Principles of astrophysical fluid dynamics / Cathie Clarke and Bob Carswell.

Format:

Book

Author/Creator:

Clarke, Catherine Jane.

Contributor:

Carswell, Bob, 1940-

Language:

English

Subjects (All):

Astrophysics.

Fluid dynamics.

Physical Description:

ix, 226 pages : illustrations ; 25 cm

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Summary:

Fluid dynamical forces drive most of the fundamental processes in the Universe and so play a crucial role in our understanding of astrophysics. This comprehensive textbook introduces the fluid dynamics necessary to understand a wide range of astronomical phenomena, from stellar structures to supernovae blast waves, to accretion discs.

The authors' approach is to introduce and derive the fundamental equations, supplemented by text that conveys a more intuitive understanding of the subject, and to emphasise the observable phenomena that rely on fluid dynamical processes. It has been developed for use by final year undergraduate and starting graduate students of astrophysics, based on the authors' many years of teaching their astrophysical fluid dynamics course at the University of Cambridge. It contains over 50 exercises.

Contents:

1.1 Fluids in the Universe 2

1.2 The concept of a 'fluid element' 4

1.3 Formulation of the fluid equations 5

1.4 Relation between the Eulerian and Lagrangian descriptions 7

1.5 Kinematical concepts 8

2 The fluid equations 12

2.1 Conservation of mass 12

2.2 Pressure 14

2.3 Momentum equations 15

2.4 Momentum equation in conservative form: the stress tensor and concept of ram pressure 17

3 Gravitation 20

3.1 The gravitational potential 20

3.2 Poisson's equation 22

3.3 Using Poisson's equation 24

3.4 The potential associated with a spherical mass distribution 27

3.5 Gravitational potential energy 28

3.6 The virial theorem 30

4 The energy equation 32

4.1 Ideal gases 32

4.2 Barotropic equations of state: the isothermal and adiabatic cases 33

4.3 Energy equation 37

4.4 Energy transport 39

4.5 The form of Q[subscript cool] 45

5 Hydrostatic equilibrium 46

5.1 Basic equations 46

5.2 The isothermal slab 47

5.3 An isothermal atmosphere with constant g 49

5.4 Stars as self-gravitating polytropes 50

5.5 Solutions for the Lane-Emden equation 52

5.6 The case of n = [infinity] 55

5.7 Scaling relations 56

5.8 Examples of astrophysical interest 60

5.9 Summary: general method for scaling relations 62

6 Propagation of sound waves 63

6.1 Sound waves in a uniform medium 63

6.2 Propagation of sound waves in a stratified atmosphere 68

6.3 General approach to wave propagation problems 73

6.4 Transmission of sound waves at interfaces 74

7 Supersonic flows 77

7.1 Shocks 78

7.2 Isothermal shocks 85

8 Blast waves 89

8.1 Strong explosions in uniform atmospheres 89

8.2 Blast waves in astrophysics and elsewhere 96

8.3 Structure of the blast wave 99

8.4 Breakdown of the similarity solution 102

8.5 The effects of cooling and blow out from galactic discs 104

9 Bernoulli's equation 107

9.1 Basic equation 107

9.2 De Laval nozzle 113

9.3 Spherical accretion and winds 118

9.4 Stellar winds 123

9.5 General steady state solutions 126

10 Fluid instabilities 128

10.1 Rayleigh-Taylor instability 128

10.2 Gravitational instability (Jeans instability) 139

10.3 Thermal instability 142

10.4 Method summary 149

11 Viscous flows 150

11.1 Linear shear and viscosity 150

11.2 Navier-Stokes equation 153

11.3 Evolution of vorticity in viscous flows 157

11.4 Energy dissipation in incompressible viscous flows 158

11.5 Viscous flow through a circular pipe and the transition to turbulence 159

12 Accretion discs in astrophysics 163

12.1 Derivation of viscous evolution equations for accretion discs 165

12.2 Viscous evolution equation with constant viscosity 167

12.3 Steady thin discs 173

12.4 Radiation from steady thin discs 176

13 Plasmas 179

13.1 Magnetohydrodynamic equations 180

13.2 Charge neutrality 184

13.3 Ideal hydromagnetic equations 186

13.4 Waves in plasmas 190

13.5 The Rayleigh-Taylor instability revisited 195

Appendix Equations in curvilinear coordinates 200

Books for background and further reading 222.

Notes:

Includes bibliographical references and index.

ISBN:

9780521853316

0521853311

OCLC:

75713471