Extra readings:

Excellent introdoctory article on turbulence: The Turbulence Problem by Robert Ecke (2005).
Here is the remarkable New Yorker piece about the Poincare Conjecture saga: Manifold Destiny by Nasar & Gruber (2006)
Here is a good summary about the status of the Fermi bubbles: Fermi bubbles are bursting from our galaxy. Their origins remain a mystery by Mann, PNAS (2023)

Problem Set 9 (due 6pm Wednesday December 10) Note: Please handwrite your solutions and do not use LaTeX or any other text editor.
Reading: Balbus Chapters 2, 4; Balbus & Hawley MRI review paper.

Problem Set 8 (due 6pm Friday November 21)

Problem Set 7 (due 6pm Friday November 7)
Reading: Thorne & Blandford Ch 13.7.

Problem Set 6 (due 6pm Friday October 24)

Problem Set 5 (due 6pm Friday October 17): An outline (1-2 pages) of your presentation. Sketch the scope of the talk.
Provide references (i.e. review/journal papers; web links) that you are using to learn the topic. Follow "Presentation Guidelines" below.
The more detail you provide, the more feedback we can give you.
Please upload to Gradescope as usual.

Problem Set 4 (due 6pm Friday October 10) Note: Please handwrite your solutions and do not use LaTeX or any other text editor.
Reading: Thorne & Blandford Ch 17.1, 17.2, 17.5, 17.6

Problem Set 3 (due 6pm Friday October 3)
Reading: Thorne & Blandford Ch 16.1, 16.2, 16.5

Problem Set 2 (due 6pm Friday September 26)

Problem Set 1 (due 6pm Friday September 19)
Reading: Thorne & Blandford Ch 13.1-13.6

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

November 3 Monday

Erica Badaracco: RT instability in inertial confinement fusion. Talk slides.

Riley Owens: Air motion in subway tunnel

November 5 Wednesday

Tamojeet Roychowdhury: Cloud collapse & protostar formation. Talk slides.

Eliza Diggins: AGN feedback in cosmological simulations and the formation of the Fermi Bubbles. Talk slides.

November 10 Monday

Ella Chevalier : Fluid dynamics of Jupiter's Great Red Spot. Talk slides.

Lillian Sweet: Nth order numerical methods for compressible flow applied to shocks over airfoils/rockets. Talk slides.

November 12 Wednesday

Anastasia Wei: Energy transport in blast waves and supernova remnants. Talk slides.

Kendrick Nguyen: Cold dark matter and its alternatives. Talk slides.

November 17 Monday

Ben Jacobson-Bell: Interstellar scattering of radio pulses and its effects on pulsar timing. Talk slides.

Noah Stiegler: Atmospheric turbulence and seeing. Talk slides.

November 24 Monday

Brianna Peck: Avalanche dynamics of pour over coffee

Linus Upson: Accretion disks or astrophysical jets

December 1 Monday

Danny Sun: Shocks from magnetic reconnection

Robert Loewe: MHD instabilities in the auroral acceleration region

Presentation Guidelines

Email me your preferred topic by noon Monday October 6. 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.

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: 4-5pm Tuesdsays by zoom

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

Grading: 60% problem sets; 25% in-class presentation; 15% attendance & participation. Class attendance and participation are a key component of the course. You will not receive the 15% participation grade if you miss more than two lectures.

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.