Essentials of Atmospheric and Oceanic Dynamics

See also the quick links at the left and top.


In response to various comments from readers and instructors, I have written a short, supplementary chapter on vorticity, circulation, and another derivation of the QG equations.

Download the supplementary chapter here.

Material can be added to this chapter as needed, so please email with comments and/or requests.


Essentials of Atmospheric and Oceanic Dynamics is an introductory book written for advanced undergraduates or beginning graduate students, or for scientists who are not 'professional dynamicists' and who may want an accessible introduction to the field, with an emphasis on large-scale phenomena and circulation.

The book is divided into three parts: (i) Geophysical Fluid Dynamics; (ii) Atmospheric Circulation (including a chapter on planetary atmospheres) and (iii) Ocean Circulation. The book could be used as a text for upper-level undergraduates, or as a first course in graduate school. Prerequisites are familiarity with vector calculus and basic classical physics, or at least willingness to do some reading on those topics while studying this book. It contains enough material for about two semesters' worth of courses, and there are various ways it can be partitioned into two self-contained courses of one semester each.

As well as basic material the book includes some elementary introductions to a few 'advanced' topics, such as geostrophic turbulence and the Transformed Eulerian Mean. These could easily be omitted for a first course. Essentials differs from its parent book, Atmospheric and Oceanic Fluid Dynamics, in two main ways:

  • It is much shorter, about 1/3 the size. Many advanced or inessential sections are omitted.
  • The explanations are simplified where possible.
There is, though, a brand new chapter on planetary atmospheres that is not present in the big book.

Browse and Buy

The book is published by Cambridge University Press (CUP).

To download a PDF sample (5 MB) click here

A few reviews are here

All the figures from the book are freely available here

Hard Copy:

To obtain a print copy you can use one of the links below, or the Amazon in your country, or your favorite bookstore. The google link has previews and links to many sellers:

         CUP (international)         CUP (USA)         CUP (UK)

Barnes and Noble (USA)           Waterstones (UK)           Blackwells (UK)

Amazon (all countries)         Amazon USA           Amazon UK         Amazon Japan
          Amazon Italy         Amazon Germany         Amazon Canada
Amazon France       Amazon India         Amazon Australia         Amazon Spain


Individuals may obtain the e-book from:   or   Google play   or   Amazon Kindle,
or one of other Amazon links above.

It is also available electronically from
Cambridge Core
but only if your library purchases it (ask them!), and then everyone at your institution can download it.

Input is Welcome

I have already had some emails and comments suggesting things that are missing (e.g. Kelvin's circulation theorem). Here are two things I can do in the future:

  • I am providing a freely downloadable chapter containing the missing material, in the style of and at the level of the Essentials. A draft of this can be downloaded here. Additional material will be added in the future.
  • You can help by providing links to your own, undoubtedly better, notes, material and problem sets on matters related to this book
If this might be useful to you, either as a student or an instructor teaching a course, or if you have other comments, please email me and/or comment on twitter with the hashtag #vallisbook. Please also email me if you see mistakes or typos.

Table of Contents


Chapter 1. Fluid Fundamentals

Chapter 2. Equations for a Rotating Planet

Chapter 3. Dynamics on a Rotating Planet

Chapter 4. Shallow Water Equations

Chapter 5. Geostrophic Theory

Chapter 6. Rossby Waves

Chapter 7. Gravity Waves

Chapter 8. Instability

Chapter 9. Waves and Mean Flows

Chapter 10. Turbulence


Chapter 11. The Tropical Atmosphere

Chapter 12. Midlatitudes and the Stratosphere

Chapter 13. Planetary Atmospheres


Chapter 14. Wind-Driven Gyres

Chapter 14. The Overturning Circulation and Thermocline

Chapter 16. Equatorial Oceans and El Nino