Introduction
Contents
Introduction¶
Astrophysical Fluid Dynamics¶
These course notes were put together by Jacob Pilawa for graduate Astronomy 207: Astrophysical Fluid Dynamics in the Spring of 2022. The course was taught my Chung-Pei Ma at UC Berkeley.
Overview:
Many things in the world can be described as a fluid! This makes this class awesome and far-reaching, from tsunamis and storms, to Jackson Pollock’s drip-painting, to the physics of baseball, to deep accretion disks around black holes. Things are different from what we have seen in the past in that we are dealing with a continuum of fluid elements we must examine, as opposed to point partciles of classical mechanics. Here, we will deal with lots of vector calculus, and non-linear, partial differential equations, some of the most difficult problems in mathematics.
We begin with basic things about fluids, and how we shift our thinking from classical mechanics to fluid dynamics. We then move to stable solutions of the fundamental equations of fluid dynamics by looking at waves and flows in Part 2 of the class. After that, we look at unstable solutions to our equations in Part 3 by looking at instabilities in fluids. Up to now, we have only considered gravity and pressure. As we move on, we see sticky stuff in Part 4 of the class by adding viscosity to our equations, resulting in the Navier-Stokes equation. Part 5 of the class brings kinetic theory (when fluid approximations break down), the Boltzmann equation, and physics of the CMB. In Part 6, we add in magnetic fields and get introduced to magneto-hydro-dynamics by adding Maxwell’s equations to our fluid equations. And, lastly in Part 7, we will look at turbulence (when viscosity is negligible), and further applications of fluid dynamics.
The main references in the class are:
Thorne and Blandford: Modern Classical Physics (Princeton University Press 2017). A pre-published version (January 2013) is available here.
Balbus Texts: Hydrodynamics and Magnetohydrodynamics.
Some supplementary references are:
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)