MTMW97-Fluid dynamics of the atmosphere and oceans (HDR)

Module Provider: Meteorology
Number of credits: 10 [5 ECTS credits]
Terms in which taught: Autumn term module
Non-modular pre-requisites:
Modules excluded:
Current from: 2022/3

Module Convenor: Prof Danny Feltham

Type of module:

Summary module description:

The atmosphere and oceans support motions on a vast range of scales - from planetary to molecular. Although the fundamental equations of fluid dynamics have been known since the 1850s, solutions are still only known for very idealised situations. Fluids support diverse phenomena such as vortices and wave motions. These typically make fluid flow vary with time, and result in chaotic behaviour that limits predictability. This module starts from first principles to build up the equations of fluid dynamics for situations with increasing complexity including the effects of friction, density stratification and the Earth's rotation. Approximations are then introduced which help us to understand important fluid phenomena that emerge.


  • To derive the differential equations governing the evolution of fluid flows from physical principles;



  • To examine the phenomena supported by fluid motion: laminar flows, waves, vortices and turbulence;



  • Analyse approximations that are appropriate to describe the atmosphere and oceans on different scales.

Assessable learning outcomes:

By the end of the module it is expected that the student will be able to:



  • Recognise the laws of physics applied to a fluid in the form of partial differential equations and to give physical interpretation of the various terms;



  • Recognise and interpret the new terms that are introduced as a consequence of the Earth’s rotation;



  • Apply the techniques of scale analysis to deduce the dominant processes operating in various examples of fluid flow, and to approximate the equations in various limits;



  • Understand the concept of vorticity and use that concept to explain the properties of Rossby waves.


Additional outcomes:

The student is expected to reach a level of understanding and experience at which different fluid motions can be identified and links can be made to the underlying physical mechanisms.

Outline content:

1. Fluids and flow kinematics;



2. Fluid dynamics for incompressible flows;



3. Effects of rotation;



4. Effects of density variations;



5. Combining effects of rotation and stratification;



6. Effects of earth geometry;



7. Vorticity and circulation;



8. Rossby waves;



9. Potential vorticity.


Brief description of teaching and learning methods:

The module will be based around lectures, with associated problem sheets. There will be opportunities for class discussion of some problems.



Reading lists for meteorology modules are available here:  .

Contact hours:
  Autumn Spring Summer
Lectures 18
Tutorials 18
Demonstration 3
Guided independent study: 61
Total hours by term 100 0 0
Total hours for module 100

Summative Assessment Methods:
Method Percentage
Class test administered by School 100

Summative assessment- Examinations:

2 hour exam with a choice of two from three questions in January.


Summative assessment- Coursework and in-class tests:

Formative assessment methods:

Nine problem sheets linked to lectures will match the one-hour tutorial sessions.

Penalties for late submission:

The below information applies to students on taught programmes except those on Postgraduate Flexible programmes. Penalties for late submission, and the associated procedures, which apply to Postgraduate Flexible programmes are specified in the policy “Penalties for late submission for Postgraduate Flexible programmes”, which can be found here:
The Support Centres will apply the following penalties for work submitted late:

  • where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of five working days;
  • where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.
The University policy statement on penalties for late submission can be found at:
You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Assessment requirements for a pass:

A mark of 50% overall.

Reassessment arrangements:

For candidates who have failed, an opportunity to take a resit examination will be provided within the lifetime of the course.

Additional Costs (specified where applicable):

1) Required text books: 2) Specialist equipment or materials: 3) Specialist clothing, footwear or headgear: 4) Printing and binding: 5) Computers and devices with a particular specification: 6) Travel, accommodation and subsistence:

Last updated: 22 September 2022


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