Description

Many systems of both everyday and astrophysical importance can be studied using the equations and concepts of fluid dynamics. The cup of coffee you drink in the morning, the waves you see at the beach, the blood pumping through your body -- but also the interiors of stars and planets, and the disks in which they form -- are all governed by some version of these equations.

In this module, you will learn the fundamental concepts of fluid mechanics and apply them to a variety of problems in physics, everyday life, and astronomy. You will learn how to solve the Navier-Stokes equations (which govern the flow) in simple cases, and how to describe some aspects of fluid dynamical phenomena even in cases where no analytical solution is possible.

Module Aims

This module aims to provide students with an understanding of the basic concepts of fluid dynamics, and practice in using these to solve problems of interest. It also aims to highlight some of the many important applications of fluid dynamics in physics and astronomy, and to develop some physical intuition for the many problems in which no complete solution for the flow can be obtained.

Intended Learning Outcomes (ILOs)

A student who has passed this module should be able to:

• Module Specific Skills and Knowledge:
  1. Explain the basic concepts and equations of fluid dynamics;
  2. Use the Navier-Stokes (and/or Euler, as appropriate) equations to solve or constrain the fluid flow in simple geometries;
  3. Identify and describe non-dimensional parameters that frequently govern the flow;
  4. Interpret solutions of partial differential equations in physical terms.
• Discipline Specific Skills and Knowledge:
  5. Describe astronomical and physical phenomena whose behaviour is governed by fluid flow;
  6. Translate a complex physical problem into an approximate problem that can be solved or constrained.
• Personal and Key Transferable / Employment Skills and Knowledge:
  7. Develop problem-solving skills;
  8. Develop self-study skills.

Syllabus Plan

1. Fundamental ideas and equations of fluid dynamics
   1. Continuity equation; mass conservation
   2. Euler equation; momentum conservation
   3. Navier-Stokes equation
   4. Governing non-dimensional parameters
   5. Laminar flow and other limiting states
   6. Energetics and Bernoulli's principle
   7. Boundary layers
2. Vorticity and rotating fluids
   1. Vorticity equation
   2. Kelvin's circulation theorem
   3. Irrotational flow
   4. Flow in rotating reference frames
3. Waves and instabilities
   1. Linearisation
   2. Examples of classic waves (including inertial and gravity waves)
   3. Classic instabilities (including Rayleigh-Taylor, convection)
4. Compressible fluid dynamics
   1. The speed of sound and the Mach number
   2. Shock waves
   3. Effects of stratification
5. Applications to problems in physics, geophysics, and astronomy:
   1. (Examples to be chosen at instructor's discretion; below list is illustrative)
   2. Convection in stars and planets
   3. Accretion and accretion disks
   4. Planetary winds
   5. Aerodynamic
   6. Biophysical fluids
6. Survey of advanced topics (as time permits)
   1. Introduction to magnetohydrodynamics (MHD)
   2. Non-Newtonian fluids
   3. Turbulence

Learning and Teaching

Learning Activities and Teaching Methods

Assessment

Resources

The following list is offered as an indication of the type & level of information that students are expected to consult. Further guidance will be provided by the Module Instructor(s).

Core text:

• Not applicable

Supplementary texts:

• Not applicable

ELE:

• http://newton.ex.ac.uk/redirects/ELE/PHY3220

Further Information

Prior Knowledge Requirements

Re-assessment

Re-assessment is not available except when required by referral or deferral.

Notes: Coursework is not referrable, but deferral assessment is via ref/def written examination

KIS Data Summary

Miscellaneous