13.1 The main hypotheses and ideas of the wave turbulence approach
379(10)
13.1.1 A reminder on Hamiltonian description of wave systems
379(4)
13.1.2 The principal idea of wave turbulence approach
383(1)
13.1.3 Kinetic equations for decay and non-decay dispersion laws
383(1)
13.1.4 Exact solutions of kinetic equations
384(4)
13.1.5 Conservation laws and dimensional estimates
388(1)
13.2 Applications of the wave turbulence theory to waves in rotating shallow water
389(12)
13.2.1 Wave turbulence of inertia-gravity waves on the f plane
389(4)
13.2.2 Weak turbulence of short inertia-gravity waves on the equatorial 8 plane
393(6)
13.2.3 Weak turbulence of the Rossby waves on the $ plane
399(2)
13.3 Turbulence of inertia-gravity waves in rotating shallow water: theory vs numerical experiment
401(2)
13.4 Historical comments, summary, and bibliographic remarks
403(6)
Part III: Generalisations of Standard Rotating Shallow-water Model, and their Applications
14 Rotating Shallow-Water model with Horizontal Density and/or Temperature Gradients
409(12)
14.1 Derivation of the thermal rotating shallow-water model and its properties
409(5)
14.1.1 Derivation of the model
409(2)
14.1.2 Gas dynamics analogy
411(1)
14.1.3 Waves and vortices
411(1)
14.1.4 Quasi-geostrophic TRSW
412(1)
14.1.5 Variational principle for TRSW
413(1)
14.2 Instabilities of jets and vortices in thermal rotating shallow water
414(5)
14.2.1 New instabilities in TRSW: first example
414(1)
14.2.2 Instabilities of thermal vortices in TRSW
414(1)
14.2.3 Stationary vortex solutions
415(1)
14.2.4 Results of the linear stability analysis of a thermal cyclone
415(3)
14.2.5 Nonlinear saturation of the instability
418(1)
14.2.6 Discussion of the results
419(1)
14.3 Summary, comments, and bibliographic remarks
419(2)
15 Rotating Shallow-Water Models with Moist Convection
421(25)
15.1 Constructing moist-convective shallow-water models
421(6)
15.1.1 General context and philosophy of the approach
421(1)
15.1.2 Introducing moisture in primitive equations
422(1)
15.1.3 Vertical averaging with convective fluxes
422(2)
15.1.4 Linking convection and condensation
424(1)
15.1.5 Surface evaporation and its parameterisations
425(1)
15.1.6 Two-layer model with a dry upper layer and its one-layer limit
426(1)
15.2 Properties of moist-convective RSW models
427(3)
15.2.1 Limiting cases
427(2)
15.2.2 Conservation laws
429(1)
15.3 Mathematics of moist-convective rotating shallow water
430(4)
15.3.1 Quasilinear form and characteristic equations
430(2)
15.3.2 Discontinuities and Rankine-Hugoniot conditions
432(1)
15.3.3 Illustration: wave scattering on a moisture front
432(2)
15.4 Applications to 'moist' instabilities of geostrophic jets and vortices
434(5)
15.4.1 Moist instability of the baroclinic Bickley jet
434(1)
15.4.2 Moist instability of geostrophic vortices
435(4)
15.5 Moist dynamics of tropical cyclone-like vortices
439(2)
15.6 Summary, discussion, and bibliographic remarks
441(5)
16 Rotating Shallow-Water Models with Full Coriolis Force
446(29)
16.1 'Non-traditional' rotating shallow-water model in the tangent plane approximation
446(4)
16.1.1 Vertical averaging of 'non-traditional' primitive equations
446(3)
16.1.2 Non-traditional RSW models
449(1)
16.2 'Non-traditional' rotating shallow-water model on the sphere
450(13)
16.2.1 Including the effects of curvature in the RSW with full Coriolis force
450(2)
16.2.2 Variational principle for the primitive equations in spherical geometry
452(3)
16.2.3 Characteristic scales and parameters
455(1)
16.2.4 Columnar motion reduction in the variational principle
456(4)
16.2.5 Derivation of the non-traditional rotating shallow-water equations
460(3)
16.3 Example of crucial influence of non-traditional corrections: inertial instability with full Coriolis force
463(9)
16.3.1 Inertial instability with full Coriolis force: theoretical considerations
463(4)
16.3.2 Inertial instability with full Coriolis force: direct approach to the linear stability analysis
467(5)
16.4 Summary, discussion, and bibliographic remarks
472(3)
References 475(10)
Index 485
Vladimir Zeitlin graduated from Dnipropetrovsk University (Ukraine) in 1976, and gained his PhD in theoretical and mathematical physics in 1980 from the Physical Institute (Moscow). Trained as a theoretical physicist, he moved his focus to geophysical fluid dynamics in the early 1980s. He worked at the Institute of Atmospheric Physics (Moscow) on vortex dynamics, wave-vortex interactions and turbulence. Later, after moving to France, Zeitlin joined the Laboratory of Dynamical Meteorology and then became Professor at the University P. and M. Curie (now Sorbonne University) and École Normale Supérieure (Paris).