ADVANCED FLUID DYNAMICS
Oxford Master Course in Mathematical and Theoretical Physics
("MMathPhys")
&
Centre for Postgraduate Training in Plasma Physics and High Energy Density Science
 |
Dr Paul Dellar and Prof Alexander Schekochihin
TA: David Hosking
This is an MMathPhys course which we also expect to be of interest to graduate students specialising in the physics (or applied mathematics) of gases and plasmas, astrophysics, and condensed matter.
 A sketch of students (or, perhaps, fellows) in a manuscript of William of Ockham's commentary on Aristotle's Physics (MS293 from the Merton College library, image courtesy of J. Walwarth). |
Hilary
Term
2021 LECTURES Monday 10:00-11:00 & 17:00-18:00 weekly on ZOOM (links by email from Jasmine, not public; or ask the lecturers) Virtual blackboard for Part II (MHD) lectures CLASSES TBA (week 4) (with Paul Dellar) TBA (week 9) (with David Hosking) Course materials, reading suggestions, scheduling notices, problem sets to appear below shortly. Syllabi currently given below are subject to revision. |
A sketch of students (or, perhaps, fellows) in a manuscript of William of Ockham's commentary on Aristotle's Physics (MS293 from the Merton College library, image courtesy of J. Walwarth). |
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| PART I: COMPLEX FLUIDS |
Lectures 1-6
Dr Paul Dellar
Fluid
mechanics with general extra stress. Dilute suspension of spheres:
Einstein viscosity. Dilute suspension of beads on springs: Oldroyd-B
model for polymeric liquids, elastic waves, anisotropic pressure.
Dilute suspension of orientable particles (ellipsoids): road map to
liquid crystals, swimmers and active matter.
Lectures 1-2 (Mon 18.01.21) Lectures 3-4 (Mon 25.01.21) Lectures 5-6 (Mon 1.02.21) |
Problem
Set 1 Paul Dellar's course webpage |
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| PART II: MAGNETOHYDRO- DYNAMICS |
Lectures 7-16 Prof Alexander
Schekochihin MHD
equations: conservation laws in a conducting fluid; Maxwell
stress/magnetic forces; induction equation; Lundquist theorem, flux
freezing, amplification of magnetic field. MHD in a strong guide field:
MHD waves; high-beta and anisotropic limits and orderings;
incompressible MHD, Elsasser MHD, Reduced MHD. Static MHD equilibria,
force-free solutions, helicity, Taylor relaxation. Energy principle.
Instabilities: interchange, Z-pinch.
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Problem Set 2 You will find it at the back of the typed Lecture Notes, Part II It is to be handed in to David Hosking, by 11:59 on Saturday 13.03.21 |
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| Lectures 7-8 (Mon 8.02.21) MHD
equations: conservation laws in a conducting fluid; Maxwell
stress/magnetic forces; induction equation; Lundquist theorem, flux
freezing, amplification of magnetic field. You are ready to do
Q1-4 of the Problem Set
(and the optional Q5 if you study the section on Lagrangian MHD) Lectures 9-10 (Mon 15.02.21) MHD in a strong guide field: MHD waves; high-beta and anisotropic limits and orderings. Lectures 11-12 (Mon 22.02.21) MHD in a strong guide field: incompressible MHD, Reduced MHD. You are ready to do Q6-8 of the Problem Set
Lectures 13-14 (Mon 1.03.21) Static MHD equilibria, force-free solutions, helicity, Taylor relaxation. Energy principle started. You are ready to do Q9 of the Problem Set
Lectures 15-16 (Mon 8.03.21) Energy principle finished. Instabilities: interchange, Z-pinch. You are ready to do Q10-11 of the Problem
Set
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You will find typed lecture
notes as Part II in this file They will be occasionally updated during this term. The current version is of 1.01.21. I will be very grateful to those of you who offer criticisms, suggestions or point out errors. |
READING LIST
(we will provide detailed reading recommendations from the list below as the course progresses)
(we will provide detailed reading recommendations from the list below as the course progresses)
PART
I: see Paul
Dellar's course webpage
PART II: Here are four very different textbooks, all well worth reading:
1. P. A. Sturrock, Plasma Physics (CUP 1994) Chapters 11-16 cover MHD (~100 pages)
2. R. M. Kulsrud, Plasma Physics for Astrophysics (Princeton U Press 2005) Chapters 3-7 cover MHD (~150 pages)
3. P. A. Davidson, An Introduction to Magnetohydrodynamics (CUP 2001) Part A covers the fundamental MHD (~300 pages)
4. H. Goedbloed & S. Poedts, Principles of Magnetohydrodynamics (CUP 2004) (~600 pages)
PART II: Here are four very different textbooks, all well worth reading:
1. P. A. Sturrock, Plasma Physics (CUP 1994) Chapters 11-16 cover MHD (~100 pages)
2. R. M. Kulsrud, Plasma Physics for Astrophysics (Princeton U Press 2005) Chapters 3-7 cover MHD (~150 pages)
3. P. A. Davidson, An Introduction to Magnetohydrodynamics (CUP 2001) Part A covers the fundamental MHD (~300 pages)
4. H. Goedbloed & S. Poedts, Principles of Magnetohydrodynamics (CUP 2004) (~600 pages)