Astro 6531: Astrophysical Fluid Dynamics
Prof. Dong Lai
- Phone: 5-4936. Office: 618 SSB. Email: dong_at_astro.cornell.edu
- Office hours: After class on M & W. Other times are fine;
best contact by email, which I usually answer within 24 hours.
Time & Place:
Tentative: Monday and Wednesday 3:30 pm - 4:45 pm in 622 SSB
Four-credit lecture course, aimed at general astrophysics/physics/engineering
graduate students as well as well-prepared undergraduate students.
A knowledge of fluid dynamics is essential for understanding many of
the most interesting problems in astrophysics (and applied physical
sciences). This course will survey fluid dynamics (including
magnetohydrodynamics and some plasma physics -- time permitting)
important for understanding various astronomical (and terrestrial)
phenomena. Topics include basic fluid and MHD concepts and equations,
waves and instabilities of various types (e.g., sound, gravity,
Rossby, hydromagnetic, spiral density waves; Rayleigh-Taylor, thermal,
Jeans, rotational, magnetorotational instabilities), shear and viscous
flows, turbulence, shocks and blast waves, etc. These topics will be
discussed in different astrophysical contexts and applications, such
as atmosphere and ocean, star and planet formation, stellar
oscillation/rotation/magnetism, compact objects, interstellar medium,
galaxies and clusters. This course is intended mainly for graduate
students (both theory and observation) interested in astrophysics and
space physics. Students in other areas of applied science and
engineering may find the broad astrophysical and terrestrial
applications useful. Well-prepared undergradate students may also take the course. No
previous exposure to fluid dynamics and astronomy is required.
Weekly lectures. There will be about 6-8 problem sets.
No final exam (the last problem set may serve as take-home final exam
or there may be an oral exam/interview).
There may be a student project during the second half of the semester (TBD).
Grades will be determined by these HWs, project and participations in class.
Either Letter or S/U grade option is possible. (S = attend lectures and do
50% of HWs with passing grades)
(all should be on reserve in the Math Library).
We will not follow any book too closely, especially when it comes to
- The Physics of Astrophysics II: Gas Dynamics by Frank Shu
You may buy this book, although we will not follow
the book too closely: Some of the material in the book will not be covered,
and some of the material covered in lectures will not be found
in this book. Still it is a good book to have.
- Fluid Mechanics: An Introduction by Michel Rieutord
- Fluid Mechanics by Landau & Lifshitz
A classic book, good to have. No MHD, but a good presentation of
fluid dynamics, particularly the basics.
- Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena
by Zeldovich and Raizer
A classic book by a master. Nice discussion of shock waves and
- Plasma Physics for Astrophysics by Russel Kulsrud
We almost certainly will not have time to do most of this book. But
it has nice chapters on MHD.
- Astrophysical Flows by Jim Pringle & Andrew King
A recent textbook from Cambridge Univ. Press
- The Physics of Fluids and Plasmas by Arnab Raichoudhuri
A general textbook, somewhat less comprehensive.
- Astrophysical Fluid Dynamics Lecture Note by Gordon Ogilvie
Kip Thorne and Roger Blandford have been
writing a book on "Application of Classical Physics" for many years.
Here is their lecture notes (see Ch.13-19 on Fluid and MHD)
The book is finally coming out in 8/2017.
You may consider buying this book for your long career in physics !
There are many other nice (famous) fluid dynamics books, many containing
interesting applications (not necessarily astrophysical), such as
"Physical fluid dynamics" by Tritton
"An Introduction to fluid dynamics" by Batcheler
"Waves in Fluid" by Lighthill
"Elements of Fluid Dynamics" by Acheson
Fluid Mechanics Films
Topics covered in class:
(suggested reading from Shu, LL=Landau & Lifshitz, TB=Thorne-Blandford,
or other sources). I will update this regularly (usually after each lecture).
- 8/23: Basic assumptions of Fluid Dynamics: collisions in gas and
plasma. Qualitative discussion of collisionless plasma (gyro-radius
condition). Basic fluid equations: mass conservation; Euler equation
and Navier-Stokes eqn (just give the viscous force but not deriving
it); quick review of gravity and magnetic forces.
Reading: Shu: Chapter 1; p.45-46; skim Chap.5
(You have learned that in Stellar Structure). LL: P.1-7.
- 8/28: Momentum equation in conservative form; EOS and energy equation.
Barotropic flows (examples of barotropic relations: adiabatic vs
isentropic flows, ISM, degenerate stars, etc).
Sound wave. Incompressible flow (why/when valid?).
Properties of inviscid barotropic flow: vorticity equation and
Reading: LL: sections 1,2,3,7. Shu: p.44-46, p.64, p.107; BT: Skim through
section 13.1-13.6. PROBLEM SET 1 HAND OUT.
- 8/30: Properties of inviscid barotropic flow (continued):
vorticity equation and Bernoulli's theorem. Interpretation of vorticity.
Applications: irrotational flows, coalescing NS binaries, Magnus effect.
Reading: Shu: Chap.6. LL: p.8-9, p.12-18.
- 9/4: Labor day, no class.
- 9/6: Bondi flow (estimate and formal derivation). Bondi-Lyttleton accretion, Parker stella wind
solution. Sub-sonic solution (relevance to giant planet formation; qualitative discussion).
Reading: Shu: Chap.6. For those interested in giant planet formation: Section III.C of
- 9/11: Sound wave with gravity, Jean's instability. Isothermal
cloud and Jean Mass (digression on Virial theorem).
Sound wave generation: oscillating ball, monopolar radiation,
higher-order radiation. Lighthill's law.
Reading: Shu: Chap.6.
Shu: p.110-112. Sound wave is discussed thoroughly in Chap.8 of LL.
See also relevant chapters in TB.
PROBLEM SET 2 HAND OUT.
- 9/13 (extended class): Lighthill's law.
Gravity waves (surface waves on a pond). Eulerian vs
Lagrangian perturbation. Derive the dispersion relation.
Order-of-magnitude discussion on deep-water and shallow-water waves,
Reading: LL section 12.
Stevenson's article on Tsunami and\
- 9/18: Nonlinear shallow water waves and hydraulic jumps, physical
discussion of wave steepening. Nonlinear shallow wave equations. Method
of characteristics applied to propagating waves, Burger's equation.
Reading: Thorne-Blandford: Sections 16.2-16.3
- 9/20 (extended class):
Surface gravity waves: Effect of surface tension (capillary waves).
Rayleigh-Taylor instability (and application to SN explosion).
Waves in plane-parallel atmospheres: Review Lagrangian perturbation.
Derive the basic equations of waves in atmospheres.
PROBLEM SET 3 HAND OUT.
- 9/25: Waves in plane-parallel atmospheres (continued):
derive local dispersion relation, sound waves vs
gravity waves, Physics of Brunt-Vasala frequency. Convective
instability. Digression of local (WKB) analysis.
Stellar oscillations: brief observation background.
Reading: Pringle-King, Chap.5.
- 9/27 (extended class): Stellar oscillations theory: Radial pulsation: equations, estimate
of discrete modes, radial pulsational instability of massive stars.
Nonradial pulsations: derive eqns in convenient forms, boundary conditiions.
propagation diagram, mode classification.
- 10/2: Oscillation modes (continued). Gravity waves and
convection: Composition gradients and Ledoux criterion. Nonadiabatic
effect and mode excitation (intro): energy equation.
- 10/4: No class (made-up before)
- 10/9: Fall break
- 10/11: Nonadiabatic effect and mode excitation (kappa and epsilon mechanism).
Application of stellar oscillations: two scaling relations
for solar-type oscillations.
Kelvin-Helmholtz instability: derivation
PROBLEM SET 4 HAND OUT.
- 10/16: Kelvin-Helmholtz instability: excitation of ocean wave by wind;
Shear flow instability: Rayleigh inflexion point theorem.
Reading: Shu, Chap.8 (pp.93-105). Pringle-King: 10.1-10.3, 10.8.
- 10/18: Competition between shear and stable stratification: Richardson criterion.
Rotation: Rayleigh's criterion for rotational instability.
Fluid dynamics in rotating frame.
Inertial waves in rotating fluid (barotropic).
- 10/23 (extended class): Rossby number. Geostrophic flows. Taylor-Proudman theorem. Rossby waves.
Global Rossby waves (r-mode). CFS instability. Maclauglin spheroid, bar-mode.
PROBLEM SET 5 HAND OUT.
- 10/25: Rotational splitting of mode frequencies (f-modes etc).
Viscous flows: Viscous flows (1D equation,
viscous stress tensor, shear and bulk viscosities, microphysics of viscosity).
Scaling and Reynolds number. Flow passing a sphere:
Low-Re flow (Stokes flow).
- 10/30: No class (made-up)
- 11/1 (extended class): Flow passing a sphere: behavior as a function of Re.
Viscous boundary layer (estimate), drag force in the presence of
BL. General drag force formula (Esptein, Stokes, etc) for application
is dust dynamics in pre-solar nebula. Ekman layer intro and estimate of width;
flow in Teacup. Turbulence: examples of transition to
turbulence (Poiseuille flow, boundary layer turbulence), Kolmogorov theory (derive spectrum).
PROBLEM SET 6 HAND OUT.
- 11/6: 3D and 2D turbulence: conservation laws, energy and
enstrophy cascade (Kraichnan theory). Viscous accretion disks:
Introduction; basic equations for axisymmetric thin disks.
Reading: Shu: Chap.7.
- 11/8: Accretion disks:
boundary layers; origin of viscosity, disk turbulence.
energy dissipation. Waves in disks -- intro.
PROBLEM SET 7 HAND OUT.
Waves in disks: dispersion relation, Toomre criterion,
Reading: Shu, Chap.12,13
- 11/15: Spiral density waves: kinematics, wave propgation zone,
Q-barrier, corotation and Lindblad resonances.
Negative energy waves, super-reflection and corotation amplifier.
Nonlinear sound wave steepening. Shock waves: Shock jump condition.
Reading: Shu, Chap.12,13
- 11/20: No class (makeup class later).
- 11/22: Thanksgiving
- 11/27: Blast waves: Sedov-Taylor solution.
Forward an reverse shock, evolution of supernova remnants, shock produced by
stellar wind (including pulsar wind nebula, bow shock etc).
Reading: Shu, Chap.15
- 11/29: MHD equations: magnetic forces (pressure and tension),
magnetic evolution (diffusion, flux freezing). Hydromagnetic waves.
PROBLEM SET 8 HAND OUT.
- 12/4 (Make-up class): Magnetostatic equilibrium: pressue-balanced plasma column,
sausage and kink instabilities. Magnetic cloud,
Virial theorem. critical mass to flux ratio (magnetic flux problem of star
formation). Ambipolar diffusion. Qualitative discussion of
torsional Alfven waves and magnetic braking.
MRI: physical discussion.
Reading: Shu, Chap. 24, 22.
- 12/4 (Additional):
MRI: mechanical derivation.
Magnetic buoyancy (Parker's idea). Magnetic RT instability. Parker instability.
Student Project Information can be found here (TBD)
Dong's Homepage .