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ADVANCED FLUID DYNAMICS

Oxford Master Course in Mathematical and Theoretical Physics
("MMathPhys")
&
Centre for Postgraduate Training in Plasma Physics and High Energy Density Science



magnetic field



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.

clericsMS293.jpg
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.

clericsMS293_reflected.jpg
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)
.
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




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.

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

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


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)

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)