# Mathematics

## ECMM719 - Fluid Dynamics of Atmospheres and Oceans (2018)

MODULE TITLE CREDIT VALUE Fluid Dynamics of Atmospheres and Oceans 15 ECMM719 Prof Geoffrey Vallis (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 12 0 0
 Number of Students Taking Module (anticipated) 32
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.

Prerequisite module: ECM3707 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 33 117
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
Written exercise to derive key results 20 minutes All Lecturer presents to class

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
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 Exam Period 1,2,5 Meeting with lecturer
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
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 50% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

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

ELE – http://vle.exeter.ac.uk