Holdings: Atmospheric dynamics

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Bibliographic Details
Main Author:	Achatz, Ulrich 1963- (Author)
Format:	Book
Language:	English
Published:	Berlin, Germany Springer Spektrum [2022]
Series:	Textbook
Subjects:	Physik Atmosphäre Dynamik Gravity waves waves action atmospheric dynamics wave impact wave behavior Equations of Motion
Online Access:	Inhaltstext Inhaltsverzeichnis Inhaltsverzeichnis
Physical Description:	xiv, 553 Seiten Diagramme 24 cm, 1168 g
ISBN:	9783662639405 3662639408

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adam_text	CONTENTS 1 THE BASIC EQUATIONS OF ATMOSPHERIC MOTION ................................................ 1 1.1 TIME DERIVATIVES IN FLUIDS ...................................................................... 1 1.1.1 THE FLUID DESCRIPTION ACCORDING TO EULER AND LAGRANGE .... 1 1.1.2 THE MATERIAL DERIVATIVE OF A FLUID ELEMENT ............................ 3 1.1.3 THE MATERIAL DERIVATIVE OF VOLUME INTEGRALS .......................... 5 1.1.4 SUMMARY ................................................................................ 8 1.2 THE EQUATION OF CONTINUITY .................................................................... 8 1.2.1 A EULERIAN DERIVATION ............................................................ 8 1.2.2 A LAGRANGIAN DERIVATION USING THE MATERIAL DERIVATIVE ......... 9 1.2.3 SUMMARY ................................................................................ 10 1.3 THE MOMENTUM EQUATION ...................................................................... 10 1.3.1 THE VOLUME FORCES .................................................................. 10 1.3.2 SURFACE FORCES (1): THE PRESSURE GRADIENT FORCE .................. 11 1.3.3 SURFACE FORCES (2): FRICTION .................................................... 13 1.3.4 THE TOTAL MOMENTUM EQUATION ............................................... 18 1.3.5 SUMMARY ................................................................................ 18 1.4 THE EQUATIONS OF MOTION IN A ROTATING FRAME OF REFERENCE .................. 19 1.4.1 THE TIME DERIVATIVE IN A ROTATING FRAME OF REFERENCE ......... 19 1.4.2 THE MOMENTUM EQUATION IN THE ROTATING FRAME OF REFERENCE ............................................................................ 20 1.4.3 THE EQUATION OF CONTINUITY IN THE ROTATING FRAME OF REFERENCE ............................................................................ 22 1.4.4 SUMMARY ................................................................................ 23 1.5 THE EQUATIONS OF MOTION ON THE SPHERE ................................................ 23 1.5.1 VELOCITY AND MATERIAL DERIVATIVE IN SPHERICAL COORDINATES ............................................................................ 24 1.5.2 THE TRANSFORMED EQUATIONS OF MOTION .................................. 26 1.5.3 SUMMARY ................................................................................ 28 VIII CONTENTS 1.6 SYNOPTIC SCALE ANALYSIS .......................................................................... 28 1.6.1 THE GEOSTROPHIC EQUILIBRIUM .................................................. 29 1.6.2 THE HYDROSTATIC EQUILIBRIUM .................................................. 31 1.6.3 SUMMARY ................................................................................ 34 1.7 RECOMMENDATIONS FOR FURTHER READING ................................................... 34 2 ELEMENTARY THERMODYNAMICS AND ENERGETICS OF DRY AIR ............................ 35 2.1 FUNDAMENTALS ........................................................................................... 35 2.1.1 THERMODYNAMIC SYSTEMS ........................................................ 35 2.1.2 THERMODYNAMIC STATE AND THERMODYNAMIC EQUILIBRIUM .... 36 2.1.3 TEMPERATURE ............................................................................ 37 2.1.4 EQUATIONS OF STATE .................................................................. 38 2.1.5 ENERGY CHANGE OF A THERMODYNAMIC SYSTEM ........................ 38 2.1.6 SUMMARY ................................................................................ 41 2.2 THE FUNDAMENTAL LAWS OF THERMODYNAMICS .......................................... 41 2.2.1 THE FIRST LAW OF THERMODYNAMICS AND INTERNAL ENERGY ........ 42 2.2.2 THE HEAT CAPACITIES OF AN IDEAL GAS ...................................... 43 2.2.3 ADIABATIC AND ISOTHERMAL CHANGES OF STATE OF AN IDEAL GAS ........................................................................ 44 2.2.4 THE SECOND LAW OF THERMODYNAMICS .................................... 46 2.2.5 THE CARNOT PROCESS ................................................................ 50 2.2.6 ENTROPY AS STATE VARIABLE ........................................................ 52 2.2.7 ENTROPY AND POTENTIAL TEMPERATURE OF DRY AIR ....................... 57 2.2.8 SUMMARY ................................................................................ 59 2.3 THE PROGNOSTIC EQUATIONS FOR TEMPERATURE AND ENTROPY IN DRY AIR .... 60 2.3.1 PREDICTION OF TEMPERATURE ...................................................... 60 2.3.2 THE PREDICTION OF ENTROPY AND POTENTIAL TEMPERATURE ............ 65 2.3.3 THE EQUATIONS IN A ROTATING FRAME OF REFERENCE ................... 66 2.3.4 SPHERICAL COORDINATES ............................................................ 66 2.3.5 SUMMARY ................................................................................ 66 2.4 POTENTIAL TEMPERATURE AND STATIC STABILITY .............................................. 67 2.4.1 STABLE AND UNSTABLE STRATIFICATION .......................................... 67 2.4.2 BUOYANCY OSCILLATIONS ............................................................ 69 2.4.3 SUMMARY .............................. 70 2.5 RECOMMENDATIONS FOR FURTHER READING .................................................. 71 3 ELEMENTARY PROPERTIES AND APPLICATIONS OF THE BASIC EQUATIONS ................ 73 3.1 SUMMARY OF THE BASIC EQUATIONS ............................................................ 73 3.2 THE IMPORTANCE OF THE BASIC EQUATIONS FOR WEATHER PREDICTION ............ 74 3.3 CONSERVATION LAWS .................................................................................. 75 3.3.1 CONSERVATION OF ENERGY .......................................................... 75 3.3.2 CONSERVATION OF ANGULAR MOMENTUM ...................................... 77 3.3.3 SUMMARY ................................................................................ 79 CONTENTS IX 3.4 THE PRIMITIVE EQUATIONS .......................................................................... 80 3.5 THE PRIMITIVE EQUATIONS IN PRESSURE COORDINATES .................................. 82 3.5.1 ARBITRARY VERTICAL COORDINATES ................................................ 82 3.5.2 PRESSURE COORDINATES .............................................................. 85 3.5.3 SUMMARY ................................................................................ 86 3.6 BALANCED FLOWS ...................................................................................... 87 3.6.1 THE NATURAL COORDINATES ........................................................ 87 3.6.2 GEOSTROPHIC FLOW .................................................................... 89 3.6.3 INERTIAL FLOW ............................................................................ 90 3.6.4 CYCLOSTROPHIC FLOW ................................................................ 91 3.6.5 THE GRADIENT WIND .................................................................. 92 3.6.6 SUMMARY ................................................................................ 94 3.7 THERMAL WIND ........................................................................................ 95 3.8 RECOMMENDATIONS FOR FURTHER READING ................................................... 97 4 VORTEX DYNAMICS .............................................................................................. 99 4.1 VORTICITY .................................................................................................. 99 4.1.1 RELATIVE, ABSOLUTE, AND PLANETARY VORTICITY ............................ 99 4.1.2 VORTEX LINES, VORTEX TUBES, AND VORTEX FLUX ........................... 100 4.1.3 SUMMARY ................................................................................ 102 4.2 CIRCULATION .............................................................................................. 103 4.2.1 RELATIVE AND ABSOLUTE CIRCULATION .......................................... 103 4.2.2 THE GENERAL CIRCULATION THEOREM .......................................... 104 4.2.3 SUMMARY ................................................................................ 108 4.3 THE KELVIN THEOREM .............................................................................. 108 4.4 THE VORTICITY EQUATION ............................................................................ 110 4.4.1 THE DERIVATION ........................................................................ 110 4.4.2 VORTEX-TUBE STRETCHING AND VORTEX TILTING .............................. ILL 4.4.3 SUMMARY OF THE IMPACTS ON RELATIVE VORTICITY ...................... 113 4.4.4 THE FROZEN-IN PROPERTY OF ABSOLUTE VORTICITY ........................ 113 4.4.5 SUMMARY ................................................................................ 114 4.5 POTENTIAL VORTICITY .................................................................................... 115 4.5.1 AN ALGEBRAIC DERIVATION OF THE PROGNOSTIC EQUATION FOR POTENTIAL VORTICITY .............................................................. 115 4.5.2 A DERIVATION OF POTENTIAL-VORTICITY CONSERVATION FROM THE GENERAL CIRCULATION THEOREM .................................. 117 4.5.3 SUMMARY ................................................................................ 119 4.6 VORTEX DYNAMICS AND THE PRIMITIVE EQUATIONS ...................................... 120 4.6.1 THE PRIMITIVE EQUATIONS IN ISENTROPIC COORDINATES ................ 120 4.6.2 THE PRIMITIVE VORTICITY EQUATION IN ISENTROPIC COORDINATES ........................................................ 123 4.6.3 THE POTENTIAL VORTICITY OF THE PRIMITIVE EQUATIONS .................. 125 X CONTENTS 4.6.4 FLOW OVER A MOUNTAIN RIDGE .................................................. 125 4.6.5 SUMMARY ................................................................................ 129 4.7 RECOMMENDATIONS FOR FURTHER READING ................................................... 129 5 THE DYNAMICS OF THE SHALLOW-WATER EQUATIONS ............................................ 131 5.1 DERIVATION OF THE EQUATIONS .................................................................... 131 5.1.1 THE MOMENTUM EQUATION ...................................................... 132 5.1.2 THE CONTINUITY EQUATION ........................................................ 133 5.1.3 SUMMARY ................................................................................ 134 5.2 CONSERVATION PROPERTIES .......................................................................... 134 5.2.1 ENERGY CONSERVATION .............................................................. 134 5.2.2 POTENTIAL VORTICITY.................................................................... 136 5.2.3 SUMMARY ................................................................................ 137 5.3 QUASIGEOSTROPHIC DYNAMICS .................................................................. 137 5.3.1 THE TANGENTIAL /-PLANE ............................................................ 137 5.3.2 SCALING THE SHALLOW-WATER EQUATIONS ON THE /-PLANE ............. 140 5.3.3 THE QUASIGEOSTROPHIC APPROXIMATION: DERIVATION BY SCALE ASYMPTOTICS ............................................ 144 5.3.4 THE QUASIGEOSTROPHIC APPROXIMATION: DERIVATION FROM THE CONSERVATION OF SHALLOW-WATER POTENTIAL VORTICITY .......... 148 5.3.5 SUMMARY ................................................................................ 150 5.4 WAVE SOLUTIONS OF THE SHALLOW-WATER EQUATIONS .................................... 150 5.4.1 PERTURBATION APPROACH ............................................................ 151 5.4.2 WAVES ON THE/-PLANE .............................................................. 153 5.4.3 WAVES ON THE / PLANE: QUASIGEOSTROPHIC ROSSBY WAVES ......... 160 5.4.4 SUMMARY ................................................................................ 165 5.5 GEOSTROPHIC ADJUSTMENT .......................................................................... 166 5.5.1 THE GENERAL SOLUTION OF THE LINEAR SHALLOW-WATER EQUATIONS ON AN / PLANE .......................................................... 166 5.5.2 THE ADJ USTMENT PROCESS .......................................................... 170 5.5.3 SUMMARY ................................................................................ 177 5.6 RECOMMENDATIONS FOR FURTHER READING .................................................. 177 6 QUASIGEOSTROPHIC DYNAMICS OF THE STRATIFIED ATMOSPHERE .......................... 179 6.1 QUASIGEOSTROPHIC THEORY AND ITS POTENTIAL VORTICITY ............................... 179 6.1.1 ANALYSIS OF MOMENTUM AND CONTINUITY EQUATION .................. 179 6.1.2 ANALYSIS OF THE ENTROPY EQUATION .......................................... 188 6.1.3 QUASIGEOSTROPHIC POTENTIAL VORTICITY IN THE STRATIFIED ATMOSPHERE ............................................................................ 191 6.1.4 THE RELATIONSHIP WITH GENERAL POTENTIAL VORTICITY ................... 195 6.1.5 QUASIGEOSTROPHIC THEORY IN PRESSURE COORDINATES ................ 198 6.1.6 A QUASIGEOSTROPHIC TWO-LAYER MODEL .................................. 202 6.1.7 SUMMARY ................................................................................ 204 CONTENTS XI 6.2 QUASIGEOSTROPHIC ENERGETICS OF THE STRATIFIED ATMOSPHERE .................... 205 6.2.1 THE CONTINUOUSLY STRATIFIED ATMOSPHERE ................................. 206 6.2.2 THE TWO-LAYER MODEL ............................................................ 211 6.2.3 SUMMARY ................................................................................ 214 6.3 ROSSBY WAVES IN THE STRATIFIED ATMOSPHERE .......................................... 214 6.3.1 ROSSBY WAVES IN THE TWO-LAYER MODEL .................................. 214 6.3.2 ROSSBY WAVES IN AN ISOTHERMAL CONTINUOUSLY STRATIFIED ATMOSPHERE .............................................................. 221 6.3.3 SUMMARY ................................................................................ 222 6.4 BAROCLINIC INSTABILITY .............................................................................. 223 6.4.1 BAROCLINIC INSTABILITY IN THE TWO-LAYER MODEL ...................... 224 6.4.2 BAROCLINIC INSTABILITY IN A CONTINUOUSLY STRATIFIED ATMOSPHERE ............................................................................ 236 6.4.3 SUMMARY ................................................................................ 246 6.5 RECOMMENDATIONS FOR FURTHER READING .................................................. 248 7 THE PLANETARY BOUNDARY LAYER ...................................................................... 249 7.1 ANELASTICS AND THE BOUSSINESQ THEORY .................................................... 250 7.1.1 THE ANELASTIC EQUATIONS .......................................................... 250 7.1.2 THE BOUSSINESQ EQUATIONS ...................................................... 253 7.1.3 SUMMARY ................................................................................ 255 7.2 INSTABILITIES IN THE BOUNDARY LAYER ........................................................ 256 7.2.1 THE TAYLOR-GOLDSTEIN EQUATION ............................................... 256 7.2.2 NEUTRAL STRATIFICATION (A 2 = 0) .............................................. 258 7.2.3 NO SHEAR (DU/DZ = 0) AND CONSTANT STRATIFICATION N 2 ............ 264 7.2.4 THE GENERAL CASE: THE RICHARDSON CRITERION OF HOWARD AND MILES .............................................................. 266 7.2.5 SUMMARY ................................................................................ 268 7.3 THE AVERAGED EQUATIONS OF MOTION ........................................................ 269 7.3.1 TURBULENCE AND MEAN FLOW .................................................... 269 7.3.2 THE REYNOLDS EQUATIONS ........................................................ 271 7.3.3 SUMMARY ................................................................................ 272 7.4 GRADIENT ANSATZ AND MIXING LENGTH ...................................................... 273 7.5 THE TURBULENT KINETIC ENERGY ................................................................ 275 7.5.1 THE PROGNOSTIC EQUATION ........................................................ 275 7.5.2 SOURCES AND SINKS .................................................................. 278 7.5.3 SUMMARY ................................................................................ 280 7.6 THE PRANDTL LAYER .................................................................................. 281 7.6.1 THE MOMENTUM FLUX .............................................................. 281 7.6.2 THE WIND PROFILE .................................................................... 282 7.6.3 THE INFLUENCE OF STRATIFICATION ................................................ 283 7.6.4 SUMMARY ................................................................................ 285 XII CONTENTS 7.7 THE EKMAN LAYER .................................................................................... 286 7.7.1 THE EKMAN-SPIRAL .................................................................. 288 7.7.2 EKMAN PUMPING ...................................................................... 296 7.7.3 SUMMARY ................................................................................ 298 7.8 RECOMMENDATIONS FOR FURTHER READING .................................................. 299 8 THE INTERACTION BETWEEN ROSSBY WAVES AND THE MEAN FLOW ...................... 301 8.1 BASICS OF QUASIGEOSTROPHIC THEORY ........................................................ 302 8.1.1 THE GOVERNING EQUATIONS ........................................................ 302 8.1.2 CONSERVATION PROPERTIES .......................................................... 304 8.1.3 THE QUASIGEOSTROPHIC ENSTROPHY EQUATION WITHIN LINEAR DYNAMICS ........................................................ 305 8.1.4 SUMMARY ................................................................................ 306 8.2 ROSSBY-WAVE PROPAGATION ...................................................................... 306 8.2.1 WAVE PROPAGATION WITHIN WKB THEORY ................................ 307 8.2.2 ROSSBY-WAVE PROPAGATION INTO THE STRATOSPHERE .................... 313 8.2.3 SUMMARY ................................................................................ 316 8.3 THE ELIASSEN-PALM FLUX .......................................................................... 317 8.3.1 DEFINITION ................................................................................ 318 8.3.2 THE ELIASSEN-PALM RELATIONSHIP ............................................ 319 8.3.3 WAVE ACTION AND ELIASSEN-PALM FLUX WITHIN WKB THEORY .............................................................. 320 8.3.4 SUMMARY ................................................................................ 324 8.4 THE TRANSFORMED EULERIAN MEAN (TEM) ................................................ 324 8.4.1 THE TEM IN THE CONTEXT OF QUASIGEOSTROPHY ........................ 325 8.4.2 THE MASS-WEIGHTED CIRCULATION IN ISENTROPIC COORDINATES ........................................................ 332 8.4.3 THE RELATION BETWEEN THE RESIDUAL CIRCULATION AND THE MASS-WEIGHTED CIRCULATION ........................................ 334 8.4.4 SUMMARY ................................................................................ 337 8.5 THE NON-ACCELERATION THEOREM .............................................................. 339 8.6 RECOMMENDATIONS FOR FURTHER READING .................................................. 342 9 THE MERIDIONAL CIRCULATION ............................................................................ 343 9.1 SOME ESSENTIALS OF THE EMPIRICAL BASIS .................................................. 343 9.2 THE HADLEY CIRCULATION .......................................................................... 344 9.2.1 THE BASIC EQUATIONS OF A MODEL WITHOUT WAVE DRIVING ......... 344 9.2.2 A SOLUTION WITHOUT MERIDIONAL CIRCULATION ............................ 348 9.2.3 HIDE S THEOREM ...................................................................... 350 9.2.4 A SIMPLIFIED DESCRIPTION OF THE HADLEY CELL .......................... 353 9.2.5 THE SUMMER-WINTER ASYMMETRY .......................................... 364 9.2.6 THE WAVE-DRIVEN HADLEY CIRCULATION .................................... 367 9.2.7 SUMMARY ................................................................................ 376 CONTENTS XIII 9.3 THE CIRCULATION IN THE MIDLATITUDES ........................................................ 377 9.3.1 THE PHENOMENOLOGY OF THE FERREL CELL .................................. 377 9.3.2 EDDY FLUXES AND BAROTROPIC JET STREAM .................................. 380 9.3.3 A TWO-LAYER MODEL ................................................................ 388 9.3.4 THE CONTINUOUSLY STRATIFIED ATMOSPHERE ................................ 400 9.3.5 SUMMARY ................................................................................ 404 9.4 RECOMMENDATIONS FOR FURTHER READING .................................................. 405 10 GRAVITY WAVES AND THEIR IMPACT ON THE ATMOSPHERIC FLOW ........................ 407 10.1 SOME EMPIRICAL FACTS ............................................................................ 407 10.2 THE FUNDAMENTAL WAVE MODES OF AN ATMOSPHERE AT REST .................... 409 10.2.1 EQUATIONS OF MOTION AND ENERGETICS ...................................... 410 10.2.2 FREE WAVES ON THE /-PLANE IN AN ISOTHERMAL ATMOSPHERE .... 414 10.2.3 SUMMARY ................................................................................ 429 10.3 THE INTERACTION BETWEEN MESOSCALE GRAVITY WAVES AND A SYNOPTIC-SCALE FLOW ...................................................................... 431 10.3.1 A REFORMULATION OF THE DYNAMICAL EQUATIONS ........................ 431 10.3.2 SCALING FOR SYNOPTIC-SCALE FLOW AND FOR INERTIA-GRAVITY WAVES ................................................ 432 10.3.3 NON-DIMENSIONAL EQUATIONS AND WKB ANSATZ ...................... 442 10.3.4 LEADING-ORDER RESULTS: EQUILIBRIA, DISPERSION AND POLARIZATION RELATIONS, EIKONAL EQUATIONS .............................. 447 10.3.5 THE NEXT ORDER OF THE EQUATIONS ............................................ 460 10.3.6 WAVE ACTION ............................................................................ 466 10.3.7 WAVE IMPACT ON THE SYNOPTIC-SCALE FLOW .............................. 476 10.3.8 GENERALIZATION TO GRAVITY-WAVE SPECTRA: PHASE-SPACE WAVE-ACTION DENSITY ........................................ 480 10.3.9 CONSERVATION PROPERTIES .......................................................... 483 10.3.10 SUMMARY ................................................................................ 488 10.4 CRITICAL LEVELS AND REFLECTING LEVELS .................................................... 490 10.4.1 CRITICAL LEVELS ........................................................................ 490 10.4.2 REFLECTING LEVELS .................................................................... 494 10.4.3 SUMMARY ................................................................................ 495 10.5 THE MIDDLE-ATMOSPHERE GRAVITY-WAVE IMPACT .................................... 496 10.5.1 EXTENSION OF THE TEM BY GRAVITY-WAVE EFFECTS ..................... 497 10.5.2 THE GRAVITY-WAVE EFFECT ON THE RESIDUAL CIRCULATION AND ON THE ZONAL-MEAN FLOW .................................................. 500 10.5.3 SUMMARY ................................................................................ 504 10.6 REFERENCES AND RECOMMENDATIONS FOR FURTHER READING ........................ 504 XIV CONTENTS 11 APPENDICES ......................................................................................................... 507 11.1 APPENDIX A: USEFUL ELEMENTS OF VECTOR ANALYSIS .................................. 507 11.1.1 THE GRADIENT ............................................................................ 507 11.1.2 THE DIVERGENCE AND THE INTEGRAL THEOREM FROM GAUSS .......... 507 11.1.3 THE CURL AND THE INTEGRAL THEOREM FROM STOKES ..................... 508 11.1.4 SOME IDENTITIES .......................................................................... 508 11.1.5 RECOMMENDATIONS FOR FURTHER READING .................................. 509 11.2 APPENDIX B: ROTATIONS ............................................................................. 509 11.2.1 RECOMMENDATIONS FOR FURTHER READING .................................. 512 11.3 APPENDIX C: ISOTROPIC TENSORS ............................................................... 512 11.3.1 ISOTROPIC TENSORS OF RANK ONE ................................................ 513 11.3.2 ISOTROPIC TENSORS OF RANK TWO ................................................ 513 11.3.3 ISOTROPIC TENSORS OF RANK THREE ............................................ 514 11.3.4 ISOTROPIC TENSORS OF RANK FOUR ............................................... 515 11.3.5 RECOMMENDATIONS FOR FURTHER READING .................................. 517 11.4 APPENDIX D: SPHERICAL COORDINATES ...................................................... 517 11.4.1 THE LOCAL BASIS VECTORS ............................................................ 517 11.4.2 THE GRADIENT IN SPHERICAL COORDINATES .................................. 518 11.4.3 THE DIVERGENCE IN SPHERICAL COORDINATES ............................... 519 11.4.4 THE CURL IN SPHERICAL COORDINATES ............................................ 521 11.4.5 RECOMMENDATIONS FOR FURTHER READING .................................. 523 11.5 APPENDIX E: FOURIER INTEGRALS AND FOURIER SERIES .................................. 523 11.5.1 FOURIER INTEGRALS ...................................................................... 523 11.5.2 FOURIER SERIES .......................................................................... 525 11.5.3 RECOMMENDATIONS FOR FURTHER READING .................................. 527 11.6 APPENDIX F: ZONALLY SYMMETRIC ROSSBY WAVES IN THE QUASIGEOSTROPHIC TWO-LAYER MODEL ...................................................... 527 11.7 APPENDIX G: EXPLICIT SOLUTION OF THE INITIAL-VALUE PROBLEM OF BAROCLINIC INSTABILITY IN A QUASIGEOSTROPHIC TWO-LAYER MODEL ............ 528 11.8 APPENDIX H: POLARIZATION RELATIONS OF THE GEOSTROPHIC MODE AND ALL /-PLANE MODES WITHOUT BUOYANCY OSCILLATIONS ........................ 529 11.9 APPENDIX I: THE HIGHER HARMONICS OF A GRAVITY-WAVE FIELD IN WKB THEORY ............................................................................. 532 11.9.1 LEADING-ORDER RESULTS ............................................................ 533 11.9.2 NEXT-ORDER RESULTS .................................................................. 536 11.9.3 RECOMMENDATIONS FOR FURTHER READING ................................... 539 LITERATURE .................................................................................................................. 541 INDEX .......................................................................................................................... 547
adam_txt	CONTENTS 1 THE BASIC EQUATIONS OF ATMOSPHERIC MOTION . 1 1.1 TIME DERIVATIVES IN FLUIDS . 1 1.1.1 THE FLUID DESCRIPTION ACCORDING TO EULER AND LAGRANGE . 1 1.1.2 THE MATERIAL DERIVATIVE OF A FLUID ELEMENT . 3 1.1.3 THE MATERIAL DERIVATIVE OF VOLUME INTEGRALS . 5 1.1.4 SUMMARY . 8 1.2 THE EQUATION OF CONTINUITY . 8 1.2.1 A EULERIAN DERIVATION . 8 1.2.2 A LAGRANGIAN DERIVATION USING THE MATERIAL DERIVATIVE . 9 1.2.3 SUMMARY . 10 1.3 THE MOMENTUM EQUATION . 10 1.3.1 THE VOLUME FORCES . 10 1.3.2 SURFACE FORCES (1): THE PRESSURE GRADIENT FORCE . 11 1.3.3 SURFACE FORCES (2): FRICTION . 13 1.3.4 THE TOTAL MOMENTUM EQUATION . 18 1.3.5 SUMMARY . 18 1.4 THE EQUATIONS OF MOTION IN A ROTATING FRAME OF REFERENCE . 19 1.4.1 THE TIME DERIVATIVE IN A ROTATING FRAME OF REFERENCE . 19 1.4.2 THE MOMENTUM EQUATION IN THE ROTATING FRAME OF REFERENCE . 20 1.4.3 THE EQUATION OF CONTINUITY IN THE ROTATING FRAME OF REFERENCE . 22 1.4.4 SUMMARY . 23 1.5 THE EQUATIONS OF MOTION ON THE SPHERE . 23 1.5.1 VELOCITY AND MATERIAL DERIVATIVE IN SPHERICAL COORDINATES . 24 1.5.2 THE TRANSFORMED EQUATIONS OF MOTION . 26 1.5.3 SUMMARY . 28 VIII CONTENTS 1.6 SYNOPTIC SCALE ANALYSIS . 28 1.6.1 THE GEOSTROPHIC EQUILIBRIUM . 29 1.6.2 THE HYDROSTATIC EQUILIBRIUM . 31 1.6.3 SUMMARY . 34 1.7 RECOMMENDATIONS FOR FURTHER READING . 34 2 ELEMENTARY THERMODYNAMICS AND ENERGETICS OF DRY AIR . 35 2.1 FUNDAMENTALS . 35 2.1.1 THERMODYNAMIC SYSTEMS . 35 2.1.2 THERMODYNAMIC STATE AND THERMODYNAMIC EQUILIBRIUM . 36 2.1.3 TEMPERATURE . 37 2.1.4 EQUATIONS OF STATE . 38 2.1.5 ENERGY CHANGE OF A THERMODYNAMIC SYSTEM . 38 2.1.6 SUMMARY . 41 2.2 THE FUNDAMENTAL LAWS OF THERMODYNAMICS . 41 2.2.1 THE FIRST LAW OF THERMODYNAMICS AND INTERNAL ENERGY . 42 2.2.2 THE HEAT CAPACITIES OF AN IDEAL GAS . 43 2.2.3 ADIABATIC AND ISOTHERMAL CHANGES OF STATE OF AN IDEAL GAS . 44 2.2.4 THE SECOND LAW OF THERMODYNAMICS . 46 2.2.5 THE CARNOT PROCESS . 50 2.2.6 ENTROPY AS STATE VARIABLE . 52 2.2.7 ENTROPY AND POTENTIAL TEMPERATURE OF DRY AIR . 57 2.2.8 SUMMARY . 59 2.3 THE PROGNOSTIC EQUATIONS FOR TEMPERATURE AND ENTROPY IN DRY AIR . 60 2.3.1 PREDICTION OF TEMPERATURE . 60 2.3.2 THE PREDICTION OF ENTROPY AND POTENTIAL TEMPERATURE . 65 2.3.3 THE EQUATIONS IN A ROTATING FRAME OF REFERENCE . 66 2.3.4 SPHERICAL COORDINATES . 66 2.3.5 SUMMARY . 66 2.4 POTENTIAL TEMPERATURE AND STATIC STABILITY . 67 2.4.1 STABLE AND UNSTABLE STRATIFICATION . 67 2.4.2 BUOYANCY OSCILLATIONS . 69 2.4.3 SUMMARY . 70 2.5 RECOMMENDATIONS FOR FURTHER READING . 71 3 ELEMENTARY PROPERTIES AND APPLICATIONS OF THE BASIC EQUATIONS . 73 3.1 SUMMARY OF THE BASIC EQUATIONS . 73 3.2 THE IMPORTANCE OF THE BASIC EQUATIONS FOR WEATHER PREDICTION . 74 3.3 CONSERVATION LAWS . 75 3.3.1 CONSERVATION OF ENERGY . 75 3.3.2 CONSERVATION OF ANGULAR MOMENTUM . 77 3.3.3 SUMMARY . 79 CONTENTS IX 3.4 THE PRIMITIVE EQUATIONS . 80 3.5 THE PRIMITIVE EQUATIONS IN PRESSURE COORDINATES . 82 3.5.1 ARBITRARY VERTICAL COORDINATES . 82 3.5.2 PRESSURE COORDINATES . 85 3.5.3 SUMMARY . 86 3.6 BALANCED FLOWS . 87 3.6.1 THE NATURAL COORDINATES . 87 3.6.2 GEOSTROPHIC FLOW . 89 3.6.3 INERTIAL FLOW . 90 3.6.4 CYCLOSTROPHIC FLOW . 91 3.6.5 THE GRADIENT WIND . 92 3.6.6 SUMMARY . 94 3.7 THERMAL WIND . 95 3.8 RECOMMENDATIONS FOR FURTHER READING . 97 4 VORTEX DYNAMICS . 99 4.1 VORTICITY . 99 4.1.1 RELATIVE, ABSOLUTE, AND PLANETARY VORTICITY . 99 4.1.2 VORTEX LINES, VORTEX TUBES, AND VORTEX FLUX . 100 4.1.3 SUMMARY . 102 4.2 CIRCULATION . 103 4.2.1 RELATIVE AND ABSOLUTE CIRCULATION . 103 4.2.2 THE GENERAL CIRCULATION THEOREM . 104 4.2.3 SUMMARY . 108 4.3 THE KELVIN THEOREM . 108 4.4 THE VORTICITY EQUATION . 110 4.4.1 THE DERIVATION . 110 4.4.2 VORTEX-TUBE STRETCHING AND VORTEX TILTING . ILL 4.4.3 SUMMARY OF THE IMPACTS ON RELATIVE VORTICITY . 113 4.4.4 THE FROZEN-IN PROPERTY OF ABSOLUTE VORTICITY . 113 4.4.5 SUMMARY . 114 4.5 POTENTIAL VORTICITY . 115 4.5.1 AN ALGEBRAIC DERIVATION OF THE PROGNOSTIC EQUATION FOR POTENTIAL VORTICITY . 115 4.5.2 A DERIVATION OF POTENTIAL-VORTICITY CONSERVATION FROM THE GENERAL CIRCULATION THEOREM . 117 4.5.3 SUMMARY . 119 4.6 VORTEX DYNAMICS AND THE PRIMITIVE EQUATIONS . 120 4.6.1 THE PRIMITIVE EQUATIONS IN ISENTROPIC COORDINATES . 120 4.6.2 THE PRIMITIVE VORTICITY EQUATION IN ISENTROPIC COORDINATES . 123 4.6.3 THE POTENTIAL VORTICITY OF THE PRIMITIVE EQUATIONS . 125 X CONTENTS 4.6.4 FLOW OVER A MOUNTAIN RIDGE . 125 4.6.5 SUMMARY . 129 4.7 RECOMMENDATIONS FOR FURTHER READING . 129 5 THE DYNAMICS OF THE SHALLOW-WATER EQUATIONS . 131 5.1 DERIVATION OF THE EQUATIONS . 131 5.1.1 THE MOMENTUM EQUATION . 132 5.1.2 THE CONTINUITY EQUATION . 133 5.1.3 SUMMARY . 134 5.2 CONSERVATION PROPERTIES . 134 5.2.1 ENERGY CONSERVATION . 134 5.2.2 POTENTIAL VORTICITY. 136 5.2.3 SUMMARY . 137 5.3 QUASIGEOSTROPHIC DYNAMICS . 137 5.3.1 THE TANGENTIAL /-PLANE . 137 5.3.2 SCALING THE SHALLOW-WATER EQUATIONS ON THE /-PLANE . 140 5.3.3 THE QUASIGEOSTROPHIC APPROXIMATION: DERIVATION BY SCALE ASYMPTOTICS . 144 5.3.4 THE QUASIGEOSTROPHIC APPROXIMATION: DERIVATION FROM THE CONSERVATION OF SHALLOW-WATER POTENTIAL VORTICITY . 148 5.3.5 SUMMARY . 150 5.4 WAVE SOLUTIONS OF THE SHALLOW-WATER EQUATIONS . 150 5.4.1 PERTURBATION APPROACH . 151 5.4.2 WAVES ON THE/-PLANE . 153 5.4.3 WAVES ON THE / PLANE: QUASIGEOSTROPHIC ROSSBY WAVES . 160 5.4.4 SUMMARY . 165 5.5 GEOSTROPHIC ADJUSTMENT . 166 5.5.1 THE GENERAL SOLUTION OF THE LINEAR SHALLOW-WATER EQUATIONS ON AN / PLANE . 166 5.5.2 THE ADJ USTMENT PROCESS . 170 5.5.3 SUMMARY . 177 5.6 RECOMMENDATIONS FOR FURTHER READING . 177 6 QUASIGEOSTROPHIC DYNAMICS OF THE STRATIFIED ATMOSPHERE . 179 6.1 QUASIGEOSTROPHIC THEORY AND ITS POTENTIAL VORTICITY . 179 6.1.1 ANALYSIS OF MOMENTUM AND CONTINUITY EQUATION . 179 6.1.2 ANALYSIS OF THE ENTROPY EQUATION . 188 6.1.3 QUASIGEOSTROPHIC POTENTIAL VORTICITY IN THE STRATIFIED ATMOSPHERE . 191 6.1.4 THE RELATIONSHIP WITH GENERAL POTENTIAL VORTICITY . 195 6.1.5 QUASIGEOSTROPHIC THEORY IN PRESSURE COORDINATES . 198 6.1.6 A QUASIGEOSTROPHIC TWO-LAYER MODEL . 202 6.1.7 SUMMARY . 204 CONTENTS XI 6.2 QUASIGEOSTROPHIC ENERGETICS OF THE STRATIFIED ATMOSPHERE . 205 6.2.1 THE CONTINUOUSLY STRATIFIED ATMOSPHERE . 206 6.2.2 THE TWO-LAYER MODEL . 211 6.2.3 SUMMARY . 214 6.3 ROSSBY WAVES IN THE STRATIFIED ATMOSPHERE . 214 6.3.1 ROSSBY WAVES IN THE TWO-LAYER MODEL . 214 6.3.2 ROSSBY WAVES IN AN ISOTHERMAL CONTINUOUSLY STRATIFIED ATMOSPHERE . 221 6.3.3 SUMMARY . 222 6.4 BAROCLINIC INSTABILITY . 223 6.4.1 BAROCLINIC INSTABILITY IN THE TWO-LAYER MODEL . 224 6.4.2 BAROCLINIC INSTABILITY IN A CONTINUOUSLY STRATIFIED ATMOSPHERE . 236 6.4.3 SUMMARY . 246 6.5 RECOMMENDATIONS FOR FURTHER READING . 248 7 THE PLANETARY BOUNDARY LAYER . 249 7.1 ANELASTICS AND THE BOUSSINESQ THEORY . 250 7.1.1 THE ANELASTIC EQUATIONS . 250 7.1.2 THE BOUSSINESQ EQUATIONS . 253 7.1.3 SUMMARY . 255 7.2 INSTABILITIES IN THE BOUNDARY LAYER . 256 7.2.1 THE TAYLOR-GOLDSTEIN EQUATION . 256 7.2.2 NEUTRAL STRATIFICATION (A 2 = 0) . 258 7.2.3 NO SHEAR (DU/DZ = 0) AND CONSTANT STRATIFICATION N 2 . 264 7.2.4 THE GENERAL CASE: THE RICHARDSON CRITERION OF HOWARD AND MILES . 266 7.2.5 SUMMARY . 268 7.3 THE AVERAGED EQUATIONS OF MOTION . 269 7.3.1 TURBULENCE AND MEAN FLOW . 269 7.3.2 THE REYNOLDS EQUATIONS . 271 7.3.3 SUMMARY . 272 7.4 GRADIENT ANSATZ AND MIXING LENGTH . 273 7.5 THE TURBULENT KINETIC ENERGY . 275 7.5.1 THE PROGNOSTIC EQUATION . 275 7.5.2 SOURCES AND SINKS . 278 7.5.3 SUMMARY . 280 7.6 THE PRANDTL LAYER . 281 7.6.1 THE MOMENTUM FLUX . 281 7.6.2 THE WIND PROFILE . 282 7.6.3 THE INFLUENCE OF STRATIFICATION . 283 7.6.4 SUMMARY . 285 XII CONTENTS 7.7 THE EKMAN LAYER . 286 7.7.1 THE EKMAN-SPIRAL . 288 7.7.2 EKMAN PUMPING . 296 7.7.3 SUMMARY . 298 7.8 RECOMMENDATIONS FOR FURTHER READING . 299 8 THE INTERACTION BETWEEN ROSSBY WAVES AND THE MEAN FLOW . 301 8.1 BASICS OF QUASIGEOSTROPHIC THEORY . 302 8.1.1 THE GOVERNING EQUATIONS . 302 8.1.2 CONSERVATION PROPERTIES . 304 8.1.3 THE QUASIGEOSTROPHIC ENSTROPHY EQUATION WITHIN LINEAR DYNAMICS . 305 8.1.4 SUMMARY . 306 8.2 ROSSBY-WAVE PROPAGATION . 306 8.2.1 WAVE PROPAGATION WITHIN WKB THEORY . 307 8.2.2 ROSSBY-WAVE PROPAGATION INTO THE STRATOSPHERE . 313 8.2.3 SUMMARY . 316 8.3 THE ELIASSEN-PALM FLUX . 317 8.3.1 DEFINITION . 318 8.3.2 THE ELIASSEN-PALM RELATIONSHIP . 319 8.3.3 WAVE ACTION AND ELIASSEN-PALM FLUX WITHIN WKB THEORY . 320 8.3.4 SUMMARY . 324 8.4 THE TRANSFORMED EULERIAN MEAN (TEM) . 324 8.4.1 THE TEM IN THE CONTEXT OF QUASIGEOSTROPHY . 325 8.4.2 THE MASS-WEIGHTED CIRCULATION IN ISENTROPIC COORDINATES . 332 8.4.3 THE RELATION BETWEEN THE RESIDUAL CIRCULATION AND THE MASS-WEIGHTED CIRCULATION . 334 8.4.4 SUMMARY . 337 8.5 THE NON-ACCELERATION THEOREM . 339 8.6 RECOMMENDATIONS FOR FURTHER READING . 342 9 THE MERIDIONAL CIRCULATION . 343 9.1 SOME ESSENTIALS OF THE EMPIRICAL BASIS . 343 9.2 THE HADLEY CIRCULATION . 344 9.2.1 THE BASIC EQUATIONS OF A MODEL WITHOUT WAVE DRIVING . 344 9.2.2 A SOLUTION WITHOUT MERIDIONAL CIRCULATION . 348 9.2.3 HIDE ' S THEOREM . 350 9.2.4 A SIMPLIFIED DESCRIPTION OF THE HADLEY CELL . 353 9.2.5 THE SUMMER-WINTER ASYMMETRY . 364 9.2.6 THE WAVE-DRIVEN HADLEY CIRCULATION . 367 9.2.7 SUMMARY . 376 CONTENTS XIII 9.3 THE CIRCULATION IN THE MIDLATITUDES . 377 9.3.1 THE PHENOMENOLOGY OF THE FERREL CELL . 377 9.3.2 EDDY FLUXES AND BAROTROPIC JET STREAM . 380 9.3.3 A TWO-LAYER MODEL . 388 9.3.4 THE CONTINUOUSLY STRATIFIED ATMOSPHERE . 400 9.3.5 SUMMARY . 404 9.4 RECOMMENDATIONS FOR FURTHER READING . 405 10 GRAVITY WAVES AND THEIR IMPACT ON THE ATMOSPHERIC FLOW . 407 10.1 SOME EMPIRICAL FACTS . 407 10.2 THE FUNDAMENTAL WAVE MODES OF AN ATMOSPHERE AT REST . 409 10.2.1 EQUATIONS OF MOTION AND ENERGETICS . 410 10.2.2 FREE WAVES ON THE /-PLANE IN AN ISOTHERMAL ATMOSPHERE . 414 10.2.3 SUMMARY . 429 10.3 THE INTERACTION BETWEEN MESOSCALE GRAVITY WAVES AND A SYNOPTIC-SCALE FLOW . 431 10.3.1 A REFORMULATION OF THE DYNAMICAL EQUATIONS . 431 10.3.2 SCALING FOR SYNOPTIC-SCALE FLOW AND FOR INERTIA-GRAVITY WAVES . 432 10.3.3 NON-DIMENSIONAL EQUATIONS AND WKB ANSATZ . 442 10.3.4 LEADING-ORDER RESULTS: EQUILIBRIA, DISPERSION AND POLARIZATION RELATIONS, EIKONAL EQUATIONS . 447 10.3.5 THE NEXT ORDER OF THE EQUATIONS . 460 10.3.6 WAVE ACTION . 466 10.3.7 WAVE IMPACT ON THE SYNOPTIC-SCALE FLOW . 476 10.3.8 GENERALIZATION TO GRAVITY-WAVE SPECTRA: PHASE-SPACE WAVE-ACTION DENSITY . 480 10.3.9 CONSERVATION PROPERTIES . 483 10.3.10 SUMMARY . 488 10.4 CRITICAL LEVELS AND REFLECTING LEVELS . 490 10.4.1 CRITICAL LEVELS . 490 10.4.2 REFLECTING LEVELS . 494 10.4.3 SUMMARY . 495 10.5 THE MIDDLE-ATMOSPHERE GRAVITY-WAVE IMPACT . 496 10.5.1 EXTENSION OF THE TEM BY GRAVITY-WAVE EFFECTS . 497 10.5.2 THE GRAVITY-WAVE EFFECT ON THE RESIDUAL CIRCULATION AND ON THE ZONAL-MEAN FLOW . 500 10.5.3 SUMMARY . 504 10.6 REFERENCES AND RECOMMENDATIONS FOR FURTHER READING . 504 XIV CONTENTS 11 APPENDICES . 507 11.1 APPENDIX A: USEFUL ELEMENTS OF VECTOR ANALYSIS . 507 11.1.1 THE GRADIENT . 507 11.1.2 THE DIVERGENCE AND THE INTEGRAL THEOREM FROM GAUSS . 507 11.1.3 THE CURL AND THE INTEGRAL THEOREM FROM STOKES . 508 11.1.4 SOME IDENTITIES . 508 11.1.5 RECOMMENDATIONS FOR FURTHER READING . 509 11.2 APPENDIX B: ROTATIONS . 509 11.2.1 RECOMMENDATIONS FOR FURTHER READING . 512 11.3 APPENDIX C: ISOTROPIC TENSORS . 512 11.3.1 ISOTROPIC TENSORS OF RANK ONE . 513 11.3.2 ISOTROPIC TENSORS OF RANK TWO . 513 11.3.3 ISOTROPIC TENSORS OF RANK THREE . 514 11.3.4 ISOTROPIC TENSORS OF RANK FOUR . 515 11.3.5 RECOMMENDATIONS FOR FURTHER READING . 517 11.4 APPENDIX D: SPHERICAL COORDINATES . 517 11.4.1 THE LOCAL BASIS VECTORS . 517 11.4.2 THE GRADIENT IN SPHERICAL COORDINATES . 518 11.4.3 THE DIVERGENCE IN SPHERICAL COORDINATES . 519 11.4.4 THE CURL IN SPHERICAL COORDINATES . 521 11.4.5 RECOMMENDATIONS FOR FURTHER READING . 523 11.5 APPENDIX E: FOURIER INTEGRALS AND FOURIER SERIES . 523 11.5.1 FOURIER INTEGRALS . 523 11.5.2 FOURIER SERIES . 525 11.5.3 RECOMMENDATIONS FOR FURTHER READING . 527 11.6 APPENDIX F: ZONALLY SYMMETRIC ROSSBY WAVES IN THE QUASIGEOSTROPHIC TWO-LAYER MODEL . 527 11.7 APPENDIX G: EXPLICIT SOLUTION OF THE INITIAL-VALUE PROBLEM OF BAROCLINIC INSTABILITY IN A QUASIGEOSTROPHIC TWO-LAYER MODEL . 528 11.8 APPENDIX H: POLARIZATION RELATIONS OF THE GEOSTROPHIC MODE AND ALL /-PLANE MODES WITHOUT BUOYANCY OSCILLATIONS . 529 11.9 APPENDIX I: THE HIGHER HARMONICS OF A GRAVITY-WAVE FIELD IN WKB THEORY . 532 11.9.1 LEADING-ORDER RESULTS . 533 11.9.2 NEXT-ORDER RESULTS . 536 11.9.3 RECOMMENDATIONS FOR FURTHER READING . 539 LITERATURE . 541 INDEX . 547
any_adam_object	1
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author	Achatz, Ulrich 1963-
author_GND	(DE-588)11340039X
author_facet	Achatz, Ulrich 1963-
author_role	aut
author_sort	Achatz, Ulrich 1963-
author_variant	u a ua
building	Verbundindex
bvnumber	BV048623913
classification_rvk	RB 10429
ctrlnum	(OCoLC)1302738242 (DE-599)DNB1236109260
dewey-full	551.5
dewey-hundreds	500 - Natural sciences and mathematics
dewey-ones	551 - Geology, hydrology, meteorology
dewey-raw	551.5
dewey-search	551.5
dewey-sort	3551.5
dewey-tens	550 - Earth sciences
discipline	Geologie / Paläontologie Geographie
discipline_str_mv	Geologie / Paläontologie Geographie
format	Book
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open_access_boolean
owner	DE-703
owner_facet	DE-703
physical	xiv, 553 Seiten Diagramme 24 cm, 1168 g
publishDate	2022
publishDateSearch	2022
publishDateSort	2022
publisher	Springer Spektrum
record_format	marc
series2	Textbook
spelling	Achatz, Ulrich 1963- Verfasser (DE-588)11340039X aut Atmospheric dynamics Ulrich Achatz Berlin, Germany Springer Spektrum [2022] xiv, 553 Seiten Diagramme 24 cm, 1168 g txt rdacontent n rdamedia nc rdacarrier Textbook Physik (DE-588)4045956-1 gnd rswk-swf Atmosphäre (DE-588)4003397-1 gnd rswk-swf Dynamik (DE-588)4013384-9 gnd rswk-swf Gravity waves waves action atmospheric dynamics wave impact wave behavior Equations of Motion Atmosphäre (DE-588)4003397-1 s Dynamik (DE-588)4013384-9 s Physik (DE-588)4045956-1 s DE-604 Erscheint auch als Online-Ausgabe 978-3-662-63941-2 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=d0fd63d111f44a4d823e562392427786&prov=M&dok_var=1&dok_ext=htm Inhaltstext B:DE-101 application/pdf https://d-nb.info/1236109260/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033999065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
spellingShingle	Achatz, Ulrich 1963- Atmospheric dynamics Physik (DE-588)4045956-1 gnd Atmosphäre (DE-588)4003397-1 gnd Dynamik (DE-588)4013384-9 gnd
subject_GND	(DE-588)4045956-1 (DE-588)4003397-1 (DE-588)4013384-9
title	Atmospheric dynamics
title_auth	Atmospheric dynamics
title_exact_search	Atmospheric dynamics
title_exact_search_txtP	Atmospheric dynamics
title_full	Atmospheric dynamics Ulrich Achatz
title_fullStr	Atmospheric dynamics Ulrich Achatz
title_full_unstemmed	Atmospheric dynamics Ulrich Achatz
title_short	Atmospheric dynamics
title_sort	atmospheric dynamics
topic	Physik (DE-588)4045956-1 gnd Atmosphäre (DE-588)4003397-1 gnd Dynamik (DE-588)4013384-9 gnd
topic_facet	Physik Atmosphäre Dynamik
url	http://deposit.dnb.de/cgi-bin/dokserv?id=d0fd63d111f44a4d823e562392427786&prov=M&dok_var=1&dok_ext=htm https://d-nb.info/1236109260/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=033999065&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT achatzulrich atmosphericdynamics

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