# Part IB - Fluid Dynamics

## Lectured by P. F. Linden, Lent 2016

These notes are not endorsed by the lecturers, and I have modified them (often significantly) after lectures. They are nowhere near accurate representations of what was actually lectured, and in particular, all errors are almost surely mine.

This is an HTML version of the notes, generated using some horribly-written scripts and pdf2htmlEX. These are not guaranteed to display well, but do let me know if something is broken. Note however that I cannot help you if your browser does not support standard HTML features (eg. this part is known not to work well with w3m). You can either view all sections in a single page (Full version), or access individual sections below. If you want to download a pdf, head to the Notes page.

# Contents

- V Full version
- 0 Introduction
- 1 Parallel viscous flow
- 1.1 Preliminaries
- 1.2 Stress
- 1.3 Steady parallel viscous flow
- 1.4 Derived properties of a flow
- 1.5 More examples
- 2 Kinematics
- 2.1 Material time derivative
- 2.2 Conservation of mass
- 2.3 Kinematic boundary conditions
- 2.4 Streamfunction for incompressible flow
- 3 Dynamics
- 3.1 Navier-Stokes equations
- 3.2 Pressure
- 3.3 Reynolds number
- 3.4 A case study: stagnation point flow (u = 0)
- 3.5 Momentum equation for inviscid (nu = 0) incompressible fluid
- 3.6 Linear flows
- 3.7 Vorticity equation
- 4 Inviscid irrotational flow
- 4.1 Three-dimensional potential flows
- 4.2 Potential flow in two dimensions
- 4.3 Time dependent potential flows
- 5 Water waves
- 5.1 Dimensional analysis
- 5.2 Equation and boundary conditions
- 5.3 Two-dimensional waves (straight crested waves)
- 5.4 Group velocity
- 5.5 Rayleigh-Taylor instability
- 6 Fluid dynamics on a rotating frame