Study information

# Fluid Dynamics of Atmospheres and Oceans - 2023 entry

MODULE TITLE CREDIT VALUE Fluid Dynamics of Atmospheres and Oceans 15 MTHM019 Dr William Seviour (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 0 0
 Number of Students Taking Module (anticipated) 23
DESCRIPTION - summary of the module content

This module lays the foundations for an understanding of large scale weather patterns and ocean circulation. It will introduce you to the kinds of dynamics that can occur in stratified and rotating fluids, and introduce key concepts, such as conservation and balance, that are used to understand and analyse such flows.

You will learn to explain, manipulate and analyse mathematical descriptions of different kinds of wave and vortical motion that can occur in stratified and rotating fluids. Furthermore, you will be able to explain the relevance of the mathematical descriptions to large scale motion of the atmosphere and oceans. In addition, you will study the application of a range of mathematical methods, including differential equations, fluid dynamics, Fourier analysis, and the use of small parameters to approximate and simplify problems. The material should develop your ability to relate physical problems to their mathematical formulation.

Pre-requisite module: MTH3001 or equivalent

AIMS - intentions of the module

This is an introductory module on the dynamics of stratified and rotating fluids, with application to atmosphere and ocean dynamics. It will introduce you to the kinds of dynamics that can occur in stratified and rotating fluids, and introduce key concepts, such as conservation and balance, that are used to understand and analyse such flows.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:

1 Explain, manipulate, and analyse mathematical descriptions of different kinds of wave and vortical motion that can occur in stratified and rotating fluids; explain the relevance of the mathematical descriptions to large scale motion of the atmosphere and oceans;

Discipline Specific Skills and Knowledge:

2 Demonstrate the application of a range of mathematical methods, including differential equations, fluid dynamics, Fourier analysis, and the use of small parameters to approximate and simplify problems;

3 Relate weather and ocean circulations to the underpinning of mathematical formulation;

Personal and Key Transferable/ Employment Skills and Knowledge:

4 Monitor their own progress;

5 Manage time;

6 Formulate and solve complex problems.

SYLLABUS PLAN - summary of the structure and academic content of the module

- Equations of motion; hydrostatic balance; equations of motion in a rotating coordinate frame;

- Shallow water gravity waves, phase and group velocity, internal gravity waves, mountain waves and mountain wave drag;

- Rossby number; geostrophic balance; potential vorticity, invertibility; circulation and Kelvin's Theorem;

- Rossby Waves; Poincare waves, the Rossby Adjustment Problem, Rossby radius; Kelvin Waves;

- Quasi-Geostrophic Theory; vertical propagation of planetary waves; Eady model of baroclinic instability;

- Ekman layer, Ekman pumping, Sverdrup balance.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 33 117 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled Learning and Teaching Activities 33 Lectures/example classes Guided Independent Study 117 Book work from lectures; study using reading list; past exam papers.

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Coursework – Example Sheets 4 hours per problem sheet All Problems class and meeting with lecturer

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams Practical Exams 20 80 0
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written Exam – Closed Book 80 2 hours (Summer) 1-3, 6 Written/verbal on request
Coursework - example sheet 1 10 4-6 questions, 1-2 pages 1-5 Problems class and meeting with lecturer
Coursework - example sheet 2 10 4-6 questions, 1-2 pages 1-5 Problems class and meeting with lecturer

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
Written Exam* Written Exam (2 hours) All August Ref/Def Period
Coursework 1* Coursework 1 All August Ref/Def Period
Coursework 2* Coursework 2 All August Ref/Def Period

*Please refer to reassessment notes for details on deferral vs. Referral reassessment

RE-ASSESSMENT NOTES
Deferrals: Reassessment will be by coursework and/or written exam in the deferred element only. For deferred candidates, the module mark will be uncapped.

Referrals: Reassessment will be by a single written exam worth 100% of the module only. As it is a referral, the mark will be capped at 50%.
RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener