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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



Prof Alexander Schekochihin and Dr Paul Dellar
TA: Ching Lok Chong

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 2019

LECTURES
Lindemann LT
Monday 10:00-11:00 & 16:00-17:00 weekly
 
CLASSES

Tuesday 19 Feb (week 6) 16:00-18:00 in 501 DWB (with Ching Chong)
  TBA (week 9) TBA in TBA

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: MAGNETOHYDRO-
DYNAMICS
Lectures 1-10 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 1
You will find it at the back of
the typed Lecture Notes, Part II
It is to be handed in
to Ching Lok Chong,
by 15:00 Friday 15.02.19

Lectures 1-2 (Mon 14.01.19) 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

Lectures 3-4 (Mon 21.01.19) MHD in a strong guide field: MHD waves; high-beta and anisotropic limits and orderings.

Lectures 5-6
(Mon 28.01.19) MHD in a strong guide field: incompressible MHD, Reduced MHD.

You are ready to do Q5-7 of the Problem Set (Q7 is optional)

Lectures 7-8
(Mon 4.02.19) Static MHD equilibria, force-free solutions, helicity, Taylor relaxation. Energy principle started.

You are ready to do Q8 of the Problem Set

Lectures 9-10
(Mon 11.02.19) Energy principle finished. Instabilities: interchange, Z-pinch.

You are ready to do Q9-10 of the Problem Set


You will find typed lecture notes
as Part II in this file
(start from p. 94)
They will be occasionally updated
during this term.
The current version is of 22.01.19.
I will be very grateful to those
of you who offer criticisms,
suggestions or point out errors.
PART II: COMPLEX
FLUIDS
Lectures 11-16 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 11-12 (Mon 18.02.19)
Lectures 13-14 (Mon 25.02.19)
Lectures 15-16 (Mon 4.03.19)

Problem Set 2

Paul Dellar's
course webpage

READING LIST
(we will provide detailed reading recommendations from the list below as the course progresses)

PART I: 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: see Paul Dellar's course webpage