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Produktbild: Fundamentals of Ocean Climate Models

Fundamentals of Ocean Climate Models

Fr. 193.00

inkl. gesetzl. MwSt., Versandkostenfrei

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

05.09.2004

Verlag

University Presses

Seitenzahl

528

Maße (L/B/H)

24/16.1/3.4 cm

Gewicht

1134 g

Sprache

Englisch

ISBN

978-0-691-11892-5

Beschreibung

Produktdetails

Einband

Gebundene Ausgabe

Erscheinungsdatum

05.09.2004

Verlag

University Presses

Seitenzahl

528

Maße (L/B/H)

24/16.1/3.4 cm

Gewicht

1134 g

Sprache

Englisch

ISBN

978-0-691-11892-5

Herstelleradresse

Libri GmbH
Europaallee 1
36244 Bad Hersfeld
DE

Email: gpsr@libri.de

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  • Produktbild: Fundamentals of Ocean Climate Models
  • FOREWORD XIII
    PREFACE XV
    ACKNOWLEDGMENTS XXV
    ABOUT THE COVER XXVII
    LIST OF SYMBOLS XXIX
    Chapter 1. OCEAN CLIMATE MODELS 1
    1.1 Ocean models as tools for ocean science 1
    1.2 Ocean climate models 2
    1.3 Challenges of climate change 3
    PART 1. FUNDAMENTAL OCEAN EQUATIONS 5
    Chapter 2. BASICS OF OCEAN FLUID MECHANICS 7
    2.1 Some fundamental ocean processes 7
    2.2 The continuum hypothesis 9
    2.3 Kinematics of fluid motion 10
    2.4 Kinematical and dynamical approximations 16
    2.5 Averaging over scales and realizations 20
    2.6 Numerical discretization 21
    2.7 Chapter summary 22
    Chapter 3. KINEMATICS 24
    3.1 Introduction 24
    3.2 Mathematical preliminaries 24
    3.3 The divergence theorem and budget analyses 29
    3.4 Volume and mass conserving kinematics 31
    3.5 Chapter summary 40
    Chapter 4. DYNAMICS 42
    4.1 Introduction 42
    4.2 Motion on a rotating sphere 43
    4.3 Principles of continuum dynamics 47
    4.4 Dynamics of fluid parcels 51
    4.5 Hydrostatic pressure 56
    4.6 Dynamics of hydrostatic fluid columns 58
    4.7 Fluid motion in a rapidly rotating system 62
    4.8 Vertical stratification 68
    4.9 Vorticity and potential vorticity 70
    4.10 Particle dynamics on a rotating sphere 75
    4.11 Symmetry and conservation laws 80
    4.12 Chapter summary 83
    Chapter 5. THERMO-HYDRODYNAMICS 87
    5.1 General types of ocean tracers 87
    5.2 Basic equilibrium thermodynamics 91
    5.3 Energy of a fluid parcel 95
    5.4 Global mechanical energy balance 105
    5.5 Basic non-equilibrium thermodynamics 110
    5.6 Thermodynamical tracers 111
    5.7 Ocean density 114
    5.8 Chapter summary 118
    Chapter 6. GENERALIZED VERTICAL COORDINATES 121
    6.1 Introduction 121
    6.2 Concerning the choice of vertical coordinate 122
    6.3 Generalized surfaces 128
    6.4 Local orthonormal coordinates 130
    6.5 Mathematics of generalized vertical coordinates 131
    6.6 Metric tensors 136
    6.7 The dia-surface velocity component 138
    6.8 Conservation of mass and volume for parcels 141
    6.9 Kinematic boundary conditions 143
    6.10 Primitive equations 145
    6.11 Transformation of SGS tracer flux components 147
    6.12 Chapter summary 149
    PART 2. AVERAGED DESCRIPTIONS 153
    Chapter 7. CONCERNI NG UNRESOLVED PHYSICS 155
    7.1 Represented dynamics and parameterized physics 155
    7.2 Lateral (neutral) and vertical processes 157
    7.3 Basic mechanisms for dianeutral transport 159
    7.4 Dianeutral transport in models 161
    7.5 Numerically induced spurious dianeutral transport 166
    7.6 Chapter summary 167
    Chapter 8. EULERIAN AVERAGED EQUATIONS 169
    8.1 Introduction 169
    8.2 The nonhydrostatic shallow ocean equations 171
    8.3 Averaged kinematics 173
    8.4 Averaged kinematics over finite domains 174
    8.5 Averaged tracer 179
    8.6 Averaged momentum budget 182
    8.7 Summary of the Eulerian averaged equations 183
    8.8 Mapping to ocean model variables 185
    8.9 Chapter summary 187
    Chapter 9. KINEMATICS OF AN ISENTROPIC ENSEMBLE 189
    9.1 Parameterizing mesoscale eddies 189
    9.2 Advection and skewsion 191
    9.3 Volume conservation 194
    9.4 Ensemble mean tracer equation 203
    9.5 Quasi-Stokes transport in z-models 206
    9.6 Chapter summary 212
    PART 3. SEMI-DISCRETE EQUATIONS AND ALGORITHMS 215
    Chapter 10. DISCRETIZATION BASICS 217
    10.1 Discretization methods 217
    10.2 An introduction to Arakawa grids 218
    10.3 Time stepping 219
    10.4 Chapter summary 221
    Chapter 11. MASS AND TRACER BUDGETS 222
    11.1 Summary of the continuous model equations 222
    11.2 Tracer and mass/volume compatibility 223
    11.3 Mass budget for a grid cell 223
    11.4 Mass budget for a discrete fluid column 227
    11.5 Tracer budget for a grid cell 228
    11.6 Fluxes for turbulence mixed layer schemes 232
    11.7 Flux plus restore boundary conditions 233
    11.8 Z-like vertical coordinate models 234
    11.9 Chapter summary 235
    Chapter 12. ALGORITHMS FOR HYDROSTATIC OCEAN MODELS 237
    12.1 Summary of the continuous model equations 237
    12.2 Budget of linear momentum for a grid cell 238
    12.3 Strategies for time stepping momentum 244
    12.4 A leap-frog algorithm 248
    12.5 Discretization of time tendencies 251
    12.6 A time staggered algorithm 258
    12.7 Barotropic updates with a predictor-corrector 262
    12.8 Stability considerations 265
    12.9 Smoothing the surface height in B-grid models 277
    12.10 Rigid lid streamfunction method 278
    12.11 Chapter summary 280
    PART 4. NEUTRAL PHYSICS 281
    Chapter 13. BASICS OF NEUTRAL PHYSICS 283
    13.1 Concerning the utility of neutral physics 283
    13.2 Notation and summary of scalar budgets 286
    13.3 Compatibility in the mean field budgets 287
    13.4 The SGS tracer transport tensor 288
    13.5 Advection and skewsion 290
    13.6 Neutral tracer fluxes 291
    13.7 Chapter summary and a caveat on the conjecture 294
    Chapter 14. NEUTRAL TRANSPORT OPERATORS 296
    14.1 Neutral diffusion 296
    14.2 Gent-McWilliams stirring 304
    14.3 Summarizing the neutral physics fluxes 308
    14.4 Flow-dependent diffusivities 309
    14.5 Biharmonic operators 317
    14.6 Chapter summary and some challenges 326
    Chapter 15. NEUTRAL PHYSICS NEAR THE SURFACE BOUNDARY 328
    15.1 Linear stability for neutral diffusion 328
    15.2 Linear stability for GM stirring 332
    15.3 Neutral physics near boundaries 333
    15.4 Chapter summary and caveats 343
    Chapter 16. FUNCTIONAL DISCRETIZATION OF NEUTRAL PHYSICS 345
    16.1 Foundations for discrete neutral physics 345
    16.2 Introduction to the discretization 350
    16.3 A one-dimensional warm-up 352
    16.4 Elements of the discrete dissipation functional 354
    16.5 Triad stencils and some more notation 361
    16.6 The discrete diffusion operator 363
    16.7 Diffusive flux components 367
    16.8 Further issues of numerical implementation 371
    16.9 Chapter summary 374
    PART 5. HORIZONTAL FRICTION 377
    Chapter 17. HORIZONTAL FRICTION IN MODELS 379
    17.1 Boussinesq and non-Boussinesq friction 379
    17.2 Introduction and general framework 379
    17.3 Properties of the stress tensor 380
    17.4 Properties of the viscosity tensor 387
    17.5 Transverse isotropy 389
    17.6 Transverse anisotropy 393
    17.7 Generalized orthogonal coordinates 396
    17.8 Dissipation functional 398
    17.9 Biharmonic friction 402
    17.10 Some mathematical details 404
    17.11 Chapter summary 407
    Chapter 18. CHOOSING THE HORIZONTAL VISCOSITY 409
    18.1 Stability and resolution considerations 409
    18.2 Comparing Laplacian and biharmonic mixing 415
    18.3 Smagorinsky viscosity 416
    18.4 Background viscosity 420
    18.5 Viscosities for anisotropic friction 421
    18.6 Chapter summary 422
    Chapter 19. FUNCTIONAL DISCRETIZATION OF FRICTION 424
    19.1 Comments on notation 424
    19.2 Summary of the various formulations 425
    19.3 Horizontal friction discretization 426
    19.4 Laplacian plus metric form of isotropic friction 436
    19.5 Chapter summary 439
    PART 6. TENSOR ANALYSIS 441
    Chapter 20. ELEMENTARY TENSOR ANALYSIS 443
    20.1 Introduction 443
    20.2 Some practical motivation 444
    20.3 Coordinates and vectors 446
    20.4 The metric and coordinate transformations 448
    20.5 Transformations of a vector 451
    20.6 One-forms 452
    20.7 Mapping between vectors and one-forms 454
    20.8 Transformation of a one-form 454
    20.9 Arbitrary tensors and their transformations 455
    20.10 Tensorial properties of the gradient operator 456
    20.11 The invariant volume element 457
    20.12 Determinants and the Levi-Civita symbol 459
    20.13 Surfaces embedded in Euclidean space 461
    20.14 Chapter summary 464
    Chapter 21. CALCULUS ON CURVED MANIFOLDS 466
    21.1 Fundamental character of tensor equations 466
    21.2 Covariant differentiation 468
    21.3 Covariant derivative of a second order tensor 470
    21.4 Christoffel symbols in terms of the metric 471
    21.5 Covariant divergence of a vector 471
    21.6 Covariant divergence of a second order tensor 472
    21.7 Covariant Laplacian of a scalar 473
    21.8 Covariant curl of a vector 473
    21.9 Covariant Laplacian of a vector 473
    21.10 Integral theorems 474
    21.11 Orthogonal curvilinear coordinates 474
    21.12 Summary of curvilinear tensor analysis 481
    PART 7. EPILOGUE 487
    Chapter 22. SOME CLOSING COMMENTS AND CHALLENGES 489
    BIBLIOGRAPHY 493
    Index 511