Geophysical fluid dynamics: understanding (almost) everything with rotating shallow water models
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| Sprache: | English |
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Oxford
Oxford University Press
2018
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| Ausgabe: | Reprinted 2018 with corrections |
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| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xix, 488 Seiten Illustrationen, Diagramme |
| ISBN: | 9780198804338 |
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| 100 | 1 | |a Zeitlin, Vladimir |e Verfasser |0 (DE-588)1153923181 |4 aut | |
| 245 | 1 | 0 | |a Geophysical fluid dynamics |b understanding (almost) everything with rotating shallow water models |c Vladimir Zeitlin, Laboratory of Dynamical Meteorology, Sorbonne University and École Normale Supérieure Paris, France |
| 250 | |a Reprinted 2018 with corrections | ||
| 264 | 1 | |a Oxford |b Oxford University Press |c 2018 | |
| 300 | |a xix, 488 Seiten |b Illustrationen, Diagramme | ||
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| 653 | 0 | |a Geophysics | |
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Datensatz im Suchindex
| _version_ | 1804179036622028800 |
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| adam_text | Contents
Part I Modelling Large-scale Oceanic and Atmospheric
Flows: From Primitive to Rotating Shallow-Water Equations
and Beyond
1 Introduction 3
2 Primitive Equations Model 6
2.1 Preliminaries 6
2.2 A crash course in fluid dynamics 6
2.2.1 The perfect fluid 6
2.2.2 Real fluids: incorporating molecular transport 13
2.3 Rotation, sphericity, and tangent plane approximation 14
2.3.1 Hydrodynamics in the rotating frame with gravity 14
2.3.2 Hydrodynamics in spherical coordinates
and the ‘traditional’ approximation in GFD 15
2.3.3 The tangent plane approximation 17
2.4 Primitive equations in the oceanic and atmospheric context 17
2.4.1 Oceanic context 18
2.4.2 Atmospheric context 19
2.4.3 Remarkable properties of the PE dynamics 22
2.4.4 What do we lose by assuming hydrostatics? 26
2.5 Summary, comments, and bibliographic remarks 27
2.6 Problems 28
3 Simplifying Primitive Equations: Rotating Shallow-Water
Models and their Properties 29
3.1 Vertical averaging of horizontal momentum and mass conservation equations 29
3.2 Archetype models 33
3.2.1 One-layer RSW model 33
3.2.2 Two-layer RSW model with a rigid lid 34
3.2.3 Two-layer RSW model with a free upper surface 34
3.2.4 RSW model on the sphere 36
3.3 Vortices and waves in rotating shallow-water models 36
3.3.1 One-layer RSW model 36
3.3.2 Two-layer RSW model 40
3.4 Lagrangian approach and variational principles for shallow-water models 42
3.4.1 Lagrangian formulation of one-layer RSW 42
3.4.2 Lagrangian formulation of two-layer RSW 46
xii Contents
3.5 Summary, comments, and bibliographic remarks 47
3.6 Problems 48
4 Wave Motions in Rotating Shallow Water with Boundaries,
Topography, at the Equator, and in Laboratory 49
4.1 Introducing lateral boundaries and shelf 49
4.1.1 Kelvin waves in RSW with an idealised coast 49
4.1.2 Waves in RSW with idealised coast and a shelf 52
4.2 Waves over topography/bathymetry far from lateral boundaries 57
4.2.1 Topographic waves 57
4.2.2 Mountain (lee) waves in RSW 59
4.3 Waves in outcropping flows 62
4.4 Equatorial waves 67
4.4.1 Equatorial waves in one-layer model 67
4.4.2 Waves in two-layer RSW with a rigid lid on the equatorial
beta plane 75
4.5 Waves in rotating annulus 77
4.5.1 RSW in cylindrical geometry 77
4.5.2 Analytic solution of the eigenvalue problem 79
4.6 Summary, comments, and bibliographic remarks 83
4.7 Problems 85
5 Getting Rid of Fast Waves: Slow Dynamics 86
5.1 General properties of the horizontal motion. Geostrophic equilibrium 86
5.2 Slow dynamics in a one-layer model 88
5.2.1 Derivation of the QG equations 88
5.2.2 Rossby waves and vortex dynamics: plane vs/ plane 90
5.2.3 QG dynamics in the presence of topography. Mountain
Rossby waves 91
5.2.4 Frontal geostrophic dynamics 95
5.3 Slow dynamics in the two-layer model with a rigid lid 96
5.3.1 Derivation of the QG equations 96
5.3.2 Rossby waves in the two-layer QG model 98
5.3.3 Baroclinic instability: first acquaintance 98
5.3.4 Frontal geostrophic regimes 100
5.4 Slow dynamics in two-layer model with a free surface 101
5.4.1 Equations of motion, parameters, and scaling 101
5.4.2 QG equations 102
5.5 Large-scale slow dynamics in the presence of wave guides 102
5.5.1 A reminder on multi-scale asymptotic expansions 102
5.5.2 Slow motions in the presence of a lateral boundary 103
5.5.3 Slow motions over escarpment 106
5.5.4 Slow motions at the equator 108
Contents xiii
5.6 Summary, comments, and bibliographic remarks 114
5.7 Problems 116
6 Vortex Dynamics on the f and beta Plane and Wave Radiation
by Vortices 117
6.1 Two-dimensional vortex dynamics 117
6.1.1 2D Euler equations in stream-function-vorticity variables 117
6.1.2 Lagrangian formulation of 2D hydrodynamics of a perfect
fluid 119
6. L 3 Dynamics of point vortices 120
6.1.4 Contour dynamics 121
6.1.5 Structure (Casimir)-preserving discretisations of vorticity
equation in Fourier space 122
6.2 Quasi-geostrophic modons in the /- and /-plane approximations 124
6.2.1 Influence of the beta effect upon a monopolar vortex 124
6.2.2 Constructing QG modon solutions: one-layer case 125
6.2.3 Constructing QG modon solutions: two-layer case 127
6.3 A crash course in 2D turbulence 134
6.3.1 Reminder on statistical description of turbulence 134
6.3.2 Developed turbulence: energy and enstrophy cascades 136
6.4 When vortices emit waves: Lighthill radiation 137
6.4.1 2D hydrodynamics and vortex-pair solution in complex
notation 138
6.4.2 Gravity waves in cylindrical geometry 138
6.4.3 Lighthill radiation 139
6.4.4 Back-reaction of wave radiation 140
6.4.5 Lighthill radiation in the presence of rotation 141
6.5 Summary, comments, and bibliographic remarks 142
6.6 Problems 143
7 Rotating Shallow-Water Models as Quasilinear Hyperbolic
Systems, and Related Numerical Methods 144
7.1 One-layer model 145
7.1.1 1.5-dimensional one-layer RSW model 145
7.1.2 Lagrangian approach to the 1.5-dimensional model 145
7.1.3 Quasilinear and hyperbolic systems 147
7.1.4 Wave breaking in non-rotating and rotating one-layer RSW 148
7.1.5 Hydraulic theory applied to rotating shallow water 150
7.1.6 A brief description of finite-volume numerical methods for
one-layer RSW 153
7.1.7 Illustration: breaking of equatorial waves 158
7.2 Two-layer model 159
7.2.1 1.5 dimensional two-layer RSW 159
xiv Contents
7.2.2 Characteristic equation and loss of hyperbolicity 160
7.2.3 Rankine-Hugoniot conditions 162
7.2.4 A finite-volume numerical method for two-layer RSW 163
7.3 Summary, comments, and bibliographic remarks 164
7.4 Problems 166
Part II Understanding Fundamental Dynamical Phenomena
with Rotating Shallow-Water Models
8 Geostrophic Adjustment and Wave-Vortex (Non)Interaction 169
8.1 Geostrophic adjustment in the barotropic (one-layer) model 169
8.1.1 Quasi-geostrophic regime 169
8.1.2 Frontal geostrophic regime 175
8.2 Geostrophic adjustment in the baroclinic (two-layer) model 180
8.2.1 Quasi-geostrophic regime 180
8.2.2 Frontal geostrophic regime 181
8.3 Geostrophic adjustment in one dimension and the first idea
of frontogenesis 183
8.3.1 Theoretical considerations 183
8.3.2 Numerical simulations: Rossby adjustment 189
8.4 Geostrophic adjustment in the presence of boundaries, topography,
and at the equator 191
8.4.1 Geostrophic adjustment with a lateral boundary 191
8.4.2 Geostrophic adjustment over escarpment 191
8.4.3 Geostrophic adjustment in the equatorial beta plane 192
8.5 Summary, comments, and bibliographic remarks 194
9 RSW Modons and their Surprising Properties: RSW Turbulence 197
9.1 QG vs RSW modons; one-layer model 197
9.1.1 General properties of steady solutions 197
9.1.2 *Ageostrophic adjustment5 of QG modons 198
9.1.3 Properties of RSW modons 201
9.2 QG vs RSW modons: two-layer model 203
9.2.1 Adjustment of barotropic QG modons 203
9.2.2 Adjustment of baroclinic QG modons 204
9.2.3 Adjustment of essentially ageostrophic modons 204
9.3 Shock modons 206
9.4 Interactions of RSW modons 208
9.4.1 2 modons —► 2 modons collision 209
9.4.2 2 — 2 ‘loose5 modon collision 209
9.4.3 2 modons - tripole collisions 210
9.4.4 2 modons tripole + monopole collisions 210
9.4.5 Collisions of shock modons 213
Contents xv
9.5 2D vs RSW turbulence 213
9.5.1 Set-up and initialisations 214
9.5.2 General features of the evolution of the vortex system 215
9.5.3 Non-universality of RSW turbulence 218
9.6 Summary, comments, and bibliographic remarks 219
10 Instabilities of Jets and Fronts and their Nonlinear Evolution 221
10.1 Instabilities: general notions and techniques 221
10.1.1 Definitions and general concepts 221
10.1.2 (In) stability criteria for plane-parallel flows 223
10.1.3 Direct approach to linear stability analysis
of plane-parallel and circular flows 225
10.2 Geostrophic barotropic and baroclinic instabilities of jets 226
10.2.1 Barotropic instability of a Bickley jet on the/ plane 226
10.2.2 Baroclinic instability of a Bickley jet in the/ plane 228
10.3 Ageostrophic instabilities in the Phillips model: Rossby-Kelvin
and shear instabilities 232
10.4 Ageostrophic instabilities of jets and their nonlinear evolution 235
10.4.1 Linear stability 235
10.4.2 Nonlinear saturation of essentially ageostrophic
instabilities 241
10.4.3 A brief summary of the results on essentially
ageostrophic instabilities of mid-latitude jets 244
10.5 Understanding the nature of inertial instability 244
10.6 Instabilities of jets at the equator and their nonlinear evolution,
with emphasis on inertial instability 248
10.6.1 Linear stability and nonlinear saturation of instabilities
in one-layer RSW model at the equator 248
10.6.2 Linear stability and nonlinear saturation of instabilities
in two-layer RSW model at the equator 254
10.6.3 A brief summary of the results on instabilities
of equatorial jets 260
10.7 Instabilities of coastal currents and their nonlinear evolution 261
10.7.1 Passive lower layer: results of the linear stability analysis 261
10.7.2 Passive lower layer: nonlinear evolution of the instability 262
10.7.3 Active lower layer: results of linear stability analysis 266
10.7.4 Active lower layer: nonlinear saturation of instabilities 269
10.7.5 A brief summary of the results on instabilities of coastal
currents 273
10.8 Instabilities of double-density fronts and the role of topography 275
10.8.1 Set-up, scaling, parameters, and boundary conditions 275
10.8.2 Linear stability analysis 277
xvi Contents
10.8.3 Nonlinear saturation of the instabilities 280
10.8.4 A brief summary of the results on instabilities of double
fronts over topography 283
10.9 Summary, comments, and bibliographic remarks 284
11 Instabilities in Cylindrical Geometry: Vortices and Laboratory Flows 289
11.1 Axisymmetric vortex solutions in rotating shallow water 290
11.1.1 One-layer model 290
11.1.2 Two-layer model 291
11.2 Instabilities of isolated quasi-geostrophic vortices and their
nonlinear evolution 292
11.2.1 One-layer configuration, barotropic vortices 292
11.2.2 Two-layer configuration, baroclinic upper-layer vortex 295
11.3 Instabilities of ageostrophic vortices and their nonlinear evolution 299
11.3.1 General considerations 29 9
11.3.2 Results of the linear stability analysis 300
11.3.3 Nonlinear saturation of the instabilities 305
11.4 Instabilities of intense hurricane-like vortices and their nonlinear evolution 310
11.4.1 Idealised rotating shallow-water hurricane 311
11.4.2 Results of the linear stability analysis 313
11.4.3 Nonlinear saturation of the hurricane’s instability 314
11.4.4 A brief summary of the results on instabilities
of idealised hurricanes 317
11.5 Instabilities of laboratory flows in rotating annuli 317
11.5.1 Stability of two-layer flows under the rigid lid 317
11.5.2 Stability of flows in rotating annulus with outcropping
and topography 325
11.5.3 A brief summary of the results of analysis of instabilities
in the rotating annulus 335
11.6 Summary, comments, and bibliographic remarks 336
12 Resonant Wave Interactions and Resonant Excitation
of Wave-guide Modes 338
12.1 Resonant wave triads: first acquaintance 338
12.1.1 Perturbation theory for Rossby waves 338
12.1.2 Wave resonances and wave modulation 340
12.2 Resonant excitation of trapped coastal waves by free
inertia-gravity waves 341
12.2.1 Resonant excitation of wave-guide modes: general
philosophy 341
12.2.2 Resonant excitation of Kelvin waves by free
inertia-gravity waves at abrupt shelf: barotropic model 342
Contents xvii
12.2.3 Resonant excitation of Kelvin waves by free
inertia-gravity waves at abrupt shelf; baroclinie model 347
12.2.4 Resonant excitation of coastal waves by free
inertia-gravity waves at the shelf with gentle slope 355
12.3 Resonant excitation of baroclinie Rossby and Yanai waves in the
equatorial wave guide 364
12.3.1 Reminder on two-layer equatorial RSW and general
conditions of removal of resonances 364
12.3.2 Wave-wave resonances 365
12.3.3 Wave mean current resonances 372
12.4 Summary, comments, and bibliographic remarks 376
13 Wave Turbulence 379
13.1 The main hypotheses and ideas of the wave turbulence approach 379
13.1.1 A reminder on Hamiltonian description of wave
systems 379
13.1.2 The principal idea of wave turbulence approach 383
13.1.3 Kinetic equations for decay and non-decay dispersion
laws 383
13.1.4 Exact solutions of kinetic equations 384
13.1.5 Conservation laws and dimensional estimates 388
13.2 Applications of the wave turbulence theory to waves in rotating
shallow water 389
13.2.1 Wave turbulence of inertia-gravity waves on the / plane 389
13.2.2 Weak turbulence of short inertia-gravity waves
on the equatorial p plane 393
13.2.3 Weak turbulence of the Rossby waves on the ft plane 399
13.3 Turbulence of inertia-gravity waves in rotating shallow water:
theory vs numerical experiment 401
13.4 Historical comments, summary, and bibliographic remarks 403
Part 111 Generalisations of Standard Rotating Shallow-water
Model, and their Applications
14 Rotating Shallow-Water model with Horizontal Density and/or
Temperature Gradients 409
14.1 Derivation of the thermal rotating shallow-water model and its properties 409
14.1.1 Derivation of the model 409
14.1.2 Gas dynamics analogy 411
14.1.3 Waves and vortices 411
14.1.4 Quasi-geostrophic TRSW 412
14.1.5 Variational principle for TRSW 413
14.2 Instabilities of jets and vortices in thermal rotating shallow water 414
xviii Contents
14.2.1 New instabilities in TRS W: first example 414
14.2.2 Instabilities of thermal vortices in TRSW 414
14.2.3 Stationary vortex solutions 415
14.2.4 Results of the linear stability analysis of a thermal
cyclone 415
14.2.5 Nonlinear saturation of the instability 418
14.2.6 Discussion of the results 419
14.3 Summary, comments, and bibliographic remarks 419
15 Rotating Shallow-Water Models with Moist Convection 421
15.1 Constructing moist-convective shallow-water models 421
15.1.1 General context and philosophy of the approach 421
15.1.2 Introducing moisture in primitive equations 422
15.1.3 Vertical averaging with convective fluxes 422
15.1.4 Linking convection and condensation 424
15.1.5 Surface evaporation and its parameterisations 425
15.1.6 Two-layer model with a dry upper layer and its
one-layer limit 426
15.2 Properties of moist-convective RSW models 427
15.2.1 Limiting cases 427
15.2.2 Conservation laws 429
15.3 Mathematics of moist-convective rotating shallow water 430
15.3.1 Quasilinear form and characteristic equations 430
15.3.2 Discontinuities and Rankine-Hugoniot conditions 432
15.3.3 Illustration: wave scattering on a moisture front 432
15.4 Applications to ‘moist’ instabilities of geostrophic jets and vortices 434
15.4.1 Moist instability of the baroclinic Bickley jet 434
15.4.2 Moist instability of geostrophic vortices 435
15.5 Moist dynamics of tropical cyclone-like vortices 439
15.6 Summary, discussion, and bibliographic remarks 441
16 Rotating Shallow-Water Models with Full Coriolis Force 446
16.1 ‘Non-traditional’ rotating shallow-water model in the tangent
plane approximation 446
16.1.1 Vertical averaging of ‘non-traditional’ primitive
equations 446
16.1.2 Non-traditional RSW models 449
16.2 ‘Non-traditional’ rotating shallow-water model on the sphere 450
16.2.1 Including the effects of curvature in the RSW with full
Coriolis force 450
16.2.2 Variational principle for the primitive equations
in spherical geometry 452
16.2.3 Characteristic scales and parameters 455
Contents xix
16.2.4 Columnar motion reduction in the variational principle 456
16.2.5 Derivation of the non-traditional rotating shallow-water
equations 460
16.3 Example of crucial influence of non-traditional corrections:
inertial instability with full Coriolis force 463
16.3.1 Inertial instability with full Coriolis force: theoretical
considerations 463
16.3.2 Inertial instability with full Coriolis force: direct
approach to the linear stability analysis 467
16.4 Summary, discussion, and bibliographic remarks 472
References 475
Index 485
Geophysical Fluid Dynamics examines the dynamics of stratified and turbulent
fluid motion in the atmosphere, ocean and outer core.
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.
is Professor at the Sorbonne Universitv, Paris, France.
OXFORD
UNIVERSITY PRESS
ISBN 978-0-19-880433-8
9 780198 804338
www.oup.com
|
| any_adam_object | 1 |
| author | Zeitlin, Vladimir |
| author_GND | (DE-588)1153923181 |
| author_facet | Zeitlin, Vladimir |
| author_role | aut |
| author_sort | Zeitlin, Vladimir |
| author_variant | v z vz |
| building | Verbundindex |
| bvnumber | BV045271546 |
| classification_rvk | RB 10115 UT 6000 |
| ctrlnum | (OCoLC)1061547225 (DE-599)BVBBV045271546 |
| dewey-full | 532.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.5 |
| dewey-search | 532.5 |
| dewey-sort | 3532.5 |
| dewey-tens | 530 - Physics |
| discipline | Physik Geographie |
| edition | Reprinted 2018 with corrections |
| format | Book |
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| id | DE-604.BV045271546 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:13:29Z |
| institution | BVB |
| isbn | 9780198804338 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030659303 |
| oclc_num | 1061547225 |
| open_access_boolean | |
| owner | DE-703 |
| owner_facet | DE-703 |
| physical | xix, 488 Seiten Illustrationen, Diagramme |
| publishDate | 2018 |
| publishDateSearch | 2018 |
| publishDateSort | 2018 |
| publisher | Oxford University Press |
| record_format | marc |
| spelling | Zeitlin, Vladimir Verfasser (DE-588)1153923181 aut Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models Vladimir Zeitlin, Laboratory of Dynamical Meteorology, Sorbonne University and École Normale Supérieure Paris, France Reprinted 2018 with corrections Oxford Oxford University Press 2018 xix, 488 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Geophysik (DE-588)4020252-5 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Fluid dynamics Geophysics Strömungsmechanik (DE-588)4077970-1 s Geophysik (DE-588)4020252-5 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030659303&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030659303&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Zeitlin, Vladimir Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models Geophysik (DE-588)4020252-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4020252-5 (DE-588)4077970-1 |
| title | Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models |
| title_auth | Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models |
| title_exact_search | Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models |
| title_full | Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models Vladimir Zeitlin, Laboratory of Dynamical Meteorology, Sorbonne University and École Normale Supérieure Paris, France |
| title_fullStr | Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models Vladimir Zeitlin, Laboratory of Dynamical Meteorology, Sorbonne University and École Normale Supérieure Paris, France |
| title_full_unstemmed | Geophysical fluid dynamics understanding (almost) everything with rotating shallow water models Vladimir Zeitlin, Laboratory of Dynamical Meteorology, Sorbonne University and École Normale Supérieure Paris, France |
| title_short | Geophysical fluid dynamics |
| title_sort | geophysical fluid dynamics understanding almost everything with rotating shallow water models |
| title_sub | understanding (almost) everything with rotating shallow water models |
| topic | Geophysik (DE-588)4020252-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Geophysik Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030659303&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030659303&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT zeitlinvladimir geophysicalfluiddynamicsunderstandingalmosteverythingwithrotatingshallowwatermodels |