Mid-Latitude Atmospheric Dynamics: A First Course / Edition 1by Jonathan E. Martin
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… See more details below
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
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- Edition description:
- New Edition
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- 6.71(w) x 9.61(h) x 0.80(d)
Table of Contents
1. Introduction and Review of Mathematical Tools.
1.1 Fluids and the nature of fluid dynamics.
1.2 Review of useful mathematical tools.
1.2.1 Elements of vector calculus.
1.2.2 The Taylor series expansion.
1.2.3 Centred difference approximations to derivatives.
1.2.4 Temporal changes of a continuous variable.
1.3 Estimating with scale analysis.
1.4 Basic kinematics of fluids.
1.4.1 Pure vorticity.
1.4.2 Pure divergence.
1.4.3 Pure stretching deformation.
1.4.4 Pure shearing deformation.
2. Fundamental and Apparent Forces.
2.1 The fundamental forces.
2.1.1 The pressure gradient force.
2.1.2 The gravitational force.
2.1.3 The frictional force.
2.2 Apparent forces.
2.2.1 The centrifugal force.
2.2.2 The Coriolis force.
3. Mass, Momentum, and Energy: The Fundamental Quantities of the Physical World.
3.1 Mass in the Atmosphere.
3.1.1 The hypsometric equation.
3.2 Conservation of momentum: The equations of motion.
3.2.1 The equations of motion in spherical coordinates.
3.2.2 Conservation of mass.
3.3 Conservation of energy: The energy equation.
4. Applications of the Equations of Motion.
4.1 Pressure as a vertical coordinate.
4.2 Potential temperature as a vertical coordinate.
4.3 The thermal wind balance.
4.4 Natural coordinates and balanced flows.
4.4.1 Geostrophic flow.
4.4.2 Inertial flow.
4.4.3 Cyclostrophic flow.
4.4.4 Gradient flow.
4.5 The relationship between trajectories and streamlines.
5. Circulation, Vorticity, and Divergence.
5.1 The Circulation theorem and its physical interpretation.
5.2 Vorticity and potential vorticity.
5.3 The relationship between vorticity and divergence.
5.4 The quasi-geostrophic system of equations.
6. The Diagnosis of Mid-Latitude Synoptic-Scale Vertical Motions.
6.1 The nature of the ageostrophic wind: Isolating the acceleration vector.
6.1.1 Sutcliffe’s expression for net ageostrophic divergence in a column.
6.1.2 Another perspective on the ageostrophic wind.
6.2 The Sutcliffe development theorem.
6.3 The quasi-geostrophic omega equation.
6.4 The Q_-vector.
6.4.1 The geostrophic pradox and its resolution.
6.4.2 A natural coordinate version of the _Q-vector.
6.4.3 The along- and across-isentrope components of _Q.
7. The Vertical Circulation at Fronts.
7.1 The structural and dynamical characteristics of mid-latitude fronts.
7.2 Frontogenesis and vertical motions.
7.3 The semi-geostrophic equations.
7.4 Upper-level frontogenesis.
7.5 Precipitation processes at fronts.
8. Dynamical Aspects of the Life Cycle of the Mid-Latitude Cyclone.
8.1 Introduction: The polar front theory of cyclones.
8.2 Basic structural and energetic characteristics of the cyclone.
8.3 The cyclogenesis stage: The QG tendency equation perspective.
8.4 The cyclogenesis stage: The QG omega equation perspective.
8.5 The cyclogenetic influence of diabatic processes: Explosive cyclogenesis.
8.6 The post-mature stage: Characteristic thermal structure.
8.7 The post-mature stage: The QG dynamics of the occluded quadrant.
8.8 The Decay Stage.
9. Potential Vorticity and Applications to Mid-Latitude Weather Systems.
9.1 Potential vorticity and isentropic divergence.
9.2 Characteristics of a positive PV anomaly.
9.3 Cyclogenesis from the PV perspective.
9.4 The influence of diabatic heating on PV.
9.5 Additional applications of the PV perspective.
9.5.1 Piecewise PV inversion and some applications.
9.5.2 A PV perspective on occlusion.
9.5.3 A PV perspective on leeside cyclogenesis.
9.5.4 The effects of PV superposition and attenuation.
Appendix A: Virtual Temperature.
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