Part II Astrophysical Fluid Dynamics

Lent Term, 24 Lectures – Dr M Wyatt

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.

Introduction. The concept of a fluid, density and velocity. Kinematics: steady and unsteady flows, streamlines and particle paths; conservation of mass. Derivative following the fluid motion. [2]

Dynamics. Pressure. (Inviscid) momentum equation for a fluid under gravity, application to force of jet on a wall, momentum equation in conservative form, role of ρuiuk Poisson's equation for the gravitational potential and its derivation. The Virial Theorem. [3]

Simple steady states. Simple (barotropic) relation between pressure and density, physical examples. Hydrostatic atmosphere under uniform gravity; self-gravitating isothermal slab and its relevance to galactic discs; self-gravitating polytropes as simple models of stars, mass-radius relation. [3]

Energy. (entropy) equation with simple cooling law. [1]

Sound waves. Sound speed (adiabatic and isothermal). Description of why shocks occur. Rankine-Hugoniot conditions. 1-D shock tube, 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. Rayleigh-Taylor instability, Schwarzschild criterion; Thermal instability, Field criterion; statement of Kelvin-Helmholtz instability, Jeans instability. [3]

Viscous flows. Linear and circular shear flows. Accretion discs. [2]

Magnetohydrodynamics. The ideal MHD equations ( E + v×B = 0 ). Alfven waves. [3]

Books

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

Batchelor, G.K. An Introduction to Fluid Dynamics, Cambridge University Press (1991)

Clarke, C.J. & Carswell, R.F. Principles of Astrophysical Fluid Dynamics, Cambridge University Press (2007)

Lamb, H. Hydrodynamics, Cambridge University Press (6th ed 1932, reprinted 1993)

Landau & Lifshitz, Fluid Mechanics, Pergamon Press (1987)

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