MTMFAO: Fluid Dynamics of the Atmosphere and Oceans

Module code: MTMFAO

Module provider: Meteorology; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Postgraduate Masters

When you'll be taught: Semester 1

Module convenor: Professor Danny Feltham, email: d.l.feltham@reading.ac.uk

Module co-convenor: Professor Keith Haines, email: k.haines@reading.ac.uk

Pre-requisite module(s): Before taking this module, you must have a BSc degree (or equivalent) in a subject with significant mathematical content, e.g. Physics, Engineering, Mathematics, Meteorology. (Open)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

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, and applies these to situations with increasing complexity, including the effects of friction, density stratification and the Earth's rotation. Approximations are introduced which help us to understand important fluid phenomena that emerge. Much of weather and climate science builds on a foundation of knowledge of fluid dynamics. 

Module learning outcomes

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

1. Recognise the laws of physics applied to a fluid in the form of partial differential equations, and give physical interpretations of the various terms, including those resulting from the Earth’s rotation; 
2. 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; 
3. Understand the concept of vorticity and use that concept to explain the properties of Rossby waves; 
4. Analyse the results of laboratory experiments and compare them with theoretical predictions. 

Module content

1. Fluids and flow kinematics; 
2. Fluid dynamics for Incompressible flows; 
3. Effects of rotation; 
4. Effects of density variations; 
5. Combined effects of rotation and stratification; 
6. Effects of earth geometry; 
7. Vorticity and circulation; 
8. Rossby waves; 
9. Potential vorticity. 

Structure

Teaching and learning methods

The module will be based around a series of connected lectures that introduce the theoretical material, building upon each other to address more complex situations. There will be a series of problem sheets associated with these lectures, and support will be provided in a series of problem classes. Laboratory classes will give students the opportunity to study various relevant fluid flows directly. 

Study hours

At least 57 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 50% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• 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 three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: https://www.reading.ac.uk/cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

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.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

The students will do four laboratory experiments and receive marks for all four. The best two sets of marks will be put forward for summative assessment. The other two are therefore formative. 

The students are expected to complete a series of problem sheets, which are not marked. The students receive assistance and are given solutions. These problem sheets help to consolidate understanding of the material given in lectures, and provide guidance and practise for the type of problems in the exam (class test). 

Reassessment

Additional costs