Mid-Latitude Atmospheric Dynamics: A First Course / Edition 1

Mid-Latitude Atmospheric Dynamics: A First Course / Edition 1

by Jonathan E. Martin
     
 

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ISBN-10: 0470864656

ISBN-13: 9780470864654

Pub. Date: 07/05/2006

Publisher: Wiley

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

Overview

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.

About the Author:
Jonathan E. Martin is a Professor in the Department of Atmospheric and Oceanic Sciences at the University of Wisconsin-Madison

Product Details

ISBN-13:
9780470864654
Publisher:
Wiley
Publication date:
07/05/2006
Edition description:
New Edition
Pages:
336
Sales rank:
429,144
Product dimensions:
6.71(w) x 9.61(h) x 0.80(d)

Table of Contents


Preface     ix
Acknowledgments     xi
Introduction and Review of Mathematical Tools     1
Objectives     1
Fluids and the nature of fluid dynamics     2
Review of useful mathematical tools     2
Elements of vector calculus     3
The Taylor series expansion     9
Centered difference approximations to derivatives     10
Temporal changes of a continuous variable     12
Estimating with scale analysis     14
Basic kinematics of fluids     15
Pure vorticity     17
Pure divergence     17
Pure stretching deformation     17
Pure shearing deformation     19
Mensuration     20
Selected references     21
Problems     21
Solutions     23
Fundamental and Apparent Forces     25
Objectives     25
The fundamental forces     26
The pressure gradient force     26
The gravitational force     27
The frictional force     28
Apparent forces     32
The centrifugal force     33
The Coriolis force     35
Selectedreferences     40
Problems     40
Solutions     41
Mass, Momentum, and Energy: The Fundamental Quantities of the Physical World     43
Objectives     43
Mass in the Atmosphere     43
The hypsometric equation     45
Conservation of momentum: The equations of motion     49
The equations of motion in spherical coordinates     53
Conservation of mass     65
Conservation of energy: The energy equation     67
Selected references     73
Problems     73
Solutions     76
Applications of the Equations of Motion     77
Objectives     77
Pressure as a vertical coordinate     77
Potential temperature as a vertical coordinate     83
The thermal wind balance     89
Natural coordinates and balanced flows     93
Geostrophic flow     97
Inertial flow     98
Cyclostrophic flow     99
Gradient flow     102
The relationship between trajectories and streamlines     108
Selected references     111
Problems     111
Solutions     114
Circulation, Vorticity, and Divergence     115
Objectives     115
The Circulation theorem and its physical interpretation     117
Vorticity and potential vorticity     122
The relationship between vorticity and divergence     130
The quasi-geostrophic system of equations     138
Selected references     142
Problems     142
Solutions     144
The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions     147
Objectives     147
The nature of the ageostrophic wind: Isolating the acceleration vector     148
Sutcliffe's expression for net ageostrophic divergence in a column     150
Another perspective on the ageostrophic wind     154
The Sutcliffe development theorem     157
The quasi-geostrophic omega equation     160
The Q-vector     166
The geostrophic paradox and its resolution     167
A natural coordinate version of the Q-vector     171
The along- and across-isentrope components of Q     178
Selected references     181
Problems     181
Solutions     186
The Vertical Circulation at Fronts     187
Objectives     187
The structural and dynamical characteristics of mid-latitude fronts     189
Frontogenesis and vertical motions     193
The semi-geostrophic equations     204
Upper-level frontogenesis     211
Precipitation processes at fronts     220
Selected references     229
Problems     229
Solutions     234
Dynamical Aspects of the Life Cycle of the Mid-Latitude Cyclone     237
Objectives     237
Introduction: The polar front theory of cyclones     237
Basic structural and energetic characteristics of the cyclone     242
The cyclogenesis stage: The QG tendency equation perspective     246
The cyclogenesis stage: The QG omega equation perspective     250
The cyclogenetic influence of diabatic processes: Explosive cyclogenesis     252
The post-mature stage: Characteristic thermal structure     258
The post-mature stage: The QG dynamics of the occluded quadrant     264
The Decay Stage     265
Selected references     269
Problems     269
Solutions     273
Potential Vorticity and Applications to Mid-Latitude Weather Systems     275
Objectives     275
Potential vorticity and isentropic divergence     276
Characteristics of a positive PV anomaly     280
Cyclogenesis from the PV perspective     286
The influence of diabatic heating on PV     290
Additional applications of the PV perspective     295
Piecewise PV inversion and some applications     295
A PV perspective on occlusion     297
A PV perspective on leeside cyclogenesis     302
The effects of PV superposition and attenuation     302
Selected references     307
Problems     307
Solutions     310
Virtual Temperature     311
Bibliography     313
Index     317

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