Atmospheric and oceanic fluid dynamics: fundamentals and large-scale circulation
Gespeichert in:
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| Format: | Buch |
| Sprache: | English |
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Cambridge [u.a.]
Cambridge Univ. Press
2006
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| Ausgabe: | 1. publ. |
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Hier auch später erschienene, unveränderte Nachdrucke |
| Beschreibung: | XXV, 745 S. Ill., graph. Darst. |
| ISBN: | 9780521849692 0521849691 |
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| 100 | 1 | |a Vallis, Geoffrey K. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Atmospheric and oceanic fluid dynamics |b fundamentals and large-scale circulation |c Geoffrey K. Vallis |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2006 | |
| 300 | |a XXV, 745 S. |b Ill., graph. Darst. | ||
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| 500 | |a Hier auch später erschienene, unveränderte Nachdrucke | ||
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Fluid dynamics |v Problems, exercises, etc | |
| 650 | 4 | |a Ocean-atmosphere interaction | |
| 650 | 4 | |a Ocean-atmosphere interaction |v Problems, exercises, etc | |
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Datensatz im Suchindex
| _version_ | 1804136245837692928 |
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| adam_text | ATMOSPHERIC AND OCEANIC FLUID DYNAMICS FUNDAMENTALS AND LARGE-SCALE
CIRCULATION G E O F F R E Y K. V A L L I S PRINCETON UNIVERSITY, NEW
JERSEY CAMBRIDGE UNIVERSITY PRESS 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 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 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 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 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 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 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 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
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 AND 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 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
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 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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ATMOSPHERIC AND OCEANIC FLUID DYNAMICS FUNDAMENTALS AND LARGE-SCALE
CIRCULATION G E O F F R E Y K. V A L L I S PRINCETON UNIVERSITY, NEW
JERSEY CAMBRIDGE UNIVERSITY PRESS 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 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 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 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 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 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 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 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
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 AND 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 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
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 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 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Vallis, Geoffrey K. |
| author_facet | Vallis, Geoffrey K. |
| author_role | aut |
| author_sort | Vallis, Geoffrey K. |
| author_variant | g k v gk gkv |
| building | Verbundindex |
| bvnumber | BV022250105 |
| callnumber-first | Q - Science |
| callnumber-label | QC809 |
| callnumber-raw | QC809.F5 |
| callnumber-search | QC809.F5 |
| callnumber-sort | QC 3809 F5 |
| callnumber-subject | QC - Physics |
| classification_rvk | RB 10115 UF 4000 UT 3000 UT 5000 |
| ctrlnum | (OCoLC)70671784 (DE-599)BVBBV022250105 |
| dewey-full | 532.05 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 532 - Fluid mechanics |
| dewey-raw | 532.05 |
| dewey-search | 532.05 |
| dewey-sort | 3532.05 |
| dewey-tens | 530 - Physics |
| discipline | Physik Geographie |
| discipline_str_mv | Physik Geographie |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV022250105 |
| illustrated | Illustrated |
| index_date | 2024-07-02T16:39:17Z |
| indexdate | 2024-07-09T20:53:20Z |
| institution | BVB |
| isbn | 9780521849692 0521849691 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015460908 |
| oclc_num | 70671784 |
| open_access_boolean | |
| owner | DE-20 DE-703 DE-1051 DE-19 DE-BY-UBM DE-706 |
| owner_facet | DE-20 DE-703 DE-1051 DE-19 DE-BY-UBM DE-706 |
| physical | XXV, 745 S. Ill., graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| spelling | Vallis, Geoffrey K. Verfasser aut Atmospheric and oceanic fluid dynamics fundamentals and large-scale circulation Geoffrey K. Vallis 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2006 XXV, 745 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Hier auch später erschienene, unveränderte Nachdrucke Fluid dynamics Fluid dynamics Problems, exercises, etc Ocean-atmosphere interaction Ocean-atmosphere interaction Problems, exercises, etc 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 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015460908&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 Fluid dynamics Fluid dynamics Problems, exercises, etc Ocean-atmosphere interaction Ocean-atmosphere interaction Problems, exercises, etc 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_exact_search_txtP | 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 | Fluid dynamics Fluid dynamics Problems, exercises, etc Ocean-atmosphere interaction Ocean-atmosphere interaction Problems, exercises, etc Strömungsmechanik (DE-588)4077970-1 gnd Meer (DE-588)4038301-5 gnd Atmosphäre (DE-588)4003397-1 gnd |
| topic_facet | Fluid dynamics Fluid dynamics Problems, exercises, etc Ocean-atmosphere interaction Ocean-atmosphere interaction Problems, exercises, etc Strömungsmechanik Meer Atmosphäre |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015460908&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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