Mid-Latitude Atmospheric Dynamics: A First Course

Mid-Latitude Atmospheric Dynamics......Page 3
Contents......Page 7
Preface......Page 11
Acknowledgments......Page 13
Objectives......Page 15
1.2 Review of Useful Mathematical Fools......Page 16
1.2.1 Elements of Vector Calculus......Page 17
1.2.2 The Taylor Series Expansion......Page 23
1.2.3 Centered Difference Approximations to Derivatives......Page 24
1.2.4 Temporal Changes of a Continuous Variable......Page 26
1.3 Estimating With Scale Analysis......Page 28
1.4 Basic Kinematics of Fluids......Page 29
1.4.3 Pure Stretching Deformation......Page 31
1.4.4 Pure Shearing Deformation......Page 33
1.5 Mensuration......Page 34
Problems......Page 35
Solutions......Page 37
Objectives......Page 39
2.1.1 The Pressure Gradient Force......Page 40
2.1.2 The Gravitational Force......Page 41
2.1.3 The Frictional Force......Page 42
2.2 Apparent Forces......Page 46
2.2.1 The Centrifugal Force......Page 47
2.2.2 The Coriolis Force......Page 49
Problems......Page 54
Solutions......Page 55
3.1 Mass in the Atmosphere......Page 57
3.1.1 The Hypsometric Equation......Page 59
3.2 Conservation of Momentum: The Equations of Motion......Page 63
3.2.1 The Equations of Motion in Spherical Coordinates......Page 67
3.2.2 Conservation of Mass......Page 79
3.3 Conservation of Energy: The Energy Equation......Page 81
Problems......Page 87
Solutions......Page 90
4.1 Pressure as a Vertical Coordinate......Page 91
4.2 Potential Temperature as a Vertical Coordinate......Page 97
4.3 The Thermal Wind Balance......Page 103
4.4 Natural Coordinates and Balanced Flows......Page 107
4.4.1 Geostrophic Flow......Page 111
4.4.2 Inertial Flow......Page 112
4.4.3 Cyclostrophic Flow......Page 113
4.4.4 Gradient Flow......Page 116
4.5 The Relationship Between Trajectories and Streamlines......Page 122
Problems......Page 125
Solutions......Page 128
Objectives......Page 129
5.1 The Circulation Theorem and its Physical Interpretation......Page 131
5.2 Vorticity and Potential Vorticity......Page 136
5.3 The Relationship Between Vorticity and Divergence......Page 144
5.4 The Quasi-Geostrophic System of Equations......Page 152
Problems......Page 156
Solutions......Page 158
Objectives......Page 161
6.1 The Nature of the Ageostrophic Wind: Isolating the Acceleration Vector......Page 162
6.1.1 Sutcliffe’s Expression for Net Ageostrophic Divergence in a Column......Page 164
6.1.2 Another Perspective on the Ageostrophic Wind......Page 168
6.2 The Sutcliffe Development Theorem......Page 171
6.3 The Quasi-Geostrophic Omega Equation......Page 174
6.4 The Q-Vector......Page 180
6.4.1 The Geostrophic Paradox and Its Resolution......Page 181
6.4.2 A Natural Coordinate Version of the Q-Vector......Page 185
6.4.3 The Along- and Across-Isentrope Components of Q......Page 192
Problems......Page 195
Solutions......Page 200
Objectives......Page 201
7.1 The Structural and Dynamical Characteristics of Mid-Latitude Fronts......Page 203
7.2 Frontogenesis and Vertical Motions......Page 207
7.3 The Semi-Geostrophic Equations......Page 218
7.4 Upper-Level Frontogenesis......Page 225
7.5 Precipitation Processes at  Fronts......Page 234
Problems......Page 243
Solutions......Page 248
8.1 Introduction: The Polar Front Theory of Cyclones......Page 251
8.2 Basic Structural and Energetic Characteristics of the Cyclone......Page 256
8.3 The Cyclogenesis Stage: The QG Tendency Equation Perspective......Page 260
8.4 The Cyclogenesis Stage: The QG Omega Equation Perspective......Page 264
8.5 The Cyclogenetic Influence of Diabatic Processes: Explosive Cyclogenesis......Page 266
8.6 The Post-Mature Stage: Characteristic Thermal Structure......Page 272
8.7 The Post-Mature Stage: The QG Dynamics of the Occluded Quadrant......Page 278
8.8 The Decay Stage......Page 279
Problems......Page 283
Solutions......Page 287
Objectives......Page 289
9.1 Potential Vorticity and Isentropic Divergence......Page 290
9.2 Characteristics of a Positive PV Anomaly......Page 294
9.3 Cyclogenesis From the PV Perspective......Page 300
9.4 The Influence of Diabatic Heating on PV......Page 304
9.5.1 Piecewise PV  Inversion and Some Applications......Page 309
9.5.2 A PV Perspective on Occlusion......Page 311
9.5.4 The Effects of PV Superposition and Attenuation......Page 316
Problems......Page 321
Solutions......Page 324
Appendix A: Virtual Temperature......Page 325
Bibliography......Page 327
Index......Page 331