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 sheetsMethods 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 websiteLast updated: 16/04/2015
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