# ASTROPHYSICAL HYDRODYNAMICS

Lecture Course
Astrophysical Hydrodynamics

February 2015 - April 2015
University Groningen

Docent:
Rien van de Weygaert,
ZG 186,   tel. 3634086,   weygaert@astro.rug.nl

Werkcollege Docent:
Stefano Antonellini
ZG 189,   tel. 3638689,   S.Antonellini@astro.rug.nl

Lecture Notes:

Lecture Topic 0:                Introduction & Practical Information

Lecture Topic 1:                Basic Fluid Equations

Key chapter !!!!!!
Know by heart: definition fluid, basic Boltzmann equation, continuity equation, Euler equation,
Bernoulli function & equation, Kelvin circulation theorem
Know: how to derive fluid equations from Boltzmann equation, derivation Continuity Equation (microscopic, via BE, and macroscopic),
derivation Euler equation (microscopic, via BE, and macroscopic), follow derivation Energy equation and explain related quantities,

know by heart: definition (in)compressible fluid, steady flow
know by heart: Stokes flow theorem; definitions divergence/compression, shear, vorticity
know: derivation Stokes flow theorem (gradient velocity vector field), physical meaning divergence, shear, vorticity
explain concept streamlines/pathlines/streaklines

Lecture Topic 2 & 3:          Bernoulli Applications; Hydrostatics

Key chapter !!!!!!
Know: Venturi meter (ie. derive related expressions), explain airflight, de Laval Nozzle (in detail)
Know: Hydrostatics: Archimedes principle, derivation isothermal sphere,
Know: Hydrostatics, Xray emission galaxy clusters and equation for cluster mass

Lecture Topic 4 & 5:          Soundwaves & Shockwaves

Key chapter !!!!!!
Know by heart: wave equation, harmonic solution wave equation, dispersion relation simple linear sound wave, definition phase and group velocity.
Know: gravity waves (ie. linear surface waves)
Know: derivation sound wave equation by simple combination continuity & Euler for small perturbations
Know: derivation detailed sound wave equation for displacement, velocity perturbation, pressure and density perturbation (Lagrangian and Eulerian),
Know: phase difference velocity and pressure perturbations, etc.
(ie. understanding the connection between pressure wave and displacement fluid elements).
Know: derivation Jeans instability, dispersion relation and Jeans scale/length/mass

Know by heart: Rankine-Hugoniot jump conditions.
Know: Riemann invariants.
Know: derivation (1-D) Rankine-Hugoniot conditions, Rankine-Hugoniot shock adiabat, (Hugoniot and Rayleigh lines in) adiabatic diagram,
Know: strong shocks (density jump), weak shock, derivation relation pre-shock velocity & post-shock pressure,
Know: explain and describe supernova remnant evolution; derivation Sedov-Taylor solution

Lecture Topic 4:                Soundwaves
A. Achterberg, Astrophysical Gas Dynamics, chapter 6

Lecture Topic 5:                Shockwaves
A. Achterberg, Astrophysical Gas Dynamics, chapter 7

Lecture Topic 6:                Diffusion & Viscosity
A. Achterberg, Astrophysical Gas Dynamics, chapter 9

Key chapter !!!!!!
Know by heart: diffusion equation, definition diffusion parameter, definition viscosity, Navier-Stokes equation, definition Reynolds number.

Know/follow: derivation diffusion equation, radiation diffusion/definition opacity, reasoning towards Navier-Stokes equation
Know: derivation Poiseuille equation, 3-D flow through canal

Lecture Topic 7:                Turbulence

Key chapter !!!!!!
Understand general properties of turbulence: know at least 7 key properties.
Description onset of turbulence; relation Reynolds number and turbulence
Know by heart: Kolmogorov spectrum