Fluid Mechanics
Introduction
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Chapter 1

Introduction

What will you learn in this course

The course aims to provide students with a solid understanding of key fluid mechanics concepts that are used in ocean physics research. This course will first refresh you on the vector calculus needed to understand fluid mechanics, and introduce the Eulerian and Lagrangian views of the flow. We then proceed to derive the conservation equations for mass and momentum. We will then consider the effects of rotation and stratification, and look at some steady solutions of the rotating Navier-Stokes equations. Then, we will simplify the flow by looking at it as a thin layer of incompressible rotating fluid that flows over a variable bottom topography and a free surface. From there, we will study turbulence and boundary layers, and complete the course with the linear theory of surface gravity waves. By the end of the course, you will be proficient in applying fluid mechanical concepts and mathematical tools to solve many ocean physics research problems. It will also prepare you for more specialized courses on turbulence, waves, and atmospheric and oceanic circulation.

Reference textbooks

No single textbook out there covers all the topics that we need for this course. However, parts of this course are covered in detail by various textbooks. These lecture notes are based on the following textbooks:

  1. Fluid Mechanics, 7th^{th} Ed., by Kundu, Cohen, Dowling, and Capecelatro (Elsevier), for the classical (Kundu et al., 2024);

  2. Atmospheric and Oceanic Fluid Dynamics (AOFD) by Geoffrey Vallis (Cambridge University Press), for the geophysical (Vallis, 2017); but see also his more concise Essentials of Atmospheric and Oceanic Dynamics (Cambridge University Press), for a shorter and more selective treatment (Vallis, 2019);

  3. Turbulent Flows by Stephen Pope (Cambridge University Press), for the turbulent (Pope, 2001);

  4. Water Wave Mechanics for Engineers and Scientists by Dean and Dalrymple (World Scientific), for the wavy (Dean and Dalrymple, 1991).

While the notes contain the distilled and required information for you to succeed in this course, please refer to these textbooks for more detailed explanations and examples. Over time, the lecture notes will evolve toward a unified, coherent, and self-contained book.