Mathematics

ECMM719 - Fluid Dynamics of Atmospheres and Oceans (2015)

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MODULE TITLEFluid Dynamics of Atmospheres and Oceans CREDIT VALUE15
MODULE CODEECMM719 MODULE CONVENERProf Geoffrey Vallis (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 0 11 weeks 0
Number of Students Taking Module (anticipated) 13
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 33.00 Guided Independent Study 117.00 Placement / Study Abroad
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 20 Written Exams 80 Practical Exams
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 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 40% 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

Reading list for this module:

Type Author Title Edition Publisher Year ISBN Search
Set Vallis, G.K. Atmospheric and Oceanic Fluid Dynamics: Fundamentals and Large Scale Circulation Cambridge University Press 2006 978-0521849692 [Library]
Set Cushman-Roisin B and Beckers JM Introduction fo Geophysical Fluid Dynamics 2nd Academic Press 2010 978-0120887590 [Library]
Set Holton, J. R An introduction to Dynamic Meteorology 4th Academic Press 2012 978-0123848666 [Library]
Set Pedlosky J. Geophysical Fluid Dynamics 2nd Springer 1992 978-0387963877 [Library]
Set Gill A. Atmosphere-Ocean dynamics Academic Press 1982 978-1483239439 [Library]
CREDIT VALUE 15 ECTS VALUE 7.5
PRE-REQUISITE MODULES ECM3707
CO-REQUISITE MODULES
NQF LEVEL (FHEQ) 7 AVAILABLE AS DISTANCE LEARNING No
ORIGIN DATE Friday 09 January 2015 LAST REVISION DATE Monday 12 January 2015
KEY WORDS SEARCH Fluid dynamics; meteorology; atmosphere; ocean.