# Part II Astrophysical Fluid Dynamics

## Astrophysical Fluid Dynamics

### Lent Term, 24 Lectures – Professor C. Reynolds

Fluids are ubiquitous in the Universe on all scales. As well as obvious fluids, (e.g. the gas that is in stars or clouds in the interstellar medium) a variety of other systems are amenable to a fluid dynamical description - including the dust that makes up the rings of Saturn and even the orbits of stars in the galactic potential. Although some of the techniques of conventional (terrestrial) fluid dynamics are relevant to astrophysical fluids, there are some important differences: astronomical objects are often self-gravitating or else may be accelerated by powerful gravitational fields to highly supersonic velocities. In the latter case, the flows are highly compressible and strong shock fronts are often observed (for example, the spiral shocks that are so prominent in the gas of galaxies like the Milky Way).

In this course, we consider a wide range of topical issues in astronomy, such as the propagation of supernova shock waves through the interstellar medium, the internal structure of stars and the variety of instabilities that affect interstellar/intergalactic gas. These include, perhaps most importantly, the Jeans instability whose action is responsible for the formation of every star and galaxy in the Universe. We also deal with exotic astronomical environments, such as the orbiting discs of gas which feed black holes.

1. Introduction: The concept of a fluid. Collisional and collisionless fluids. Kinematics. Conservation of mass. Pressure. (Inviscid) momentum equation for a fluid under gravity. Stress tensor and the concept of ram pressure. [2]

1. Basic Concepts of Gravity: Poisson's equation. Gravitational potential. The Virial Theorem. [1]

1. Equation of State: Barotropic relation between pressure and density. Energy equation. Hydrostatic equilibrium. Examples: hydrostatic atmosphere under uniform gravity; self-gravitating isothermal slab; self-gravitating polytropes as simple models of stars, mass-radius relation. [4]

1. Sound Waves: Sound speed: adiabatic and isothermal case. Sound waves in a stratified atmosphere. [1]

1. Supersonic Flows: Rankine-Hugoniot conditions for adiabatic and isothermal shocks. Application to blast waves and supernova remnants. [3]

1. Bernoulli's Equation and its Applicability: De Laval nozzle and its relevance to astrophysical jets. Bondi accretion, stellar winds and mass loss. [2]

1. Fluid Instabilities: Convective instability, Schwarzschild criterion. Jeans instability. Rayleigh-Taylor and Kelvin-Helmholtz instability. Thermal instability, Field criterion. [3]

1. Viscous Flows: Linear shear flow. Navier-Stokes equation. Vorticity and energy dissipation in viscous flows. Accretion discs. Steady thin discs. [3]

1. Magnetohydrodynamics: The ideal MHD equations. Alfven waves. [3]

1. Computational Astrophysical Fluid Dynamics [2]