Mid-latitude atmospheric dynamics : a first course / Jonathan E. Martin.

Format:

Book

Author/Creator:

Martin, Jonathan E.

Language:

English

Subjects (All):

Dynamic meteorology.

Middle atmosphere.

Physical Description:

xii, 324 pages : illustrations, maps ; 26 cm

Place of Publication:

Chichester, England ; Hoboken, NJ : Wiley, [2006]

Summary:

Mid-Latitude Atmospheric Dynamics: A First Course provides an introduction to the physical and mathematical description of mid-latitude atmospheric dynamics and its application to the diagnosis of extratropical cyclones. Requiring a background in physics and calculus but no prior knowledge of meteorology, this student-friendly text places the emphasis on conceptual understanding. Written in a conversational tone, this text is an ideal companion for a first course in the subject, delving into greater depth as the book, and the student, progresses. Real weather examples are woven through the more mathematically focused early chapters, while later chapters introduce a range of case-studies from around the globe to illustrate theoretical and phenomenological aspects of the mid-latitude cyclone life cycle. features end of chapter bibliography and problems, takes a conceptual building block approach, includes numerous real weather examples from around the globe.

Contents:

1 Introduction and Review of Mathematical Tools 1

1.1 Fluids and the nature of fluid dynamics 2

1.2 Review of useful mathematical tools 2

1.2.1 Elements of vector calculus 3

1.2.2 The Taylor series expansion 9

1.2.3 Centered difference approximations to derivatives 10

1.2.4 Temporal changes of a continuous variable 12

1.3 Estimating with scale analysis 14

1.4 Basic kinematics of fluids 15

1.4.1 Pure vorticity 17

1.4.2 Pure divergence 17

1.4.3 Pure stretching deformation 17

1.4.4 Pure shearing deformation 19

1.5 Mensuration 20

2 Fundamental and Apparent Forces 25

2.1 The fundamental forces 26

2.1.1 The pressure gradient force 26

2.1.2 The gravitational force 27

2.1.3 The frictional force 28

2.2 Apparent forces 32

2.2.1 The centrifugal force 33

2.2.2 The Coriolis force 35

3 Mass, Momentum, and Energy: The Fundamental Quantities of the Physical World 43

3.1 Mass in the Atmosphere 43

3.1.1 The hypsometric equation 45

3.2 Conservation of momentum: The equations of motion 49

3.2.1 The equations of motion in spherical coordinates 53

3.2.2 Conservation of mass 65

3.3 Conservation of energy: The energy equation 67

4 Applications of the Equations of Motion 77

4.1 Pressure as a vertical coordinate 77

4.2 Potential temperature as a vertical coordinate 83

4.3 The thermal wind balance 89

4.4 Natural coordinates and balanced flows 93

4.4.1 Geostrophic flow 97

4.4.2 Inertial flow 98

4.4.3 Cyclostrophic flow 99

4.4.4 Gradient flow 102

4.5 The relationship between trajectories and streamlines 108

5 Circulation, Vorticity, and Divergence 115

5.1 The Circulation theorem and its physical interpretation 117

5.2 Vorticity and potential vorticity 122

5.3 The relationship between vorticity and divergence 130

5.4 The quasi-geostrophic system of equations 138

6 The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions 147

6.1 The nature of the ageostrophic wind: Isolating the acceleration vector 148

6.1.1 Sutcliffe's expression for net ageostrophic divergence in a column 150

6.1.2 Another perspective on the ageostrophic wind 154

6.2 The Sutcliffe development theorem 157

6.3 The quasi-geostrophic omega equation 160

6.4 The Q-vector 166

6.4.1 The geostrophic paradox and its resolution 167

6.4.2 A natural coordinate version of the Q-vector 171

6.4.3 The along- and across-isentrope components of Q 178

7 The Vertical Circulation at Fronts 187

7.1 The structural and dynamical characteristics of mid-latitude fronts 189

7.2 Frontogenesis and vertical motions 193

7.3 The semi-geostrophic equations 204

7.4 Upper-level frontogenesis 211

7.5 Precipitation processes at fronts 220

8 Dynamical Aspects of the Life Cycle of the Mid-Latitude Cyclone 237

8.1 Introduction: The polar front theory of cyclones 237

8.2 Basic structural and energetic characteristics of the cyclone 242

8.3 The cyclogenesis stage: The QG tendency equation perspective 246

8.4 The cyclogenesis stage: The QG omega equation perspective 250

8.5 The cyclogenetic influence of diabatic processes: Explosive cyclogenesis 252

8.6 The post-mature stage: Characteristic thermal structure 258

8.7 The post-mature stage: The QG dynamics of the occluded quadrant 264

8.8 The Decay Stage 265

9 Potential Vorticity and Applications to Mid-Latitude Weather Systems 275

9.1 Potential vorticity and isentropic divergence 276

9.2 Characteristics of a positive PV anomaly 280

9.3 Cyclogenesis from the PV perspective 286

9.4 The influence of diabatic heating on PV 290

9.5 Additional applications of the PV perspective 295

9.5.1 Piecewise PV inversion and some applications 295

9.5.2 A PV perspective on occlusion 297

9.5.3 A PV perspective on leeside cyclogenesis 302

9.5.4 The effects of PV superposition and attenuation 302

Appendix A Virtual Temperature 311.

Notes:

Includes bibliographical references (pages [313]-316) and index.

ISBN:

0470864648

0470864656

OCLC:

62738543

Publisher Number:

9780470864647

9780470864654