Atmospheric and oceanic fluid dynamics: fundamentals and large-scale circulation
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
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| Ausgabe: | 1. publ., Reprinted |
| Schlagworte: | |
| Online-Zugang: | Beschreibung für Leser Inhaltsverzeichnis |
| Beschreibung: | XXV, 745 S. Ill., graph. Darst. |
| ISBN: | 0521849691 9780521849692 |
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| 245 | 1 | 0 | |a Atmospheric and oceanic fluid dynamics |b fundamentals and large-scale circulation |c Geoffrey K. Vallis |
| 250 | |a 1. publ., Reprinted | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
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| adam_text | IMAGE 1
ATMOSPHERIC AND OCEANIC
FLUID DYNAMICS
FUNDAMENTALS AND LARGE-SCALE CIRCULATION
G E O F F R EY K. V A L L IS
PRINCETON UNIVERSITY, NEW JERSEY
CAMBRIDGE UNIVERSITY PRESS
IMAGE 2
CONTENTS
AN ASTERISK INDICATES MORE ADVANCED MATERIAL THAT MAY BE OMITTED ON A
FIRST READING. A DAGGER INDICATES MATERIAL THAT IS STILL A TOPIC OF
RESEARCH OR THAT IS NOT SETTLED.
PREFACE PAGE XIX
NOTATION XXIV
PART I FUNDAMENTALS OF GEOPHYSICAL FLUID DYNAMICS 1
1 EQUATIONS OF MOTION 3
1.1 TIME DERIVATIVES FOR FLUIDS 3
1.1.1 FIELD AND MATERIAL VIEWPOINTS 3
1.1.2 THE MATERIAL DERIVATIVE OF A FLUID PROPERTY 4
1.1.3 MATERIAL DERIVATIVE OF A VOLUME 6
1.2 THE MASS CONTINUITY EQUATION 7
1.2.1 AN EULERIAN DERIVATION 7
1.2.2 MASS CONTINUITY VIA THE MATERIAL DERIVATIVE 9
1.2.3 A GENERAL CONTINUITY EQUATION 11
1.3 THE MOMENTUM EQUATION 11
1.3.1 ADVECTION 12
1.3.2 THE PRESSURE FORCE 12
1.3.3 VISCOSITY AND DIFFUSION 13
1.3.4 HYDROSTATIC BALANCE 13
1.4 THE EQUATION OF STATE 14
1.5 THERMODYNAMIC RELATIONS 16
1.5.1 A FEW FUNDAMENTALS 16
1.5.2 VARIOUS THERMODYNAMIC RELATIONS 18
1.6 THERMODYNAMIC EQUATIONS FOR FLUIDS 22
VII
IMAGE 3
VIII CONTENTS
1.6.1 THERMODYNAMIC EQUATION FOR AN IDEAL GAS 23
1.6.2 * THERMODYNAMIC EQUATION FOR LIQUIDS 26
1.7 * MORE THERMODYNAMICS OF LIQUIDS 31
1.7.1 POTENTIAL TEMPERATURE, POTENTIAL DENSITY AND ENTROPY -. 31
1.7.2 * THERMODYNAMIC PROPERTIES OF SEAWATER 33
1.8 SOUNDWAVES 37
1.9 COMPRESSIBLE AND INCOMPRESSIBLE FLOW 38
1.9.1 CONSTANT DENSITY FLUIDS 38
1.9.2 INCOMPRESSIBLE FLOWS 39
1.10 THE ENERGY BUDGET 40
1.10.1 CONSTANT DENSITY FLUID 40
1.10.2 VARIABLE DENSITY FLUIDS 42
1.10.3 VISCOUS EFFECTS 43
1.11 AN INTRODUCTION TO NON-DIMENSIONALIZATION AND SCALING 43
1.11.1 THE REYNOLDS NUMBER 44
2 EFFECTS OF ROTATION AND STRATIFICATION 51
2.1 EQUATIONS IN A ROTATING FRAME 51
2.1.1 RATE OF CHANGE OF A VECTOR 52
2.1.2 VELOCITY AND ACCELERATION IN A ROTATING FRAME 53
2.1.3 MOMENTUM EQUATION IN A ROTATING FRAME 54
2.1.4 MASS AND TRACER CONSERVATION IN A ROTATING FRAME 54
2.2 EQUATIONS OF MOTION IN SPHERICAL COORDINATES 55
2.2.1 * THE CENTRIFUGAL FORCE AND SPHERICAL COORDINATES 55
2.2.2 SOME IDENTITIES IN SPHERICAL COORDINATES 57
2.2.3 EQUATIONS OF MOTION 60
2.2.4 THE PRIMITIVE EQUATIONS 61
2.2.5 PRIMITIVE EQUATIONS IN VECTOR FORM 62
2.2.6 THE VECTOR INVARIANT FORM OF THE MOMENTUM EQUATION 63
2.2.7 ANGULAR MOMENTUM 64
2.3 CARTESIAN APPROXIMATIONS: THE TANGENT PLANE 66
2.3.1 THEF-PLANE 66
2.3.2 THE BETA-PLANE APPROXIMATION 67
2.4 THE BOUSSINESQ APPROXIMATION 67
2.4.1 VARIATION OF DENSITY IN THE OCEAN 68
2.4.2 THE BOUSSINESQ EQUATIONS 68
2.4.3 ENERGETICS OF THE BOUSSINESQ SYSTEM 72
2.5 THE ANELASTIC APPROXIMATION 73
2.5.1 PRELIMINARIES 73
2.5.2 THE MOMENTUM EQUATION 74
2.5.3 MASS CONSERVATION 75
2.5.4 THERMODYNAMIC EQUATION 76
2.5.5 * ENERGETICS OF THE ANELASTIC EQUATIONS 76
2.6 CHANGING VERTICAL COORDINATE 77
2.6.1 GENERAL RELATIONS 77
2.6.2 PRESSURE COORDINATES 78
IMAGE 4
CONTENTS IX
2.6.3 LOG-PRESSURE COORDINATES 80
2.7 SCALING FOR HYDROSTATIC BALANCE 80
2.7.1 PRELIMINARIES 80
2.7.2 SCALING AND THE ASPECT RATIO 81
2.7.3 * EFFECTS OF STRATIFICATION ON HYDROSTATIC BALANCE 82
2.7.4 HYDROSTASY IN THE OCEAN AND ATMOSPHERE 84
2.8 GEOSTROPHIC AND THERMAL WIND BALANCE 85
2.8.1 THE ROSSBY NUMBER 85
2.8.2 GEOSTROPHIC BALANCE 86
2.8.3 TAYLOR-PROUDMAN EFFECT 88
2.8.4 THERMAL WIND BALANCE 89
2.8.5 * EFFECTS OF ROTATION ON HYDROSTATIC BALANCE 91
2.9 STATIC INSTABILITY AND THE PARCEL METHOD 91
2.9.1 A SIMPLE SPECIAL CASE: A DENSITY-CONSERVING FLUID 92
2.9.2 THE GENERAL CASE: USING POTENTIAL DENSITY 93
2.9.3 LAPSE RATES IN DRY AND MOIST ATMOSPHERES 95
2.10 GRAVITY WAVES 98
2.10.1 GRAVITY WAVES AND CONVECTION IN A BOUSSINESQ FLUID 98
2.11 * ACOUSTIC-GRAVITY WAVES IN AN IDEAL GAS 100
2.11.1 INTERPRETATION * 101
2.12 THE EKMAN LAYER 104
2.12.1 EQUATIONS OF MOTION AND SCALING 105
2.12.2 INTEGRAL PROPERTIES OF THE EKMAN LAYER 107
2.12.3 EXPLICIT SOLUTIONS. I: A BOTTOM BOUNDARY LAYER 109
2.12.4 EXPLICIT SOLUTIONS. II: THE UPPER OCEAN 112
2.12.5 OBSERVATIONS OF THE EKMAN LAYER 113
2.1 2.6 * FRICTIONAL PARAMETERIZATION OF THE EKMAN LAYER 114
3 SHALLOW WATER SYSTEMS AND ISENTROPIC COORDINATES 123
3.1 DYNAMICS OF A SINGLE, SHALLOW LAYER 123
3.1.1 MOMENTUM EQUATIONS 124
3.1.2 MASS CONTINUITY EQUATION 125
3.1.3 A RIGID LID 127
3.1.4 STRETCHING AND THE VERTICAL VELOCITY 1 28
3.1.5 ANALOGY WITH COMPRESSIBLE FLOW 129
3.2 REDUCED GRAVITY EQUATIONS 129
3.2.1 PRESSURE GRADIENT IN THE ACTIVE LAYER 130
3.3 MULTI-LAYER SHALLOW WATER EQUATIONS 131
3.3.1 REDUCED-GRAVITY MULTI-LAYER EQUATION 133
3.4 GEOSTROPHIC BALANCE AND THERMAL WIND 1 34
3.5 FORM DRAG 135
3.6 CONSERVATION PROPERTIES OF SHALLOW WATER SYSTEMS 1 36
3.6.1 POTENTIAL VORTICITY: A MATERIAL INVARIANT 136
3.6.2 ENERGY CONSERVATION: AN INTEGRAL INVARIANT 139
3.7 SHALLOW WATER WAVES 140
3.7.1 NON-ROTATING SHALLOW WATER WAVES 140
IMAGE 5
CONTENTS
3.7.2 ROTATING SHALLOW WATER (POINCARE) WAVES 141
3.7.3 KELVIN WAVES 143
3.8 GEOSTROPHIC ADJUSTMENT 144
3.8.1 NON-ROTATING FLOW 145
3.8.2 ROTATING FLOW 146
3.8.3 * ENERGETICS OF ADJUSTMENT 148
3.8.4 * GENERAL INITIAL CONDITIONS 149
3.8.5 A VARIATIONAL PERSPECTIVE 151
3.9 ISENTROPIC COORDINATES 1 52
3.9.1 A HYDROSTATIC BOUSSINESQ FLUID 152
3.9.2 A HYDROSTATIC IDEAL GAS 1 53
3.9.3 ANALOGY TO SHALLOW WATER EQUATIONS 154
3.10 AVAILABLE POTENTIAL ENERGY 155
3.10.1 A BOUSSINESQ FLUID 156
3.10.2 AN IDEAL GAS 1 58
3.10.3 USE, INTERPRETATION, AND THE ATMOSPHERE AND OCEAN 1 59
VORTICITY AND POTENTIAL VORTICITY 163
4.1 VORTICITY AND CIRCULATION 163
4.1.1 PRELIMINARIES 163
4.1.2 SIMPLE AXISYMMETRIC EXAMPLES 164
4.2 THE VORTICITY EQUATION 165
4.2.1 TWO-DIMENSIONAL FLOW 167
4.3 VORTICITY AND CIRCULATION THEOREMS 168
4.3.1 THE FROZEN-IN PROPERTY OF VORTICITY 168
4.3.2 KELVIN S CIRCULATION THEOREM 171
4.3.3 BAROCLINIC FLOW AND THE SOLENOIDAL TERM 1 73
4.3.4 CIRCULATION IN A ROTATING FRAME 1 73
4.3.5 THE CIRCULATION THEOREM FOR HYDROSTATIC FLOW , 174
4.4 VORTICITY EQUATION IN A ROTATING FRAME 1 75
4.4.1 THE CIRCULATION THEOREM AND THE BETA EFFECT 1 75
4.4.2 THE VERTICAL COMPONENT OF THE VORTICITY EQUATION 1 76
4.5 POTENTIAL VORTICITY CONSERVATION 178
4.5.1 PV CONSERVATION FROM THE CIRCULATION THEOREM 178
4.5.2 PV CONSERVATION FROM THE FROZEN-IN PROPERTY 180
4.5.3 PV CONSERVATION: AN ALGEBRAIC DERIVATION 182
4.5.4 EFFECTS OF SALINITY AND MOISTURE 183
4.5.5 EFFECTS OF ROTATION, AND SUMMARY REMARKS 1 83
4.6 * POTENTIAL VORTICITY IN THE SHALLOW WATER SYSTEM 184
4.6.1 USING KELVIN S THEOREM 184
4.6.2 USING AN APPROPRIATE SCALAR FIELD 185
4.7 POTENTIAL VORTICITY IN APPROXIMATE, STRATIFIED MODELS 1 86
4.7.1 THE BOUSSINESQ EQUATIONS 186
4.7.2 THE HYDROSTATIC EQUATIONS 187
4.7.3 POTENTIAL VORTICITY ON ISENTROPIC SURFACES 1 87
4.8 * THE IMPERMEABILITY OF ISENTROPES TO POTENTIAL VORTICITY 188
IMAGE 6
CONTENTS XI
4.8.1 INTERPRETATION AND APPLICATION 190
5 SIMPLIFIED EQUATIONS FOR OCEAN AND ATMOSPHERE 197
5.1 GEOSTROPHIC SCALING 198
5.1.1 SCALING IN THE SHALLOW WATER EQUATIONS 198
5.1.2 GEOSTROPHIC SCALING IN THE STRATIFIED EQUATIONS 200
5.2 THE PLANETARY-GEOSTROPHIC EQUATIONS 203
5.2.1 USING THE SHALLOW WATER EQUATIONS 203
5.2.2 PLANETARY-GEOSTROPHIC EQUATIONS FOR STRATIFIED FLOW 205
5.3 THE SHALLOW WATER QUASI-GEOSTROPHIC EQUATIONS 207
5.3.1 SINGLE-LAYER SHALLOW WATER QUASI-GEOSTROPHIC EQUATIONS 207 5.3.2
TWO-LAYER AND MULTI-LAYER QUASI-GEOSTROPHIC SYSTEMS 211 5.3.3 T
NON-ASYMPTOTIC AND INTERMEDIATE MODELS 214
5.4 THE CONTINUOUSLY STRATIFIED QUASI-GEOSTROPHIC SYSTEM 215
5.4.1 SCALING AND ASSUMPTIONS 215
5A-.2 ASYMPTOTICS 216
5.4.3 BUOYANCY ADVECTION AT THE SURFACE 21 9
5.4.4 QUASI-GEOSTROPHY IN PRESSURE COORDINATES 220
5.4.5 THE TWO-LEVEL QUASI-GEOSTROPHIC SYSTEM 221
5.5 * QUASI-GEOSTROPHY AND ERTEL POTENTIAL VORTICITY 224
5.5.1 * USING HEIGHT COORDINATES 224
5.5.2 USING ISENTROPIC COORDINATES 225
5.6 * ENERGETICS OF QUASI-GEOSTROPHY 226
5.6.1 CONVERSION BETWEEN APE AND KE 227
5.6.2 ENERGETICS OF TWO-LAYER FLOWS 228
5.6.3 ENSTROPHY CONSERVATION 229
5.7 ROSSBYWAVES 229
5.7.1 WAVES IN A SINGLE LAYER 229
5.7.2 ROSSBY WAVES IN TWO LAYERS 232
5.8 * ROSSBY WAVES IN STRATIFIED QUASI-GEOSTROPHIC FLOW 234
5.8.1 SETTING UP THE PROBLEM 234
5.8.2 WAVE MOTION 235
APPENDIX: WAVE KINEMATICS, GROUP VELOCITY AND PHASE SPEED 236 5.A.I
KINEMATICS AND DEFINITIONS 236
5.A.2 WAVE PROPAGATION 237
5.A.3 MEANING OF GROUP VELOCITY 239
PART II INSTABILITIES, WAVE-MEAN FLOW INTERACTION AND TURBULENCE 245
6 BAROTROPIC AND BAROCLINIC INSTABILITY 247
6.1 KELVIN-HELMHOLTZ INSTABILITY 248
6.2 INSTABILITY OF PARALLEL SHEAR FLOW 250
6.2.1 PIECEWISE LINEAR FLOWS 251
IMAGE 7
XII CONTENTS
6.2.2 KELVIN-HELMHOLTZ INSTABILITY, REVISITED 253
6.2.3 EDGE WAVES 254
6.2.4 INTERACTING EDGE WAVES PRODUCING INSTABILITY 254
6.3 NECESSARY CONDITIONS FOR INSTABILITY 258
6.3.1 RAYLEIGH S CRITERION 258
6.3.2 FJ0RTOFT S CRITERION 260
6.4 BAROCLINIC INSTABILITY 261
6.4.1 A PHYSICAL PICTURE 261
6.4.2 LINEARIZED QUASI-GEOSTROPHIC EQUATIONS 263
6.4.3 NECESSARY CONDITIONS FOR BAROCLINIC INSTABILITY 264
6.5 THE EADY PROBLEM 265
6.5.1 THE LINEARIZED PROBLEM 266
6.5.2 ATMOSPHERIC AND OCEANIC PARAMETERS 268
6.6 TWO-LAYER BAROCLINIC INSTABILITY 271
6.6.1 POSING THE PROBLEM 271
6.6.2 THE SOLUTION 272
6.7 AN INFORMAL VIEW OF THE MECHANISM OF BAROCLINIC INSTABILITY 277
6.7.1 THE TWO-LAYER MODEL 278
6.7.2 INTERACTING EDGE WAVES IN THE EADY PROBLEM 280
6.8 * THE ENERGETICS OF LINEAR BAROCLIRJIC INSTABILITY 282
6.9 * BETA, SHEAR AND STRATIFICATION IN A CONTINUOUS MODEL 284
6.9.1 SCALING ARGUMENTS FOR GROWTH RATES, SCALES AND DEPTH 284
6.9.2 SOME NUMERICAL CALCULATIONS 287
7 WAVE-MEAN FLOW INTERACTION 295
7.1 QUASI-GEOSTROPHIC PRELIMINARIES 296
7.1.1 POTENTIAL VORTICITY FLUX IN THE LINEAR EQUATIONS 297
7.2 THE ELIASSEN-PALM FLUX 298
7.2.1 THE ELIASSEN-PALM RELATION 299
7.2.2 THE GROUP VELOCITY PROPERTY 300
7.2.3 * THE ORTHOGONALITY OF MODES 302
7.3 THE TRANSFORMED EULERIAN MEAN 304
7.3.1 QUASI-GEOSTROPHIC FORM 304
7.3.2 THE TEM IN ISENTROPIC COORDINATES 306
7.3.3 RESIDUAL AND THICKNESS-WEIGHTED CIRCULATION 307
7.3.4 * THE TEM IN THE PRIMITIVE EQUATIONS 309
7.4 THE NON-ACCELERATION RESULT 314
7.4.1 A DERIVATION FROM THE POTENTIAL VORTICITY EQUATION 314
7.4.2 USING TEM TO GIVE THE NON-ACCELERATION RESULT 316
7.4.3 THE EP FLUX AND FORM DRAG 317
7.5 INFLUENCE OF EDDIES ON THE MEAN FLOW IN THE EADY PROBLEM 319
7.5.1 FORMULATION 319
7.5.2 SOLUTION 321
7.5.3 THE TWO-LEVEL PROBLEM 324
7.6 * NECESSARY CONDITIONS FOR INSTABILITY 324
7.6.1 STABILITY CONDITIONS FROM PSEUDOMOMENTUM CONSERVATION 325
IMAGE 8
CONTENTS XIII
7.6.2 INCLUSION OF BOUNDARY TERMS 325
7.7 * NECESSARY CONDITIONS FOR INSTABILITY: USE OF PSEUDOENERGY 327
7.7.1 TWO-DIMENSIONAL FLOW 327
7.7.2 * STRATIFIED QUASI-GEOSTROPHIC FLOW 330
7.7.3 * APPLICATIONS TO BAROCLINIC INSTABILITY 331
8 BASIC THEORY OF INCOMPRESSIBLE TURBULENCE 337
8.1 THE FUNDAMENTAL PROBLEM OF TURBULENCE 338
8.1.1 THE CLOSURE PROBLEM 338
8.1.2 TRIAD INTERACTIONS IN TURBULENCE 339
8.2 THE KOLMOGOROV THEORY 341
8.2.1 THE PHYSICAL PICTURE 341
8.2.2 INERTIAL-RANGE THEORY 342
8.2.3 * ANOTHER EXPRESSION OF THE INERTIAL-RANGE SCALING ARGUMENT 348
8.2.4 A FINAL NOTE ON OUR ASSUMPTIONS 349
8.3 TWO-DIMENSIONAL TURBULENCE 349
8.3.1 ENERGY AND ENSTROPHY TRANSFER 351
8.3.2 INERTIAL RANGES IN TWO-DIMENSIONAL TURBULENCE 354
8.3.3 T MORE ABOUT THE PHENOMENOLOGY 358
8.3.4 NUMERICAL ILLUSTRATIONS 360
8.4 PREDICTABILITY OF TURBULENCE 361
8.4.1 LOW-DIMENSIONAL CHAOS AND UNPREDICTABILITY 362
8.4.2 * PREDICTABILITY OF A TURBULENT FLOW 363
8.4.3 IMPLICATIONS AND WEATHER PREDICTABILITY 365
8.5 * SPECTRA OF PASSIVE TRACERS 366
8.5.1 EXAMPLES OF TRACER SPECTRA 368
9 GEOSTROPHIC TURBULENCE AND BAROCLINIC EDDIES 377
9.1 EFFECTS OF DIFFERENTIAL ROTATION 377
9.1.1 THE WAVE-TURBULENCE CROSS-OVER 378
9.1.2 GENERATION OF ZONAL FLOWS AND JETS 380
9.1.3 T JOINT EFFECT OF P AND FRICTION 382
9.2 STRATIFIED GEOSTROPHIC TURBULENCE . 384
9.2.1 AN ANALOGUE TO TWO-DIMENSIONAL FLOW 384
9.2.2 TWO-LAYER GEOSTROPHIC TURBULENCE 385
9.2.3 PHENOMENOLOGY OF TWO-LAYER TURBULENCE 388
9.3 T A SCALING THEORY FOR GEOSTROPHIC TURBULENCE 391
9.3.1 PRELIMINARIES 392
9.3.2 SCALING PROPERTIES 393
9.3.3 THE HALTING SCALE AND THE ^-EFFECT 395
9.4 T PHENOMENOLOGY OF BAROCLINIC EDDIES IN THE ATMOSPHERE AND OCEAN 395
9.4.1 THE MAGNITUDE AND SCALE OF BAROCLINIC EDDIES 396
9.4.2 BAROCLINIC EDDIES AND THEIR LIFECYCLE IN THE ATMOSPHERE 397
9.4.3 BAROCLINIC EDDIES AND THEIR LIFECYCLE IN THE OCEAN 400
IMAGE 9
XIV CONTENTS
10 TURBULENT DIFFUSION AND EDDY TRANSPORT 407
10.1 DIFFUSIVE TRANSPORT 408
10.1.1 AN EXPLICIT EXAMPLE 409
10.2 TURBULENT DIFFUSION 409
10.2.1 SIMPLE THEORY 409
10.2.2 * AN ANISOTROPIC GENERALIZATION 413
10.2.3 DISCUSSION 415
10.3 TWO-PARTICLE DIFFUSIVITY 415
10.3.1 LARGE PARTICLE SEPARATION 416
10.3.2 SEPARATION WITHIN THE INERTIAL RANGE 41 7
10.4 MIXING LENGTH THEORY 419
10.4.1 REQUIREMENTS FOR TURBULENT DIFFUSION 421
10.4.2 A MACROSCOPIC PERSPECTIVE 422
10.5 HOMOGENIZATION OF A SCALAR THAT IS ADVECTED AND DIFFUSED 423 10.5.1
NON-EXISTENCE OF EXTREMA 423
10.5.2 HOMOGENIZATION IN TWO-DIMENSIONAL FLOW 424
10.6 T TRANSPORT BY BAROCLINIC EDDIES 425
10.6.1 SYMMETRIC AND ANTISYMMETRIC DIFFUSIVITY TENSORS 426 10.6.2 *
DIFFUSION WITH THE SYMMETRIC TENSOR 426
10.6.3 * SKEW DIFFUSION 427
10.6.4 THE STORY SO FAR 429
10.7 F EDDY DIFFUSION IN THE ATMOSPHERE AND OCEAN 430
10.7.1 PRELIMINARIES 430
10.7.2 MAGNITUDE OF THE EDDY DIFFUSIVITY 430
10.7.3 * STRUCTURE: THE SYMMETRIC TRANSPORT TENSOR 432
10.7.4 * STRUCTURE: THE ANTISYMMETRIC TRANSPORT TENSOR 435 10.7.5
EXAMPLES 437
10.8 T THICKNESS DIFFUSION . 440
10.8.1 EQUATIONS OF MOTION 440
10.8.2 DIFFUSIVE THICKNESS TRANSPORT 442
10.9 T EDDY TRANSPORT AND THE TRANSFORMED EULERIAN MEAN 443
10.9.1 POTENTIAL VORTICITY DIFFUSION 443
PART III LARGE-SCALE ATMOSPHERIC CIRCULATION 449
11 THE OVERTURNING CIRCULATION: HADLEY AND FERREL CELLS 451 11.1 BASIC
FEATURES OF THE ATMOSPHERE 452
11.1.1 THE RADIATIVE EQUILIBRIUM DISTRIBUTION 452
11.1.2 OBSERVED WIND AND TEMPERATURE FIELDS 453
11.1.3 MERIDIONAL OVERTURNING CIRCULATION 456
11.1.4 SUMMARY 457
11.2 A STEADY MODEL OF THE HADLEY CELL 457
11.2.1 ASSUMPTIONS 457
11.2.2 DYNAMICS 458
IMAGE 10
CONTENTS XV
11.2.3 THERMODYNAMICS 460
11.2.4 ZONAL WIND 462
1.2.5 PROPERTIES OF SOLUTION 463
1.2.6 STRENGTH OF THE CIRCULATION 464
1.2.7 T EFFECTS OF MOISTURE 465
1.2.8 THE RADIATIVE EQUILIBRIUM SOLUTION 466
11.3 A SHALLOW WATER MODEL OF THE HADLEY CELL 468
11.3.1 MOMENTUM BALANCE 468
1.3.2 THERMODYNAMIC BALANCE 468
11.4 F ASYMMETRY AROUND THE EQUATOR 469
11.5 EDDIES, VISCOSITY AND THE HADLEY CELL 473
11.5.1 QUALITATIVE CONSIDERATIONS 473
11.5.2 AN IDEALIZED EDDY-DRIVEN MODEL 474
11.6 THE HADLEY CELL: SUMMARY AND NUMERICAL SOLUTIONS 477
11.7 THE FERREL CELL 480
12 ZONALLY AVERAGED MID-LATITUDE ATMOSPHERIC CIRCULATION 485
12.1 SURFACE WESTERLIES AND THE MAINTENANCE OF A BAROTROPIC JET 486
12.1.1 OBSERVATIONS AND MOTIVATION 486
12.1.2 THE MECHANISM OF JET PRODUCTION 487
12.1.3 A NUMERICAL EXAMPLE 495
12.2 LAYERED MODELS OF THE MID-LATITUDE CIRCULATION 496
12.2.1 A SINGLE-LAYER MODEL 497
12.2.2 A TWO-LAYER MODEL 503
12.2.3 DYNAMICS OF THE TWO-LAYER MODEL 507
12.3 T EDDY FLUXES AND AN EXAMPLE OF A CLOSED MODEL 513
12.3.1 EQUATIONS FOR A CLOSED MODEL 513
12.3.2 * EDDY FLUXES AND NECESSARY CONDITIONS FOR INSTABILITY 514
12.4 A STRATIFIED MODEL AND THE REAL ATMOSPHERE 516
12.4.1 POTENTIAL VORTICITY AND ITS FLUXES 516
12.4.2 OVERTURNING CIRCULATION 522
12.5 T THE TROPOPAUSE AND THE STRATIFICATION OF THE ATMOSPHERE 522
12.5.1 A RADIATIVE-CONVECTIVE MODEL 526
12.5.2 RADIATIVE AND DYNAMICAL CONSTRAINTS 528
12.6 T BAROCLINIC EDDIES AND POTENTIAL VORTICITY TRANSPORT 529
12.6.1 A LINEAR ARGUMENT 530
12.6.2 MIXING POTENTIAL VORTICITY AND BAROCLINIC ADJUSTMENT 530
1 2.6.3 DIFFUSIVE TRANSPORT OF POTENTIAL VORTICITY 532
12.7 T EXTRATROPICAL CONVECTION AND THE VENTILATED TROPOSPHERE 534
APPENDIX: TEM FOR THE PRIMITIVE EQUATIONS IN SPHERICAL COORDINATES 536
13 PLANETARY WAVES A ND THE STRATOSPHERE 541
13.1 FORCED AND STATIONARY ROSSBY WAVES 542
13.1.1 A SIMPLE ONE-LAYER CASE 542
1 3.1.2 APPLICATION TO EARTH S ATMOSPHERE 543
IMAGE 11
XVI CONTENTS
13.1.3 * ONE-DIMENSIONAL ROSSBY WAVE TRAINS 545
13.1.4 THE ADEQUACY OF LINEAR THEORY 548
1 3.2 * MERIDIONAL PROPAGATION AND DISPERSION 549
13.2.1 RAY TRACING 549
13.2.2 ROSSBY WAVES AND ROSSBY RAYS 550
13.2.3 APPLICATION TO AN IDEALIZED ATMOSPHERE 553
1 3.3 * VERTICAL PROPAGATION OF ROSSBY WAVES IN A STRATIFIED MEDIUM 554
13.3.1 MODEL FORMULATION 554
13.3.2 MODEL SOLUTION 555
13.3.3 PROPERTIES OF THE SOLUTION 559
13.4 * EFFECTS OF THERMAL FORCING 560
13.4.1 THERMODYNAMIC BALANCES 561
13.4.2 PROPERTIES OF THE SOLUTION 562
13.4.3 NUMERICAL SOLUTIONS 563
13.5 STRATOSPHERIC DYNAMICS 566
13.5.1 A DESCRIPTIVE OVERVIEW 566
13.5.2 T DYNAMICS OF THE OVERTURNING CIRCULATION 569
13.5.3 T THE POLAR VORTEX AND THE QUASI-HORIZONTAL CIRCULATION 575
PART IV LARGE-SCALE OCEANIC CIRCULATION 581
14 WIND-DRIVEN GYRES 583
14.1 THE DEPTH INTEGRATED WIND-DRIVEN CIRCULATION 585
14.1.1 THE STOMMEL MODEL 586
14.1.2 ALTERNATIVE FORMULATIONS 587
14.1.3 APPROXIMATE SOLUTION OF STOMMEL MODEL 589
14.2 USING VISCOSITY INSTEAD OF DRAG 593
14.3 ZONAL BOUNDARY LAYERS * 597
14.4 * THE NONLINEAR PROBLEM 599
14.4.1 A PERTURBATIVE APPROACH 600
14.4.2 A NUMERICAL APPROACH 600
14.5 * INERTIAL SOLUTIONS 601
14.5.1 ROLES OF FRICTION AND INERTIA 603
14.5.2 ATTEMPTING AN INERTIAL WESTERN BOUNDARY SOLUTION 604
14.5.3 A FULLY INERTIAL APPROACH: THE FOFONOFF MODEL 606
14.6 TOPOGRAPHIC EFFECTS ON WESTERN BOUNDARY CURRENTS 608
14.6.1 HOMOGENEOUS MODEL 608
14.6.2 ADVECTIVE DYNAMICS 609
14.6.3 BOTTOM PRESSURE STRESS AND FORM DRAG 611
14.7 * VERTICAL STRUCTURE OF THE WIND-DRIVEN CIRCULATION 613
14.7.1 A TWO-LAYER QUASI-GEOSTROPHIC MODEL 613
14.7.2 THE FUNCTIONAL RELATIONSHIP BETWEEN IFJ AND Q 616
14.8 * A MODEL WITH CONTINUOUS STRATIFICATION 619
14.8.1 DEPTH OF THE WIND S INFLUENCE 619
14.8.2 THE COMPLETE SOLUTION 620
IMAGE 12
CONTENTS XVII
15 THE BUOYANCY-DRIVEN OCEAN CIRCULATION 627
15.1 SIDEWAYS CONVECTION 629
15.1.1 TWO-DIMENSIONAL CONVECTION 630
15.1.2 T PHENOMENOLOGY OF THE OVERTURNING CIRCULATION 633
1 5.2 THE MAINTENANCE OF SIDEWAYS CONVECTION 634
15.2.1 THE ENERGY BUDGET 635
1 5.2.2 CONDITIONS FOR MAINTAINING A THERMALLY-DRIVEN CIRCULATION 635
15.2.3 SURFACE FLUXES AND NON-TURBULENT FLOW AT SMALL DIFFUSIVITIES 637
1 5.2.4 THE IMPORTANCE OF MECHANICAL FORCING 639
15.3 SIMPLE BOX MODELS 640
15.3.1 A TWO-BOX MODEL 640
15.3.2 * MORE BOXES 644
1 5.4 A LABORATORY MODEL OF THE ABYSSAL CIRCULATION 646
15.4.1 SET-UP OF THE LABORATORY MODEL 646
15.4.2 DYNAMICS OF FLOW IN THE TANK 647
15.5 A MODEL FOR OCEANIC ABYSSAL FLOW 650
15.5.1 COMPLETING THE SOLUTION 652
15.5.2 APPLICATION TO THE OCEAN 653
15.5.3 A TWO-HEMISPHERE MODEL 655
15.6 * A SHALLOW WATER MODEL OF THE ABYSSAL FLOW 656
15.6.1 POTENTIAL VORTICITY AND POLEWARD INTERIOR FLOW 657
1 5.6.2 THE SOLUTION 658
1 5.7 SCALING FOR THE BUOYANCY-DRIVEN CIRCULATION 659
15.7.1 SUMMARY REMARKS ON THE STOMMEL-ARONS MODEL 661
16 THE WIND-AND BUOYANCY-DRIVEN OCEAN CIRCULATION 667
16.1 THE MAIN THERMOCLINE: AN INTRODUCTION 667
16.1.1 A SIMPLE KINEMATIC MODEL 668
16.2 SCALING AND SIMPLE DYNAMICS OF THE MAIN THERMOCLINE 670
16.2.1 AN ADVECTIVE SCALE 671
16.2.2 A DIFFUSIVE SCALE 672
16.2.3 SUMMARY OF THE PHYSICAL PICTURE 673
16.3 THE INTERNAL THERMOCLINE 674
16.3.1 THE M EQUATION 674
16.3.2 * BOUNDARY-LAYER ANALYSIS 676
16.4 THE VENTILATED THERMOCLINE 681
16.4.1 A REDUCED GRAVITY, SINGLE-LAYER MODEL 682
16.4.2 A TWO-LAYER MODEL 683
16.4.3 THE SHADOW ZONE 686
16.4.4 T THE WESTERN POOL 688
16.5 T A MODEL OF DEEP WIND-DRIVEN OVERTURNING 691
16.5.1 A SINGLE-HEMISPHERE MODEL 693
16.5.2 A CROSS-EQUATORIAL WIND-DRIVEN DEEP CIRCULATION 697
16.6 T FLOW IN A CHANNEL AND THE ANTARCTIC CIRCUMPOLAR CURRENT 700
16.6.1 STEADY AND EDDYING FLOW 701
IMAGE 13
XVIII CONTENTS
16.6.2 VERTICALLY INTEGRATED MOMENTUM BALANCE 702
16.6.3 FORM DRAG AND BAROCLINIC EDDIES 703
16.6.4 T AN IDEALIZED ADIABATIC MODEL 708
16.6.5 FORM STRESS AND EKMAN STRESS AT THE OCEAN BOTTOM 709
16.6.6 DIFFERENCES BETWEEN GYRES AND CHANNELS 710
APPENDIX: MISCELLANEOUS RELATIONSHIPS IN A LAYERED MODEL 710
16.A.1 HYDROSTATIC BALANCE 711
16.A.2 GEOSTROPHIC AND THERMAL WIND BALANCE 711
16.A.3 EXPLICIT CASES 712
REFERENCES 717
INDEX 738
|
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| author_facet | Vallis, Geoffrey K. |
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| bvnumber | BV023802902 |
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| discipline | Physik |
| edition | 1. publ., Reprinted |
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| id | DE-604.BV023802902 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T21:37:08Z |
| institution | BVB |
| isbn | 0521849691 9780521849692 |
| language | English |
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| spelling | Vallis, Geoffrey K. Verfasser aut Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation Geoffrey K. Vallis 1. publ., Reprinted Cambridge [u.a.] Cambridge Univ. Press 2007 XXV, 745 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Meer (DE-588)4038301-5 gnd rswk-swf Atmosphäre (DE-588)4003397-1 gnd rswk-swf Meer (DE-588)4038301-5 s Atmosphäre (DE-588)4003397-1 s Strömungsmechanik (DE-588)4077970-1 s DE-604 http://catdir.loc.gov/catdir/enhancements/fy0707/2007295337-d.html Beschreibung für Leser GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017445101&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Vallis, Geoffrey K. Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation Strömungsmechanik (DE-588)4077970-1 gnd Meer (DE-588)4038301-5 gnd Atmosphäre (DE-588)4003397-1 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4038301-5 (DE-588)4003397-1 |
| title | Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation |
| title_auth | Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation |
| title_exact_search | Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation |
| title_full | Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation Geoffrey K. Vallis |
| title_fullStr | Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation Geoffrey K. Vallis |
| title_full_unstemmed | Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation Geoffrey K. Vallis |
| title_short | Atmospheric and oceanic fluid dynamics |
| title_sort | atmospheric and oceanic fluid dynamics fundamentals and large scale circulation |
| title_sub | fundamentals and large-scale circulation |
| topic | Strömungsmechanik (DE-588)4077970-1 gnd Meer (DE-588)4038301-5 gnd Atmosphäre (DE-588)4003397-1 gnd |
| topic_facet | Strömungsmechanik Meer Atmosphäre |
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