Dynamics of the atmosphere: a course in theoretical meteorology
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2003
|
| Edition: | 1. publ. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 719 S. |
| ISBN: | 9780521809498 0521809495 9780521006668 052100666X |
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| 100 | 1 | |a Zdunkowski, Wilford |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Dynamics of the atmosphere |b a course in theoretical meteorology |c Wilford Zdunkowski and Andreas Bott |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2003 | |
| 300 | |a XVIII, 719 S. | ||
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Record in the Search Index
| _version_ | 1804130099676577792 |
|---|---|
| adam_text | Titel: Dynamics of the atmosphere
Autor: Zdunkowski, Wilford
Jahr: 2003
Contents
Preface page xv
Part 1 Mathematical tools 1
M1 Algebra of vectors 3
M1.1 Basic concepts and definitions 3
M 1.2 Reference frames 6
M1.3 Vector multiplication 7
M 1.4 Reciprocal coordinate systems 15
M 1.5 Vector representations 19
M 1.6 Products of vectors in general coordinate systems 22
M 1.7 Problems 23
M2 Vector functions 25
M2.1 Basic definitions and operations 25
M2.2 Special dyadics 28
M2.3 Principal-axis transformation of symmetric tensors 32
M2.4 Invariants of a dyadic 34
M2.5 Tensor algebra 40
M2.6 Problems 42
M3 Differential relations 43
M3.1 Differentiation of extensive functions 43
M3.2 The Hamilton operator in generalized coordinate
systems 48
M3.3 The spatial derivative of the basis vectors 51
M3.4 Differential invariants in generalized coordinate systems 53
M3.5 Additional applications 56
M3.6 Problems 60
M4 Coordinate transformations 62
M4.1 Transformation relations of time-independent
coordinate systems 62
viii Contents
M4.2 Transformation relations of time-dependent
coordinate systems 67
M4.3 Problems 73
M5 The method of covariant differentiation 75
M5.1 Spatial differentiation of vectors and dyadics 75
M5.2 Time differentiation of vectors and dyadics 79
M5.3 The local dyadic of P 82
M5.4 Problems 83
M6 Integral operations 84
M6.1 Curves, surfaces, and volumes in the general q system 84
M6.2 Line integrals, surface integrals, and volume integrals 87
M6.3 Integral theorems 90
M6.4 Fluid lines, surfaces, and volumes 94
M6.5 Time differentiation of fluid integrals 96
M6.6 The general form of the budget equation 101
M6.7 Gauss theorem and the Dirac delta function 104
M6.8 Solution of Poisson s differential equation 106
M6.9 Appendix: Remarks on Euclidian and Riemannian
spaces 107
M6.10 Problems 110
M7 Introduction to the concepts of nonlinear dynamics 111
M7.1 One-dimensional flow 111
M7.2 Two-dimensional flow 116
Part 2 Dynamics of the atmosphere ] 31
1 The laws of atmospheric motion 133
1.1 The equation of absolute motion 133
1.2 The energy budget in the absolute reference system 136
1.3 The geographical coordinate system 137
1.4 The equation of relative motion 146
i .5 The energy budget of the general relative system 147
1.6 The decomposition of the equation of motion 150
1.7 Problems 154
2 Scale analysis 157
2.1 An outline of the method 157
2.2 Practical formulation of the dimensionless flow
numbers 159
2.3 Scale analysis of large-scale frictionless motion 161
2.4 The geostrophic wind and the Euier wind 167
2.5 The equation of motion on a tangential plane 169
2.6 Problems 169
Contents jx
The material and the local description of flow 171
3.1 The description of Lagrange 171
3.2 Lagrange s version of the continuity equation 173
3.3 An example of the use of Lagrangian coordinates 175
3.4 The local description of Euler 182
3.5 Transformation from the Eulerian to the Lagrangian
system 186
3.6 Problems 187
Atmospheric flow fields 189
4.1 The velocity dyadic 189
4.2 The deformation of the continuum 193
4.3 Individual changes with time of geometric fluid
configurations 199
4.4 Problems 205
The Navier-Stokes stress tensor 206
5.1 The general stress tensor 206
5.2 Equilibrium conditions in the stress field 208
5.3 Symmetry of the stress tensor 209
5.4 The frictional stress tensor and the deformation
dyadic 210
5.5 Problems 212
The Helmholtz theorem 214
6.1 The three-dimensional Helmholtz theorem 214
6.2 The two-dimensional Helmholtz theorem 216
6.3 Problems 217
Kinematics of two-dimensional flow 218
7.1 Atmospheric flow fields 218
7.2 Two-dimensional streamlines and normals 222
7.3 Streamlines in a drifting coordinate system 225
7.4 Problems 228
Natural coordinates 230
8.1 Introduction 230
8.2 Differential definitions of the coordinate lines 232
8.3 Metric relationships 235
8.4 Blaton s equation 236
8.5 Individual and local time derivatives of the velocity 238
8.6 Differential invariants 239
8.7 The equation of motion for frictionless horizontal flow 242
8.8 The gradient wind relation 243
8.9 Problems 244
Contents
9 Boundary surfaces and boundary conditions 246
9.1 Introduction 246
9.2 Differential operations at discontinuity surfaces 247
9.3 Particle invariance at boundary surfaces, displacement
velocities 251
9.4 The kinematic boundary-surface condition 253
9.5 The dynamic boundary-surface condition 258
9.6 The zeroth-order discontinuity surface 259
9.7 An example of a first-order discontinuity surface 265
9.8 Problems 267
10 Circulation and vorticity theorems 268
10.1 ErteFs form of the continuity equation 268
10.2 The baroclinic Weber transformation 271
10.3 The baroclinic Ertel-Rossby invariant 275
10.4 Circulation and vorticity theorems for frictionless
baroclinic flow 276
10.5 Circulation and vorticity theorems for frictionless
barotropic flow 293
10.6 Problems 301
11 Turbulent systems 302
11.1 Simple averages and fluctuations 302
11.2 Weighted averages and fluctuations 304
11.3 Averaging the individual time derivative and the
budget operator 306
11.4 Integral means 307
11.5 Budget equations of the turbulent system 310
11.6 The energy budget of the turbulent system 313
1 1.7 Diagnostic and prognostic equations of turbulent
systems 315
1 1.8 Production of entropy in the microturbulent system 319
1 1.9 Problems 324
12 An excursion into spectral turbulence theory 326
I 2.1 Fourier Representation of the continuity equation and
the equation of motion 326
12.2 The budget equation for the amplitude of the
kinetic energy 331
12.3 Isotropie conditions, the transition to the continuous
wavenumber space 333
12.4 The Heisenberg spectrum 336
12.5 Relations for the Heisenberg exchange coefficient 340
12.6 A prognostic equation for the exchange coefficient 341
Contents xi
12.7 Concluding remarks on closure procedures 346
12.8 Problems 348
13 The atmospheric boundary layer 349
13.1 Introduction 349
13.2 Prandtl-layer theory 350
13.3 The Monin-Obukhov similarity theory of the neutral
Prandtl layer 358
13.4 The Monin-Obukhov similarity theory of the diabatic
Prandtl layer 362
13.5 Application of the Prandtl-layer theory in numerical
prognostic models 369
13.6 The fluxes, the dissipation of energy, and the exchange
coefficients 371
13.7 The interface condition at the earth s surface 372
13.8 The Ekman layer - the classical approach 375
13.9 The composite Ekman layer 381
13.10 Ekman pumping 388
13.11 Appendix A: Dimensional analysis 391
13.12 Appendix B: The mixing length 394
13.13 Problems 396
14 Wave motion in the atmosphere 398
14.1 The representation of waves 398
14.2 The group velocity 401
14.3 Perturbation theory 403
14.4 Pure sound waves 407
14.5 Sound waves and gravity waves 410
14.6 Lamb waves 418
14.7 Lee waves 418
14.8 Propagation of energy 418
14.9 External gravity waves 422
14.10 Internal gravity waves 426
14.11 Nonlinear waves in the atmosphere 431
14.12 Problems 434
15 The barotropic model 435
15.1 The basic assumptions of the barotropic model 435
15.2 The unfiltered barotropic prediction model 437
15.3 The filtered barotropic model 450
15.4 Barotropic instability 452
15.5 The mechanism of barotropic development 463
15.6 Appendix 468
15.7 Problems 470
xii Contents
16 Rossby waves 471
16.1 One-and two-dimensional Rossby waves 471
16.2 Three-dimensional Rossby waves 476
16.3 Normal-mode considerations 479
16.4 Energy transport by Rossby waves 482
16.5 The influence of friction on the stationary Rossby wave 483
16.6 Barotropic equatorial waves 484
16.7 The principle of geostrophic adjustment 487
16.8 Appendix 493
16.9 Problems 494
17 Inertial and dynamic stability 495
17.1 Inertial motion in a horizontally homogeneous
pressure field 495
17.2 Inertial motion in a homogeneous geostrophic wind field 497
17.3 Inertial motion in a geostrophic shear wind field 498
17.4 Derivation of the stability criteria in the geostrophic
wind field 501
17.5 Sectorial stability and instability 504
17.6 Sectorial stability for normal atmospheric conditions 509
17.7 Sectorial stability and instability with permanent
adaptation 510
17.8 Problems 512
18 The equation of motion in general coordinate systems 513
18.1 Introduction 513
18.2 The covariant equation of motion in general coordinate
systems 514
18.3 The contravariant equation of motion in general
19
coordinate systems 518
18.4 The equation of motion in orthogonal coordinate systems 520
18.5 Lagrange?s equation of motion 523
18.6 Hamilton s equation of motion 527
18.7 Appendix 530
18.8 Problems 531
The geographical coordinate system 532
19.1 The equation of motion 532
19.2 Application of Lagrange s equation of motion 536
19.3 The first metric simplification 538
19.4 The coordinate simplification 539
19.5 The continuity equation 540
19.6 Problems 541
Contents xi i i
20 The stereographic coordinate system 542
20.1 The stereographic projection 542
20.2 Metric forms in stereographic coordinates 546
20.3 The absolute kinetic energy in stereographic coordinates 549
20.4 The equation of motion in the stereographic
Cartesian coordinates 550
20.5 The equation of motion in stereographic
cylindrical coordinates 554
20.6 The continuity equation 556
20.7 The equation of motion on the tangential plane 558
20.8 The equation of motion in Lagrangian enumereation
coordinates 559
20.9 Problems 564
21 Orography-following coordinate systems 565
21.1 The metric of the ç system 565
21.2 The equation of motion in the ç system 568
21.3 The continuity equation in the ç system 571
21.4 Problems 571
22 The stereographic system with a generalized vertical coordinate 572
22.1 The î transformation and resulting equations 573
22.2 The pressure system 577
22.3 The solution scheme using the pressure system 579
22.4 The solution to a simplified prediction problem 582
22.5 The solution scheme with a normalized pressure
coordinate 584
22.6 The solution scheme with potential temperature as
vertical coordinate 587
22.7 Problems 589
23 A quasi-geostrophic baroclinic model 591
23.1 Introduction 591
23.2 The first law of thermodynamics in various forms 592
23.4 The vorticity and the divergence equation 593
23.5 The first and second filter conditions 595
23.6 The geostrophic approximation of the heat equation 597
23.7 The geostrophic approximation of the vorticity equation 603
23.8 The ù equation 605
23.9 The Philipps approximation of the ageostrophic
component of the horizontal wind 609
23.10 Applications of the Philipps wind 614
23.11 Problems 617
xiv Contents
24 A two-level prognostic model, baroclinic instability 619
24.1 Introduction 619
24.2 The mathematical development of the two-level model 619
24.3 The Phillips quasi-geostrophic two-level circulation model 623
24.4 Baroclinic instability 624
24.5 Problems 633
25 An excursion concerning numerical procedures 634
25.1 Numerical stability of the one-dimensional
advection equation 634
25.2 Application of forward-in-time and central-in-space
difference quotients 640
25.3 A practical method for the elimination of the weak
instability 642
25.4 The implicit method 642
25.5 The aliasing error and nonlinear instability 645
25.6 Problems 648
26 Modeling of atmospheric flow by spectral techniques 649
26.1 Introduction 649
26.2 The basic equations 650
26.3 Horizontal discretization 655
26.4 Problems 667
27 Predictability 669
27.1 Derivation and discussion of the Lorenz equations 669
27.2 The effect of uncertainties in the initial conditions 681
27.3 Limitations of deterministic predictability of the
atmosphere 683
27.4 Basic equations of the approximate stochastic
dynamic method 689
27.5 Problems 692
Answers to Problems 693
List of frequently used symbols 702
References and bibliography 706
|
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| language | English |
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| spelling | Zdunkowski, Wilford Verfasser aut Dynamics of the atmosphere a course in theoretical meteorology Wilford Zdunkowski and Andreas Bott 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2003 XVIII, 719 S. txt rdacontent n rdamedia nc rdacarrier Meteorologia larpcal Meteorology Meteorologie (DE-588)4038953-4 gnd rswk-swf Meteorologie (DE-588)4038953-4 s DE-604 Bott, Andreas 1956- Verfasser (DE-588)1111687099 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010395249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zdunkowski, Wilford Bott, Andreas 1956- Dynamics of the atmosphere a course in theoretical meteorology Meteorologia larpcal Meteorology Meteorologie (DE-588)4038953-4 gnd |
| subject_GND | (DE-588)4038953-4 |
| title | Dynamics of the atmosphere a course in theoretical meteorology |
| title_auth | Dynamics of the atmosphere a course in theoretical meteorology |
| title_exact_search | Dynamics of the atmosphere a course in theoretical meteorology |
| title_full | Dynamics of the atmosphere a course in theoretical meteorology Wilford Zdunkowski and Andreas Bott |
| title_fullStr | Dynamics of the atmosphere a course in theoretical meteorology Wilford Zdunkowski and Andreas Bott |
| title_full_unstemmed | Dynamics of the atmosphere a course in theoretical meteorology Wilford Zdunkowski and Andreas Bott |
| title_short | Dynamics of the atmosphere |
| title_sort | dynamics of the atmosphere a course in theoretical meteorology |
| title_sub | a course in theoretical meteorology |
| topic | Meteorologia larpcal Meteorology Meteorologie (DE-588)4038953-4 gnd |
| topic_facet | Meteorologia Meteorology Meteorologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010395249&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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