The Southern African Large Telescope (SALT) is the largest single optical telescope in the southern hemisphere and among the largest in the world. It has a hexagonal primary mirror array 11 metres across, comprising 91 individual 1.2m hexagonal mirrors. SALT has a redesigned optical system resulting in a larger field of view and effective collecting area.
Astrophysical Fluid Dynamics
Astrophysical Fluid Dynamics
Course Outline:
A very large number of astrophysical systems can be modelled as fluids that move under the action of two external forces (gravity and electromagnetism) as well as the forces exerted internally on the fluid by its adjacent parts as they jostle one another in their motion. An added complication is that the fluid material is a thermodynamic system: it is able to absorb, store, and expel energy as it moves. A fluid is therefore a complex system whose motion is governed by the laws of gravity, electrodynamics and thermodynamics.
The fluid flows observed here on earth occur everywhere in the universe, but on a grander scale and under far more extreme conditions. In this course, we study the elements of fluid dynamics and learn how to describe simple flows. For simplicity, we ignore electromagnetic forces. The study of their effects on flow is the subject of magnetohydrodynamics, which will be studied in the Masters course. This course concentrates of flows that are driven by gravity, pressure and thermodynamics. The theory developed in the lectures is illustrated by examples both of terrestrial and astrophysical flows.
Fluid dynamical processes are the driving force behind most fundamental processes in the universe, i.e. spiral density waves in galaxies, triggering bursts of star formation in the spiral arms as it passes through a region, solar and stellar flares, stellar evolution, instabilities in stars giving rise to stellar pulsation, accretion processes in binary systems, as well as the superrelativistic jets ejected by black holes in the heart of galaxies, and many others. Fluid dynamics is thus central to a good understanding of astrophysics and astrophysical processes.
The aim of this course is to provide aspiring astrophysicists with a broad introduction to the fundamental fluid processes that you can expect to feature in a wide range of astrophysical environments.
Syllabus:

Introduction to Fluids

Basic Concepts

Physical Nature of a Fluid

Two Ways to Model a Fluid

Continuum Model

Some Terminology

Fluid Kinematics

The Velocity Field

Description of Fluid Velocity

Visualising flows

Equations for streamlines

Pathlines

Relation Between Streamlines and Pathlines

Streaklines

Fluid Acceleration

Acceleration of a Fluid Point

Physical interpretations

Convective Derivative

Dry and Wet Observers

Advective term in different systems of coordinates

Motion of a Fluid Element

Introduction

Relative motion of fluid points

Linear strain rate

Volume strain rate

Shearing Rate

Pure Shear

Rotation Rate

General Motion of a Fluid Element

Specialised Flows

One, two and three dimensional flows

Steady and unsteady flows

Viscous and inviscid flows

Laminar and turbulent flows

Compressible and incompressible flows

Rectilinear and circular flows

Rotation of the Milky Way

Differential Rotation

Measuring of the Velocity of a Nearby Star

The Model

Velocity of Nearby Stars Relative to the Sun

Radial and Transverse Velocity

Discussion

Forces on Fluids

Forces on continuous media

Forces

Volume and surface forces

Description of volume forces

Gravitational force density

Stress

Governing Equations

Principles that Govern Fluid Flows

Equations of Motion

Forces on Fluids

Definition of Stress

Internal Stress

The Stress Tensor

Isotropic Stress

Homogeneous stress

Contact Force on a Fluid Element

Symmetry of the stress tensor

Equations of Motion

Cauchy’s equations in a general system of coordinates

Conservation Principles

Introduction

Continua

Densities

Time evolution of densities

Current densities

The Continuity Equation

Differential form of the continuity equation

Conservation Equations

Conservation of Mass

The principle of conservation of mass

Alternative derivation

Summary

Conservation of Momentum

Fluid momentum

Momentum density in a fluid

Continuity equation for fluid momentum

Physical interpretation

Alternative forms of the momentum continuity equation

Conservation of energy

Energy Transport in Fluids

Work done by Applied Forces

Kinetic Energy Equation

Internal Energy Equation

Example: Conducting Ideal Gas

Hydrostatics

Fluids at Rest

The Hydrostatic Equation

Fluid at Rest in an Uniform Gravitational Field

Archimedes’ Principle

PlaneParallel Atmospheres

Plane Parallel Atmosphere in Uniform Gravitational Field

Isothermal Atmosphere

Adiabatic atmosphere

Polytropic atmosphere

Stellar Structure

Barotropic systems

Polytropic systems

Solar Corona

Brief Description of the Solar Corona

The Model

Discussion of results

Inviscid Fluids

Euler’s Equations

Frictionless Fluids

Equation of motion for inviscid fluids

Incompressibility

Vorticity

Bernoulli’s Equation

Introduction

General principle

Steady flow of a fluid with uniform density

Steady flow of an incompressible fluid

Irrotational flow with constant density

Examples

Supersonic Jet Flows

Bernoulli’s equation for compressible flows

Nozzle flow

de Laval’s Nozzle

Supersonic jets in astrophysics

Viscous Fluids

Newton’s Law of Viscosity

Fluid Friction

Newton’s Law of Viscosity

Mathematical formulation of Newton’s law

Important property of Newton’s flow

Newtonian Fluids

Newtonian and nonNewtonian fluids

StressRate of Strain Relations in General

Newtonian Fluids

Physical Significance of α and β

Coefficient of bulk viscosity

Newtonian Flows

Equation of Motion for Newtonian Fluids

Kinetic Energy Equation

NavierStokes Equation

Stokes' Assumption

NavierStokes' Equation

Simple Solutions of the NavierStokes Equations

Channel flow

Channel flow without gravity

Channel flow with gravity


Flow through a finite rectangular slit

Pipe flow

Accretion Discs

Perturbation Theory

Perturbation Equations

The Equilibrium State

Equations for the Perturbed Flow

Adiabatic Perturbations

Isothermal Perturbations

Star and Galaxy Formation

Stability of Gas Clouds

Stability of Rotating Gas Clouds
 Appendix
 Rotating Frames of Reference