Preface ........................................................ xi
1. Overview .................................................... 1
1.1. Introduction .......................................... 1
1.2. Definitions of atmospheric scales ..................... 3
1.3. Energy generation and scale interactions .............. 7
1.4. Predictability ....................................... 10
References ................................................. 11
2. Governing equations for mesoscale motions .................. 12
2.1. Introduction ......................................... 12
2.2. Derivation of the governing equations ................ 12
2.3. Approximations to the governing equations ............ 17
References ................................................. 20
Problems ................................................... 20
3. Basic wave dynamics ........................................ 22
3.1. Introduction ......................................... 22
3.2. Basic wave properties ................................ 24
3.3. Sound waves .......................................... 28
3.4. Shallow water waves .................................. 29
3.5. Pure gravity waves ................................... 37
3.6. Inertia-gravity waves ................................ 43
3.7. Wave reflection levels ............................... 50
3.8. Critical levels ...................................... 54
Appendix 3.1 ............................................... 60
References ................................................. 62
Problems ................................................... 63
4. Mesoscale wave generation and maintenance .................. 64
4.1. Introduction ......................................... 64
4.2. Wave generation mechanisms ........................... 64
4.2.1. Density impulses and moist convection ........ 66
4.2.2. Mesoscale instabilities ...................... 71
4.2.3. Geostrophic adjustment ....................... 74
4.2.4. Nonlinear interactions ....................... 85
4.3. Wave maintenance mechanisms .......................... 85
4.3.1. Linear wave ducting mechanism ................ 86
4.3.2. Solitary wave mechanism ...................... 91
4.3.3. Wave-CISK mechanism .......................... 97
4.4. Energy propagation and momentum flux ................ 101
References ................................................ 104
Problems .................................................. 107
5. Orographically forced flows ............................... 109
5.1. Flows over two-dimensional sinusoidal mountains ..... 109
5.2. Flows over two-dimensional isolated mountains ....... 115
5.2.1. Uniform basic flow .......................... 115
5.2.2. Basic flow with variable Scorer parameter ... 121
5.2.3. Trapped lee waves ........................... 122
5.3. Nonlinear flows over two-dimensional mountains ...... 125
5.3.1. Nonlinear flow regimes ...................... 125
5.3.2. Generation of severe downslope winds ........ 131
5.4. Flows over three-dimensional mountains .............. 138
5.4.1. Linear theory ............................... 139
5.4.2. Generation of lee vortices .................. 144
5.5. Flows over larger mesoscale mountains ............... 152
5.5.1. Rotational effects .......................... 152
5.5.2. Lee cyclogenesis ............................ 157
5.5.3. Orographic influence on cyclone track ....... 167
5.6. Other orographic effects ............................ 170
5.6.1. Effects on frontal passage .................. 170
5.6.2. Coastally trapped disturbances .............. 173
5.6.3. Cold-air damming ............................ 174
5.6.4. Gap flow .................................... 176
Appendix 5.1 .............................................. 177
References ................................................ 179
Problems .................................................. 183
6. Thermally forced flows .................................... 184
6.1. Two-dimensional flows ............................... 184
6.1.1. Steady flows over a sinusoidal heat
source ...................................... 184
6.1.2. Steady flows over an isolated heat source ... 190
6.2. Transient flows ..................................... 193
6.2.1. Flow responses to pulse heating ............. 193
6.2.2. Flow responses to steady heating ............ 196
6.3. Applications to mesoscale circulations .............. 198
6.3.1. Density current formation and propagation ... 198
6.3.2. Heat island circulations .................... 199
6.3.3. Moist convection ............................ 201
6.3.4. Gravity wave generation and propagation ..... 201
6.4. Effects of shear, three dimensionality, and
rotation ............................................ 203
6.4.1. Two-dimensional shear flows ................. 203
6.4.2. Three-dimensional nonrotating flows ......... 207
6.4.3. Three-dimensional rotating flows ............ 211
6.5. Dynamics of sea and land breezes .................... 215
6.5.1. Linear theories ............................. 216
6.5.2. Nonlinear numerical studies ................. 219
6.6. Dynamics of mountain-plains solenoidal
circulations ........................................ 221
Appendix 6.1 .............................................. 224
References ................................................ 224
Problems .................................................. 227
7. Mesoscale instabilities ................................... 229
7.1. Wave energy transfer through instabilities .......... 230
7.2. Integral theorems of stratified flow ................ 233
7.2.1. Governing equations ......................... 233
7.2.2. Miles' theorem .............................. 236
7.2.3. Howard's semicircle theorem ................. 236
7.3. Static, conditional, and potential instabilities .... 238
7.3.1. Static instability .......................... 238
7.3.2. Conditional instability ..................... 244
7.3.3. Potential instability ....................... 249
7.4. Kelvin-Helmholtz instability ........................ 252
7.5. Inertial instability ................................ 253
7.6. Symmetric instability ............................... 256
7.6.1. Dry symmetric instability ................... 257
7.6.2. Moist symmetric instability ................. 260
7.7. Baroclinic instability .............................. 265
References ................................................ 268
Problems .................................................. 271
8. Isolated convective storms ................................ 272
8.1. Dynamics of single-cell storms and downbursts ....... 272
8.2. Dynamics of multicell storms ........................ 276
8.3. Effects of shear and buoyancy ....................... 283
8.3.1. Effects of shear on cold outflow ............ 283
8.3.2. Effects of buoyancy ......................... 289
8.4. Dynamics of supercell storms ........................ 293
8.4.1. General characteristics ..................... 293
8.4.2. Effects of unidirectional shear ............. 297
8.4.3. Storm splitting ............................. 300
8.4.4. Storm rotation and propagation .............. 304
8.4.5. Effects of directional shear ................ 307
8.5. Tornado dynamics .................................... 309
8.5.1. Supercell tornadogenesis .................... 309
8.5.2. Nonsupercell tornadogenesis ................. 313
8.5.3. Tornado vortex dynamics ..................... 315
References ................................................ 318
Problems .................................................. 320
9. Mesoscale convective systems .............................. 322
9.1. Squall lines and rainbands .......................... 323
9.1.1. Squall line classifications ................. 323
9.1.2. Formation mechanisms ........................ 328
9.1.3. Maintenance mechanisms ...................... 332
9.1.4. Squall line movement ........................ 335
9.1.5. Rainbands ................................... 336
9.2. Mesoscale convective complexes ...................... 338
9.2.1. General characteristics ..................... 338
9.2.2. Formation and development mechanisms ........ 341
9.3. Tropical cyclones ................................... 347
9.3.1. General characteristics ..................... 347
9.3.2. Tropical cyclogenesis ....................... 349
9.3.3. Intensity and mesoscale structure ........... 360
9.3.4. Tropical cyclone movement ................... 370
References ................................................ 373
Problems .................................................. 377
10. Dynamics of fronts and jet streaks ........................ 379
10.1. Kinematics of frontogenesis ......................... 380
10.2. Dynamics of two-dimensional frontogenesis ........... 387
10.2.1. Geostrophic momentum approximation .......... 387
10.2.2. Frontogenesis and cross-frontal
circulations ................................ 389
10.3. Frontogenesis and baroclinic waves .................. 394
10.4. Moist and frictional effects on frontogenesis ....... 401
10.5. Other types of fronts ............................... 405
10.5.1. Upper-level frontogenesis ................... 405
10.5.2. Drylines .................................... 413
10.6. Jet streak dynamics ................................. 420
10.6.1. Upper-level jet streaks ..................... 420
10.6.2. Low-level jets .............................. 433
References ................................................ 437
Problems .................................................. 441
11. Dynamics of orographic precipitation ...................... 442
11.1. Orographic influence on climatological
distribution of precipitation ....................... 442
11.2. Orographic modification of preexisting
disturbances ........................................ 446
11.2.1. Passage of troughs .......................... 447
11.2.2. Passage of midlatitude cyclones and
fronts ...................................... 451
11.2.3. Passage of tropical cyclones ................ 453
11.2.4. Common ingredients of orographic
precipitation ............................... 458
11.3. Formation and enhancement mechanisms ................ 461
11.3.1. Stable ascent mechanism ..................... 462
11.3.2. Release of moist instabilities .............. 466
11.3.3. Effects of mountain geometry ................ 470
11.3.4. Combined thermal and orographic forcing ..... 471
11.3.5. Seeder-feeder mechanism ..................... 472
11.3.6. Dynamical-microphysical interaction
mechanism .................................. 475
11.4. Control parameters and moist flow regimes ........... 477
11.4.1. Control parameters .......................... 477
11.4.2. Moist flow regimes .......................... 478
References ................................................ 484
12. Basic numerical methods ................................... 489
12.1. Introduction ........................................ 489
12.2. Finite difference approximations of derivatives ..... 491
12.3. Finite difference approximations of the advection
equation ............................................ 495
12.3.1. Two-time-level schemes ...................... 496
12.3.2. Three-time-level schemes .................... 504
12.4. Implicit schemes .................................... 508
12.5. Semi-Lagrangian methods ............................. 511
Appendix 12.1 ............................................. 514
References ................................................ 515
Problems .................................................. 516
Modeling projects ......................................... 516
13. Numerical modeling of geophysical fluid systems ........... 518
13.1. Grid systems and vertical coordinates ............... 518
13.1.1. Grid systems ................................ 520
13.1.2. Vertical coordinates ........................ 526
13.2. Boundary conditions ................................. 528
13.2.1. Lateral boundary conditions ................. 528
13.2.2. Upper boundary conditions ................... 530
13.2.3. Lower boundary conditions ................... 537
13.3. Initial conditions and data assimilation ............ 539
13.4. Nonlinear aliasing and instability .................. 547
13.5. Modeling a stratified fluid system .................. 551
13.6. Predictability and ensemble forecasting ............. 555
References ................................................ 557
Problems .................................................. 561
Modeling project .......................................... 561
14. Parameterizations of physical processes ................... 563
14.1. Reynolds averaging .................................. 563
14.2. Parameterization of planetary boundary layer
processes ........................................... 568
14.2.1. Parameterization of the surface layer ....... 570
14.2.2. Parameterization of the PBL ................. 572
14.3. Parameterization of moist processes ................. 579
14.3.1. Parameterization of microphysical
processes ................................... 580
14.3.2. Cumulus parameterization .................... 585
14.4. Parameterizations of radiative transfer
processes ........................................... 594
14.4.1. Introduction ................................ 594
14.4.2. Longwave radiation .......................... 598
14.4.3. Shortwave radiation ......................... 601
References ................................................ 605
Problems .................................................. 609
Appendices .................................................... 610
A. List of symbols ............................................ 610
B. Nomenclature ............................................... 615
Index ......................................................... 618
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