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2015/16 Undergraduate Module Catalogue

MATH3459 Astrophysical Fluid Dynamics

15 creditsClass Size: 30

Module manager: Professor D Hughes
Email: D.W.Hughes@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2015/16

Pre-requisites

MATH3620

Fluid Dynamics 2

This module is mutually exclusive with

MATH5459M

Advanced Astrophysical Fluid Dynamics

This module is not approved as a discovery module

Module summary

This module introduces some of the important concepts from Astrophysical Fluid Dynamics. The ideas of magnetohydrodynamics (MHD) will be introduced, including the properties of the induction equation and the Lorentz Force. MHD waves, including the effects of compressibility and rotation will be studied. The module will cover basic thermodynamics and derive the equations of thermal convection. Finally, it will cover accretion, winds and magnetic braking.

Objectives

At the end of this module students should be able to:
- Derive the induction equation from the pre-Maxwell equations and Ohm's Law for a moving conductor;
- Describe the Lorentz force in terms of a magnetic pressure and tension;
- Describe magnetic fields in terms of field lines and flux functions;
- Give basic properties of the induction equation at low and high magnetic Reynolds number (Rm);
- Derive the equations of linear MHD waves;
- Use basic thermodynamics to derive instability to convection;
- Derive the solutions for spherical accretion or winds.

Syllabus

- The equations of MHD. Deriving the induction equation from the pre-Maxwell Equations and Ohm's Law. Incorporating the Lorentz force into the Navier-Stokes equation;
- The Induction equation. Advection and diffusion. The magnetic Reynolds number Rm. The low Rm (diffusive) limit. The perfectly conducting limit and Cauchy solution. Simple solutions with induction and diffusion;
- Lorentz Force. Magnetic pressure and tension. Potential and force-free fields. Pressure balancing. Z and theta pinches;
- MHD Waves. Alfvén waves. Magnetoacoustic waves;
- Convection. Parcel argument. Instability to convection. The influence of rotation;
- Accretion, Winds and Braking. The equations and derivation of the transonic solutions for stellar accretion and winds. The influence of a magnetic field on angular momentum loss.

Teaching methods

Delivery type	Number	Length hours	Student hours
Lectures	33	1.00	33.00
Private study hours			117.00
Total Contact hours			33.00
Total hours (100hr per 10 credits)			150.00

Private study

Studying and revising of course materials. Completing of assignments and assessments.

Opportunities for Formative Feedback

Regular example sheets

Methods of assessment

Exams

Exam type	Exam duration	% of formal assessment
Standard exam (closed essays, MCQs etc)	2 hr 30 mins	100.00
Total percentage (Assessment Exams)		100.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated

Reading list

The reading list is available from the Library website

Last updated: 16/04/2015

Disclaimer

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