Mid-Latitude Atmospheric Dynamics

A First Course

Jonathan E. Martin

• Publisher: Wiley
• Year: 2013
• ISBN:
  9781118687895
• Edition: 1
• Topic: Scienze fisiche
• Subtopic: Meteorologia e climatologia

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

A Solutions Manual is also available for this textbook on theInstructor Companion Site www.wileyeurope.com/college/martin.

"…a student-friendly yet rigorous textbook that accomplishes what no other textbook has done before… I highly recommend this textbook. For instructors, this is a great book if they don't have their own class notes – one can teach straight from the book. And for students, this is a great book if they don't take good class notes – one can learn straight from the book. This is a rare attribute of advanced textbooks."

Bulletin of the American Meteorological Society (BAMS), 2008

1

Introduction and Review of Mathematical Tools

Objectives

The Earth’s atmosphere is majestic in its beauty, awesome in its power, and complex in its behavior. From the smallest drops of dew or the tiniest snowflakes to the enormous circulation systems known as mid-latitude cyclones, all atmospheric phenomena are governed by physical laws. These laws can be written in the language of mathematics and, indeed, must be explored in that vernacular in order to develop a penetrating understanding of the behavior of the atmosphere. However, it is equally vital that a physical understanding accompany the mathematical formalism in this comprehensive development of insight. In principle, if one had a complete understanding of the behavior of seven basic variables describing the current state of the atmosphere (these will be called basic state variables in this book), namely u, v, and w (the components of the 3-D wind), T (the temperature), P (the pressure), ϕ (the geopotential), and q (the humidity), then one could describe the future state of the atmosphere by considering the equations that govern the evolution of each variable. It is not, however, immediately apparent what form these equations might take. In this book we will develop those equations in order to develop an understanding of the basic dynamics that govern the behavior of the atmosphere at middle latitudes on Earth.

In this chapter we lay the foundation for that development by reviewing a number of basic conceptual and mathematical tools that will prove invaluable in this task. We begin by assessing the troubling but useful notion that the air surrounding us can be considered a continuous fluid. We then proceed to a review of useful mathematical tools including vector calculus, the Taylor series expansion of a function, centered difference approximations, and the relationship between the Lagrangian and Eulerian derivatives. We then examine the notion of estimating using scale analysis and conclude the chapter by considering the basic kinematics of fluid flows.

1.1 Fluids and the Nature of Fluid Dynamics

Our experience with the natural world makes clear that physical objects manifest themselves in a variety of forms. Most of these physical objects (and every one of them with which we will concern ourselves in this book) have mass. The mass of an object can be thought of as a measure of its substance. The Earth’s atmosphere is one such object. It certainly has mass¹ but differs from, say, a rock in that it is not solid. In fact, the Earth’s atmosphere is an example of a general category of substances known as fluids. A fluid can be colloquially defined as any substance that takes the shape of its container. Aside from the air around us, another fluid with which we are all familiar is water. A given mass of l...