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**(Course description last updated for academic year 2016-17)**.

##### Synopsis

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 white dwarfs and neutron stars (supported by electron and neutron degeneracy pressure respectively) as well as the orbiting discs of gas and dust which feed black holes.

On completion of the module students should:

- understand and learn to manipulate fluid dynamical equations in both Eulerian and Lagrangian form;
- be able to set up and solve simple hydrostatic equilibrium situations in spherical and disc geometries;
- be able to perform simple linear stability analyses and apply to wave propagation in hydrodynamical and magnetohydrodynamical systems;
- apply Bernoulli's theorem to astrophysical applications;
- understand the concept of shocks and their application to astrophysical blast waves;
- understand the role of viscosity in accretion discs.

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]

Basic concepts of gravity. Poisson's equation. Gravitational potential. The Virial Theorem. [2]

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. [3]

Sound waves. Sound speed: adiabatic and isothermal case. Sound waves in a stratified atmosphere. [2]

Supersonic flows. Rankine-Hugoniot conditions for adiabatic and isothermal shocks. Application to blast waves and supernova remnants. [4]

Bernoulli's equation and its applicability. De Laval nozzle and its relevance to astrophysical jets. Bondi accretion, stellar winds and mass loss. [3]

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

Viscous flows. Linear shear flow. Navier-Stokes equation. Vorticity and energy dissipation in viscous flows. Accretion discs. Steady thin discs. [4]

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

**RECOMMENDED BOOKS**

*Principles of Astrophysical Fluid Dynamics, *Clarke, C.J. & Carswell, R.F. (Cambridge University Press 2014)* Fluid Mechanics, *Landau & Lifshitz (Pergamon Press 1987)

**FURTHER SUGGESTIONS**

*Elementary Fluid Dynamics*, Acheson, D (Oxford University Press 1994)

*An Introduction to Fluid Dynamics*, Batchelor, G K (CUP 1991)

*Hydrodynamics*, Lamb, H (CUP 6th edn 1932, reprinted 1993)

*An informal introduction to theoretical Fluid Mechanics* Lighthill, M J (Oxford University Press 1993)