PRINCIPLES OF ASTROPHYSICAL FLUID DYNAMICS
CONTENTS INTRODUCTION TO CONCEPTS 1 1 FLUIDS IN THE UNIVERSE 1 2 THE CONCEPT OF A ‘?UID ELEMENT’ 1 3 FORMULATION OF THE ?UID EQUATIONS 1 4 RELATION BETWEEN THE EULERIAN AND LAGRANGIAN DESCRIPTIONS 1 5 KINEMATICAL CONCEPTS THE ?UID EQUATIONS 2 1 CONSERVATION OF MASS 2 2 PRESSURE 2 3 MOMENTUM EQUATIONS 2 4 MOMENTUM EQUATION IN CONSERVATIVE FORM: THE STRESS TENSOR AND CONCEPT OF RAM PRESSURE GRAVITATION 3 1 THE GRAVITATIONAL POTENTIAL 3 2 POISSON’S EQUATION 3 3 USING POISSON’S EQUATION 3 4 THE POTENTIAL ASSOCIATED WITH A SPHERICAL MASS DISTRIBUTION 3 5 GRAVITATIONAL POTENTIAL ENERGY 3 6 THE VIRIAL THEOREM THE ENERGY EQUATION 4 1 IDEAL GASES 4 2 BAROTROPIC EQUATIONS OF STATE: THE ISOTHERMAL AND ADI- ABATIC CASES 4 3 ENERGY EQUATION 4 4 ENERGY TRANSPORT 4 5 THE FORM OF ?QCOOL HYDROSTATIC EQUILIBRIUM 5 1 BASIC EQUATIONS 5 2 THE ISOTHERMAL SLAB 5 3 AN ISOTHERMAL ATMOSPHERE WITH CONSTANT G 5 4 STARS AS SELF-GRAVITATING POLYTROPES 5 5 SOLUTIONS FOR THE LANE–EMDEN EQUATION 5 6 THE CASE OF N = 5 7 SCALING RELATIONS 5 8 EXAMPLES OF ASTROPHYSICAL INTEREST 5 9 SUMMARY: GENERAL METHOD FOR SCALING RELATIONS PROPAGATION OF SOUND WAVES 6 1 SOUND WAVES IN A UNIFORM MEDIUM 6 2 PROPAGATION OF SOUND WAVES IN A STRATI?ED ATMOSPHERE 6 3 GENERAL APPROACH TO WAVE PROPAGATION PROBLEMS 6 4 TRANSMISSION OF SOUND WAVES AT INTERFACES SUPERSONIC ?OWS 7 1 SHOCKS 7 2 ISOTHERMAL SHOCKS BLAST WAVES 8 1 STRONG EXPLOSIONS IN UNIFORM ATMOSPHERES 8 2 BLAST WAVES IN ASTROPHYSICS AND ELSEWHERE 8 3 STRUCTURE OF THE BLAST WAVE 8 4 BREAKDOWN OF THE SIMILARITY SOLUTION 8 5 THE EFFECTS OF COOLING AND BLOW OUT FROM GALACTIC DISCS BERNOULLI’S EQUATION 9 1 BASIC EQUATION 9 2 DE LAVAL NOZZLE 9 3 SPHERICAL ACCRETION AND WINDS 9 4 STELLAR WINDS 9 5 GENERAL STEADY STATE SOLUTIONS FLUID INSTABILITIES 10 1 RAYLEIGH–TAYLOR INSTABILITY 10 2 GRAVITATIONAL INSTABILITY ( JEANS INSTABILITY) 10 3 THERMAL INSTABILITY 10 4 METHOD SUMMARY VISCOUS ?OWS 11 1 LINEAR SHEAR AND VISCOSITY 11 2 NAVIER–STOKES EQUATION 11 3 EVOLUTION OF VORTICITY IN VISCOUS ?OWS 11 4 ENERGY DISSIPATION IN INCOMPRESSIBLE VISCOUS ?OWS 11 5 VISCOUS ?OW THROUGH A CIRCULAR PIPE AND THE TRANSITION TO TURBULENCE ACCRETION DISCS IN ASTROPHYSICS 12 1 DERIVATION OF VISCOUS EVOLUTION EQUATIONS FOR ACCRETION DISCS 12 2 VISCOUS EVOLUTION EQUATION WITH CONSTANT VISCOSITY 12 3 STEADY THIN DISCS 12 4 RADIATION FROM STEADY THIN DISCS PLASMAS 13 1 MAGNETOHYDRODYNAMIC EQUATIONS 13 2 CHARGE NEUTRALITY 13 3 IDEAL HYDROMAGNETIC EQUATIONS 13 4 WAVES IN PLASMAS 13 5 THE RAYLEIGH–TAYLOR INSTABILITY REVISITED