Mid-Latitude Atmospheric Dynamics A First Course

by Martin, Jonathan E.

• ISBN13: 9780470864654
• ISBN10: 0470864656
• Edition: 1st
• Format: Paperback
• Copyright: 2006-06-16
• Publisher: Wiley

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