Astro 6531: Astrophysical Fluid Dynamics
Spring 2023
Instructor:
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:
Monday and Wednesday 9:40 am - 10:55 am, SSB 622
Class website:
http://hosting.astro.cornell.edu/~dong/a6531/a6531.html
Description:
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.
The students should be familiar with classical mechanics and
electrodynamics at the intermediate (junior) level, and should be
comfortable with vector calculus (e.g. divergence and curl of a vector).
Organization:
Weekly lectures. There will be about 6-8 problem sets.
No final exam (the last problem set may serve as take-home final exam).
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
70% of HWs with passing grades)
Policy statement: You should abide by the CU Code of Academic
Integrity. You are encouraged to discuss homework with other
students but not to collaborate on writing up the notebook
solutions (and not to copy). Anything that you turn in should be your own
work (homework, project). If you need any academic accommodations
please register with Student Disability Services at the beginning of the
term and bring me the description of the appropriate
accommodations.
Recommended Books:
We will not follow any book too closely, especially when it comes to
astrophysical applications.
- 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
- Application of Classical Physics by Kip Thorne and Roger Blandford
- 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
1D flows.
- 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
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).
Here are the topics covered in Fall 2017 .
We will cover some of the topics, and will add some new topics.
- 1/23: 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 review of gravity term.
Reading: Shu: Chapter 1; p.45-46; skim Chap.5
(You have learned that in Stellar Structure). LL: P.1-7.
- 1/25:
Navier-Stokes eqn (just give the viscous force but not deriving
it); quick review of magnetic forces.
Momentum equation in conservative form; EOS and energy equation.
Barotropic flows (examples of barotropic relations: adiabatic vs
isentropic flows, ISM, degenerate stars, etc).
Reading: LL: sections 1,2,3,7. Shu: p.44-46, p.64, p.107; BT: Skim through
section 13.1-13.6.
- 1/30: Sound wave. Incompressible flow (why/when valid?).
Properties of inviscid barotropic flow: vorticity equation and
Bernoulli's theorem.
Reading: Shu: Chap.6. LL: p.8-9, p.12-18.
- 2/1: Interpretation of vorticity. Applications: irrotational
flows, coalescing NS binaries, Magnus force.
Bondi flow (estimate and formal derivation). Bondi-Lyttleton accretion.
- 2/6: Sub-sonic solution (relevance to giant planet formation; qualitative discussion).
Parker stellar wind solution.
Sound wave generation: oscillating ball, monopolar radiation,
higher-order radiation. Lighthill's law.
Reading: Shu: Chap.6. For those interested in giant planet formation: Section III.C of
Armitage review.
Parker wind.
Sound wave is discussed thoroughly in Chap.8 of LL. See also relevant chapters in Thorne-Blandford
- 2/8 (Guest lecture): Sound wave with gravity, Jean's instability. Isothermal
cloud and Jean Mass (digression on Virial theorem). Gravity waves (surface waves on a pond).
- 2/13: Gravity waves continued:
Eulerian vs Lagrangian perturbation. Derive the dispersion relation.
Order-of-magnitude discussion on deep-water and shallow-water waves,
Tsunamis.
Reading: LL section 12.
Stevenson's article on Tsunami and\
earthquakes
- 2/15: Nonlinear shallow water wave equations. Linear regime, WKB method.
Method of characteristics applied to propagating waves, Burger's equation.
Reading: Thorne-Blandford: Sections 16.2-16.3
- 2/20: Physical discussion of wave steepening.
Rayleigh-Taylor instability (and application to SN explosion).
Waves in plane-parallel atmospheres: Review Lagrangian perturbation.
- 3/1: Waves in plane-parallel atmospheres (continued):
derive local dispersion relation, sound waves vs
gravity waves, Physics of Brunt-Vasala frequency. Convective instability.
Reading: Pringle-King, Chap.5.
- 3/3 (makeup class): Stellar oscillations: brief observation background.
Stellar oscillations theory: Radial pulsation: equations, estimate
of discrete modes.
- 3/6: Radial pulsational instability of massive stars.
Nonradial pulsations: derive eqns in convenient forms, boundary conditions.
WKB dispersion relation.
- 3/8: propagation diagram, mode classification. Gravity waves and
convection: Composition gradients and Ledoux criterion. Double diffusive instabilities,
salt fingers. Nonadiabatic effect and mode excitation (intro): energy equations.
- 3/13: Nonadiabatic effect and mode excitation (kappa and epsilon mechanisms).
Application of stellar oscillations.
- 3/15: Kelvin-Helmholtz instability: derivation, excitation of ocean wave by wind;
physical interpretation.
Shear flow instability: Rayleigh inflexion point theorem.
Reading: Shu, Chap.8 (pp.93-105). Pringle-King: 10.1-10.3, 10.8.
- 3/20: 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).
Rotational distortion.
- 3/27: Rossby number. Geostrophic flows. Taylor-Proudman theorem. Ro\
ssby waves. Global Rossby waves (r-mode). CFS instability.
- 3/29: Rotational splitting of mode frequencies (f-modes etc).
Viscous flows: Viscous flows (1D equation,
viscous stress tensor, shear and bulk viscosities.
- 4/10: Microphysics of viscosity. Scaling and Reynolds number. Flow passing a sphere:
low-Re flow (Stokes flow); behavior as a function of Re.
- 4/12: 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).
- 4/17: 3D and 2D turbulence: conservation laws, energy and
enstrophy cascade (mention Kraichnan theory). Accretion disk intro.
- 4/19: Basic equations for axisymmetric thin disks. Boundary layers; origin of viscosity, disk turbulence.
Reading: Shu: Chap.7.
- 4/24: Waves in disks: dispersion relation, Toomre criterion,
Safraonov-Goldrecih-Ward instability. Spiral density waves: kinematics, wave propgation zone,
Q-barrier, corotation and Lindblad resonances.
Negative energy waves, super-reflection and corotation amplifier.
Reading: Shu, Chap.12,13
- 4/26: Nonlinear sound wave steepening. Shock waves: Shock jump condition.
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
- 5/1: MHD equations: magnetic forces (pressure and tension),
magnetic evolution (diffusion, flux freezing). Hydromagnetic waves.
- 5/3: 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.
- 5/8: MRI: mechanical derivation.
Magnetic buoyancy (Parker's idea). Magnetic RT instability. Parker instability.
Student Project Information can be found here (TBD)
Back to
Dong's Homepage .