Excellent intro article on turbulence: The Turbulence Problem by Robert Ecke (2005).
Turbulence: golf ball dimples. What happens when only half of the ball has dimples?
Flying snake and lizard. TEDx talk.
Laminar flow

Images of billow clouds, above SF, Chung-Pei's shot, Starry Night
AREPO code: paper
K-H instability single mode, random noise initial seeds
R-T instability: injecting dye in water movie
R-T instability single mode
Crab Nebula

Presentation Schedule

October 28 Monday

Olivia Aspegren: Fluid dynamics of tennis. Talk slides.

Ethan Levin: Diffusion flames. Talk slides.

October 30 Wednesday

Savannah Cary: Supernova ejecta. Talk slides.

November 4 Monday

Fatima Yousuf: Earth climate modeling. Talk slides.

Peter Ma: Physics-inform neural networks for fluid dynamics. Talk slides.

November 6 Wednesday

Katie Sharpe: Superfluidity. Talk slides.

Cooper Jacobus: Simulating the cosmic web. Talk slides.

November 13 Wednesday

Dylan Motley: Shock wave/boundary layer interactions in hypersonic vehicles. Talk slides.

November 18 Monday

Hao-Tse Huang: Stellar oscillations and chaotic tides. Talk slides.

Keaton Ferguson: Saturn's hexagonal storm. Talk slides.

November 20 Wednesday

Evan Kaplan: Helium flash and combustion in stellar envelopes. Talk slides.

Saahit Mogan: Fluid dynamics of traffic flows. Talk slides.

November 25 Monday

Stephon Qian: Stellar rotations and the Tayler-Spruit instability. Talk slides.

Tamar Ervin: Astrophysical turbulences. Talk slides.

Presentation Guidelines

Email me your preferred topic by 5pm Wednesday October 2. See samples below. You are encouraged to select and define your own topic.

Format: Each talk is 15 minutes. The audience is your classmates, and pedagogy is important.
Each topic is likely broad and has consumed many professional astro/physicists' lives. Focus on big questions such as:

Why is it important?
How is it done?
What have we learned?
What are the current limitations in understanding this problem/phenomenon?
What to expect next?

Be sure to draw connection to the equations and theories derived in class, but don't spend time on derivations.
Instead, emphasize applications, phenomenology, and how theories/models can and can't explain and predict observations.

Sample topics: Earth climate, ocean, tsunami, tornadoes, planet atmospheres, solar wind, helioseismology, astrophysical accretion disks, examples of fluid instabilities, physics of baseball, numerical simulations of galaxy formation and many more.

Problem Set 8 (due 6pm Friday November 22)

Problem Set 7 (due 6pm Friday November 8)
Reading: Ch 13.7 of Thorne and Blandford; Ch 7 of Balbus "Hydrodynamics"

Problem Set 6 (due 6pm Friday October 25)

Problem Set 5 (due 6pm Friday October 18): An outline (1-2 pages) of your present aion. Sketch the scope of the talk.
Provide references (i.e. review/journal papers; web links ) that you are using to learn the topic. The more detail you provide, the more feedback we can give you.

Problem Set 4 (due 6pm Friday October 11)
Reading: Ch 17 of Thorne and Blandford

Problem Set 3 (due 6pm Friday October 4)
Reading: Ch 16 of Thorne and Blandford

Problem Set 2 (due 6pm Friday September 27)

Problem Set 1 (due 6pm Friday September 20)
Reading: Ch 13.1-13.6 of Thorne and Blandford

Instructor: Chung-Pei Ma
Office: Campbell Hall 319
Email: cpma(at)berkeley.edu
Office hours: 11:30-noon MW (right after class in 501B)

Reader: Jacob Pilawa
Email: jacobpilawa(at)berkeley.edu
Help sessions: 5pm Wednesdays (zoom link)

Lectures: MW 10:10-11:30am in Campbell 501B

Grading: 70% problem sets; 30% in-class presentation

Main References:

Thorne and Blandford: Modern Classical Physics (Princeton University Press 2017). A pre-published version (January 2013) is available here. Ch 13: Foundations of Fluid Dynamics

Balbus text: Hydrodynamics, Magnetohydrodynamics

Clarke and Carswell: Principles of Astrophysical Fluid Dynamics (Cambridge University Press 2007)

Pringle and King: Astrophysical Flows (Cambridge 2007)

Shu: Gas Dynamics (University Science Books 1992)

Tritton: Physical Fluid Dynamics (Oxford Press 1988)

Acheson: Elementary Fluid Dynamics (Oxford Press 1990)

Landau and Lifshitz: Fluid Mechanics (1987)

Binney and Tremaine: Galactic Dynamics (Princeton Press 2008)

Course Content:

1. Basic Stuff about Fluids

1.1 Fluid approximation; fluid element

1.2 Derivatives; Eulerian vs Lagrangian

1.3 Mass conservation: continuity equation

1.4 Momentum conservation: Euler equation; pressure; stress tensor

1.5 Energy conservation; equation of state

1.6 Examples of simple solutions: hydrostatic equilibrium; polytropic star; Lane-Emden equation

1.7 Bernoulli's principle

2. Waves and Flows

2.1 Sound waves

2.2 Gravity waves, surface water waves, capillary waves

2.3 Shock waves: jump conditions

2.4 Blast waves; Sedov-Taylor similarity solutions; supernova remnants

2.5 Supersonic flows: de Laval nozzle, Bondi accretion

3. Fluid Instabilities

3.1 Gravitational instability: Jeans length, static vs expanding medium

3.2 Gravitational instability in rotating disks: uniform vs differential rotation, epicycle frequency

3.3 Rayleigh-Taylor instability

3.4 Kelvin-Helmholtz instability

3.5 Thermal instability: conduction, multi-phase medium

4. Sticky stuff

4.1 Viscous stress tensor and force: heuristic and mathematical derivations

4.2 Navier-Stokes equation; Reynolds number

4.3 Applications: Poiseuille flow, Stokes flow

4.4 Accretion disk: molecular vs turbulent viscosity

5. Kinetic Theory

5.1 Phase space; distribution function; Boltzmann equation

5.2 Comparison to fluids: infinite hierarchy, closure relations

5.3 Collisionless vs collisional matter: physics of the cosmic microwave background

5.4 Stochastic processes; diffusion; Fokker-Planck equation

6. MagnetoHydroDynamics

6.1 Motivation; Maxwell's equations

6.2 Ohm's law; induction equation; magnetic Reynolds number

6.3 Ideal MHD; magnetohydrodynamic waves; Alfven speed

6.4 Magnetorotational instabilities

7. Turbulence

7.1 Laminar vs turbulent flows

7.2 Energy cascade; Kolmogorov spectrum

7.3 Applications: smoke, golf ball, atmospheric seeing

8. Applications (student presentations)

Examples: climate, ocean, tsunami, tornadoes, planet atmospheres, solar wind, helioseismology, astrophysical accretion disks, examples of fluid instabilities, physics of baseball, hydrodynamical simulations of galaxy formation, drip paint, flying snakes, and many more.