9780470864654

Mid-Latitude Atmospheric Dynamics : A First Course

by
  • ISBN13:

    9780470864654

  • ISBN10:

    0470864656

  • Edition: 1st
  • Format: Paperback
  • Copyright: 6/16/2006
  • Publisher: Wiley
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Summary

This exciting text provides a mathematically rigorous yet accessible textbook that is primarily aimed at atmospheric science majors. Its accessibility is due to the texts emphasis on conceptual understanding. The first five chapters constitute a companion text to introductory courses covering the dynamics of the mid-latitude atmosphere. The final four chapters constitute a more advanced course, and provide insights into the diagnostic power of the quasi-geostrophic approximation of the equations outlined in the previous chapters, the meso-scale dynamics of thefrontal zone, the alternative PV perspective for cyclone interpretation, and the dynamics of the life-cycle of mid-latitude cyclones. Written in a clear and accessible style Features real weather examples and global case studies Each chapter sets out clear learning objectives and tests students' knowledge with concluding questions and answers

Author Biography

Jonathan E. Martin is a Professor in the Department of Atmospheric and Oceanic Sciences at the University of Wisconsin-Madison where he has taught since 1994.  He has received numerous accolades for his teaching including the Underkofler Excellence in Teaching Award and is a Fellow in the Teaching Academy of the University of Wisconsin.  His teaching excellence is allied with  research expertise in the study of mid-latitude weather systems. Professor Martin has published extensively in scholarly journals and was awarded the distinction of being named a Mark H. Ingraham Distinguished Faculty Member by the College of Letters and Science at UW-Madison.

Table of Contents

Preface ix
Acknowledgments xi
1 Introduction and Review of Mathematical Tools 1(24)
Objectives
1(1)
1.1 Fluids and the nature of fluid dynamics
2(1)
1.2 Review of useful mathematical tools
2(12)
1.2.1 Elements of vector calculus
3(6)
1.2.2 The Taylor series expansion
9(1)
1.2.3 Centered difference approximations to derivatives
10(2)
1.2.4 Temporal changes of a continuous variable
12(2)
1.3 Estimating with scale analysis
14(1)
1.4 Basic kinematics of fluids
15(5)
1.4.1 Pure vorticity
17(1)
1.4.2 Pure divergence
17(1)
1.4.3 Pure stretching deformation
17(2)
1.4.4 Pure shearing deformation
19(1)
1.5 Mensuration
20(1)
Selected references
21(1)
Problems
21(2)
Solutions
23(2)
2 Fundamental and Apparent Forces 25(18)
Objectives
25(1)
2.1 The fundamental forces
26(6)
2.1.1 The pressure gradient force
26(1)
2.1.2 The gravitational force
27(1)
2.1.3 The frictional force
28(4)
2.2 Apparent forces
32(8)
2.2.1 The centrifugal force
33(2)
2.2.2 The Coriolis force
35(5)
Selected references
40(1)
Problems
40(1)
Solutions
41(2)
3 Mass, Momentum, and Energy: The Fundamental Quantities of the Physical World 43(34)
Objectives
43(1)
3.1 Mass in the Atmosphere
43(6)
3.1.1 The hypsometric equation
45(4)
3.2 Conservation of momentum: The equations of motion
49(18)
3.2.1 The equations of motion in spherical coordinates
53(12)
3.2.2 Conservation of mass
65(2)
3.3 Conservation of energy: The energy equation
67(6)
Selected references
73(1)
Problems
73(3)
Solutions
76(1)
4 Applications of the Equations of Motion 77(38)
Objectives
77(1)
4.1 Pressure as a vertical coordinate
77(6)
4.2 Potential temperature as a vertical coordinate
83(6)
4.3 The thermal wind balance
89(4)
4.4 Natural coordinates and balanced flows
93(15)
4.4.1 Geostrophic flow
97(1)
4.4.2 Inertial flow
98(1)
4.4.3 Cyclostrophic flow
99(3)
4.4.4 Gradient flow
102(6)
4.5 The relationship between trajectories and streamlines
108(3)
Selected references
111(3)
Problems '
'11
Solutions
114(1)
5 Circulation, Vorticity, and Divergence 115(32)
Objectives
5.1 The Circulation theorem and its physical interpretation
117(55)
5.2 Vorticity and potential vorticity
172
5.3 The relationship between vorticity and divergence
130(8)
5.4 The quasi-geostrophic system of equations
138(4)
Selected references
142(1)
Problems
142(2)
Solutions
144(3)
6 The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions 147(40)
Objectives
147(1)
6.1 The nature of the ageostrophic wind: Isolating the acceleration vector
148(9)
6.1.1 Sutcliffe's expression for net ageostrophic divergence in a column
150(4)
6.1.2 Another perspective on the ageostrophic wind
154(3)
6.2 The Sutcliffe development theorem
157(3)
6.3 The quasi-geostrophic omega equation
160(6)
6.4 The Q-vector
166(15)
6.4.1 The geostrophic paradox and its resolution
167(4)
6.4.2 A natural coordinate version of the ->Q -vector
171(7)
6.4.3 The along- and across-isentrope components of ->Q
178(3)
Selected references
181(1)
Problems
181(5)
Solutions
186(1)
7 The Vertical Circulation at Fronts 187(50)
Objectives
187(2)
7.1 The structural and dynamical characteristics of mid-latitude fronts
189(4)
7.2 Frontogenesis and vertical motions
193(11)
7.3 The semi-geostrophic equations
204(7)
7.4 Upper-level frontogenesis
211(9)
7.5 Precipitation processes at fronts
220(9)
Selected references
229(1)
Problems
229(5)
Solutions
234(3)
8 Dynamical Aspects of the Life Cycle of the Mid-Latitude Cyclone 237(38)
Objectives
237(1)
8.1 Introduction: The polar front theory of cyclones
237(5)
8.2 Basic structural and energetic characteristics of the cyclone
242(4)
8.3 The cyclogenesis stage: The QG tendency equation perspective
246(4)
8.4 The cyclogenesis stage: The QG omega equation perspective
250(2)
8.5 The cyclogenetic influence of diabatic processes: Explosive cyclogenesis
252(6)
8.6 The post-mature stage: Characteristic thermal structure
258(6)
8.7 The post-mature stage: The QG dynamics of the occluded quadrant
264(1)
8.8 The Decay Stage
265(4)
Selected references
269(1)
Problems
269(4)
Solutions
273(2)
9 Potential Vorticity and Applications to Mid-Latitude Weather Systems 275(36)
Objectives
275(1)
9.1 Potential vorticity and isentropic divergence
276(4)
9.2 Characteristics of a positive PV anomaly
280(6)
9.3 Cyclogenesis from the PV perspective
286(4)
9.4 The influence of diabatic heating on PV
290(5)
9.5 Additional applications of the PV perspective
295(12)
9.5.1 Piecewise PV inversion and some applications
295(2)
9.5.2 A PV perspective on occlusion
297(5)
9.5.3 A PV perspective on leeside cyclogenesis
302(1)
9.5.4 The effects of PV superposition and attenuation
302(5)
Selected references
307(1)
Problems
307(3)
Solutions
310(1)
Appendix A: Virtual Temperature 311(2)
Bibliography 313(4)
Index 317

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