PHYS 4017 Fluid Mechanics

undergraduate elective course, 3 credits

Course Description

  • An introduction to fluid dynamics from a physicist’s perspective.

Instructor

Course Objective

  • Understand the dynamics of fluids as continua

  • Become familiar with basic tensor operations and index notation

  • Get a glimpse of fluid dynamics in astrophysics

  • Prepare yourself for more advanced topics such as plasma physics or stellar dynamics

Course Prerequisites

  • Basic knowledge of vector calculus and thermodynamics

Office Hour

  • TBD in class

References

  • Modern Classical Physics: Optics, Fluids, Plasmas, Elasticity, Relativity, and Statistical Physics, by Kip S. Thorne and Roger D. Blandford

    • Highly pedagogical and insightful. Physically intuitive introduction to tensor algebra.

    • An earlier version is freely available online (see Chaps. 13 - 19)

  • The physics of astrophysics II: Gas dynamics, by Frank H. Shu

    • A rigorous treatment to fluid equations from microscopic kinetic theory. Numerous astrophysical applications.

  • Fluid Mechanics, by L. D. Landau, E.M. Lifshitz

    • A classic. A bit too terse for newbies.

Grading

  • Homework (5 assignments): 70%

    • You are encouraged to discuss with your classmates! However, you must complete the homework independently.You are free to use textbooks, Google, Wikipedia, or even ChatGPT, but you are responsible for the correctness of your answers.

    • Homework is due a week after distribution. Late homework receives a 10% penalty per day (so zero after 10 days)

  • Final Exam (closed book, cumulative): 30%

    • 12/18, in class

  • Participation (extra credits): up to 3%

    • Summarize what we’ve learned last week on stage (~ 5 mins) in the beginning of each class. Come sign up!

Schedule (tentative)

  1. Ideal fluids
    • math preamble (tensor calculus)
    • Euler equations
  2. Dissipation
    • Navier-Stokes equation
    • energy dissipation
  3. Vorticity
    • Kelvin’s theorem
    • potential flow
  4. Hydrostatic equilibrium
    • Lane-Emden equation
    • Mass-size relation
  5. Accretion
    • Bondi accretion
    • Accetion disk
  6. Waves
    • sound waves
    • gravity waves
    • shallow water waves and solitons
    • planetary waves (Rossby waves)
  7. Shocks
    • characteristics and Riemann invariants
    • Rankine-Hugoniot jump conditions
    • Sedov-Taylor blastwave
    • radiative shocks
  8. Fluid instability
    • gravitational instability
    • Kelvin-Helmholtz and Rayleigh-Taylor instability
    • convective instability
    • rotational instability
    • thermal instability
  9. Turbulence
    • Kolmogorov energy spectrum
    • supersonic turbulence
    • turbulent mixing
    • turbulent viscosity
    • turbulence in 2D and inverse cascade
  10. Magnetohydrodynamics
    • ideal MHD equations
    • Alfven waves and magnetosonic waves
    • nonideal MHD
    • dynamo theory*
    • magnetorotational instability*
  11. From kinetic theory to fluid dynamics*
    • Boltzmann equation
    • velocity moments
    • the closure problem

*if time permits

Homework Assignments

Homework 1 (due 9/25)