An introduction to astrophysical fluid dynamics:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London
Imperial College Press
2006
|
| Schlagworte: | |
| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references (p. 217-221) and index |
| Beschreibung: | XI, 227 S. graph. Darst. |
| ISBN: | 186094633X 1860946151 |
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| 245 | 1 | 0 | |a An introduction to astrophysical fluid dynamics |c Michael J. Thompson |
| 264 | 1 | |a London |b Imperial College Press |c 2006 | |
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| adam_text | AN INTRODUCTION TO ASTROPHYSICAL FLUID DYNAMICS MICHAEL J THOMPSON
UNIVERSITY OF SHEFFIELD, UK IMPERIAL COLLEGE PRESS CONTENTS PREFACE V 1.
BASIC FLUID EQUATIONS 1 1.1 THE MATERIAL DERIVATIVE 2 1.2 THE CONTINUITY
EQUATION 3 1.3 THE MOMENTUM EQUATION 3 1.4 NEWTONIAN GRAVITY 6 1.5 THE
MECHANICAL AND THERMAL ENERGY EQUATIONS 7 1.6 A LITTLE MORE
THERMODYNAMICS 9 1.7 PERFECT GASES 11 1.8 THE VIRIAL THEOREM 12 1.9
VORTICITY 14 2. SIMPLE MODELS OF ASTROPHYSICAL FLUIDS AND THEIR MOTIONS
19 2.1 HYDROSTATIC EQUILIBRIUM FOR A SELF-GRAVITATING BODY ... 20 2.1.1
SPHERICALLY SYMMETRIC CASE 20 2.1.2 PLANE-PARALLEL LAYER UNDER CONSTANT
GRAVITY . . . . 22 2.2 EQUATIONS OF STELLAR STRUCTURE 23 2.3 SMALL
PERTURBATIONS ABOUT EQUILIBRIUM 25 2.3.1 ISOTHERMAL FLUCTUATIONS 26
2.3.2 ADIABATIC FLUCTUATIONS 27 2.4 LAGRANGIAN PERTURBATIONS 28 2.5
SOUND WAVES 28 2.6 SURFACE GRAVITY WAVES 30 2.7 PHASE SPEED AND GROUP
VELOCITY 32 VIII ASTROPHYSICAL FLUID DYNAMICS 2.8 ORDER-OF-MAGNITUDE
ESTIMATES FOR ASTROPHYSICAL FLUIDS 33 2.8.1 TYPICAL SCALES 33 2.8.2
IMPORTANCE OF VISCOSITY 33 2.8.3 THE ADIABATIC APPROXIMATION 35 2.8.4
THE APPROXIMATION OF INCOMPRESSIBILITY 35 3. THEORY OF ROTATING BODIES
37 3.1 EQUATION OF MOTION IN A ROTATING FRAME 38 3.2 EQUILIBRIUM
EQUATIONS FOR A SLOWLY ROTATING BODY ... 38 3.3 THE ROCHE MODEL 40 3.4
CHANDRASEKHAR-MILNE EXPANSION 41 3.5 DYNAMICS OF ROTATING STELLAR MODELS
45 3.6 SOLAR ROTATION 46 3.7 BINARY STARS 50 4. FLUID DYNAMICAL
INSTABILITIES 55 4.1 CONVECTIVE INSTABILITY 55 4.1.1 THE SCHWARZSCHILD
CRITERION 55 4.1.2 EFFECTS OF DISSIPATION 60 4.1.3 MODELLING CONVECTION:
THE BOUSSINESQ APPROXIMATION 61 4.2 THE RAYLEIGH-TAYLOR INSTABILITY 62
4.3 ROTATIONAL INSTABILITY 63 4.4 SHEAR AND THE KELVIN-HELMHOLTZ
INSTABILITY 64 4.4.1 THE KELVIN-HELMHOLTZ INSTABILITY 64 4.4.2 CRITICAL
RICHARDSON AND REYNOLDS NUMBERS ... 67 4.4.3 TURBULENCE AND THE
KOLMOGOROV SPECTRUM .... 68 5. MAGNETOHYDRODYNAMICS 71 5.1 MAXWELL S
EQUATIONS AND THE MHD APPROXIMATION ... 71 5.2 MHD WAVES 74 5.3 SOME MHD
APPLICATIONS 76 5.3.1 SOLAR PROMINENCES 76 5.3.2 DYNAMO THEORY 78 5.3.3
CORONAL HEATING 81 5.4 MHD INSTABILITIES 82 6. NUMERICAL COMPUTATIONS 85
CONTENTS IX 6.1 THE FORMULATION OF FINITE DIFFERENCES 86 6.2 THE VON
NEUMANN STABILITY ANALYSIS 87 6.3 VARIOUS FINITE-DIFFERENCE SCHEMES 89
6.3.1 THE LAX METHOD 89 6.3.2 UPWIND DIFFERENCING 89 6.3.3 THE STAGGERED
LEAPFROG METHOD 90 6.3.4 THE LAX-WENDROFF METHOD 90 6.3.5 IMPLICIT
SCHEMES: THE CRANK-NICHOLSON METHOD . 91 6.4 CONSIDERATIONS FOR MORE
COMPLEX SYSTEMS 92 6.5 OPERATOR SPLITTING 93 6.6 EXAMPLES OF
IMPLEMENTATIONS 95 6.6.1 1-D LAGRANGIAN SCHEME WITH ARTIFICIAL VISCOSITY
. 95 6.6.2 2-D SCHEME USING OPERATOR SPLITTING 98 6.6.3 CODES FOR
COMPUTING ASTROPHYSICAL FLOWS 100 6.7 SMOOTHED PARTICLE HYDRODYNAMICS
101 7. PLANETARY ATMOSPHERE DYNAMICS 107 4 7.1 THE IMPORTANCE OF
ROTATION: THE ROSSBY NUMBER . . . . 107 7.2 RELATIVE AND ABSOLUTE
VORTICITY 108 7.3 POTENTIAL VORTICITY 110 7.4 BAROCLINICITY AND THE
THERMAL WIND EQUATION 110 7.5 GEOSTROPHIC MOTION 112 7.6 SOME
APPROXIMATE MODELS 116 7.6.1 THE SHALLOW-WATER MODEL 117 7.6.2 /-PLANE
AND /3-PLANE MODELS 119 7.7 WAVES , ... 120 7.8 EKMAN LAYERS 122 8.
ACCRETION, WINDS AND SHOCKS 127 8.1 BERNOULLI S THEOREM 128 8.2 THE DE
LAVAL NOZZLE 129 8.3 THE BONDI PROBLEM 130 8.4 THE PARKER SOLAR-WIND
SOLUTION 134 8.5 NONLINEAR ACOUSTIC WAVES 134 8.6 SHOCK WAVES 139 8.7
BLAST WAVE FROM A SUPERNOVA 140 9. VISCOUS ACCRETION DISKS 143 X
ASTROPHYSICAL FLUID DYNAMICS 9.1 ROLE OF ANGULAR MOMENTUM AND ENERGETICS
OF ACCRETION 143 9.2 THIN ACCRETION DISKS 145 9.3 DIFFUSION EQUATION FOR
SURFACE DENSITY 147 9.4 STEADY DISKS 150 9.5 THE NEED FOR ANOMALOUS
VISCOSITY 153 10. JEANS INSTABILITY AND STAR FORMATION 155 10.1 LINKS TO
OBSERVATIONS 156 10.2 JEANS INSTABILITY 156 10.3 JEANS INSTABILITY WITH
ROTATION 158 10.3.1 JEANS INSTABILITY FOR A ROTATING SYSTEM 159 10.4
AMBIPOLAR DIFFUSION 161 10.5 FRAGMENTATION 162 10.6 SOME COMMENTS ON
STAR FORMATION 163 11. RADIAL OSCILLATIONS OF STARS 165 11.1 LINEAR
ADIABATIC WAVE EQUATION FOR RADIAL OSCILLATIONS 165 11.1.1 BOUNDARY
CONDITIONS 168 11.1.2 EIGENVALUE NATURE OF THE PROBLEM 169 11.1.3
SELF-ADJOINTNESS OF THE PROBLEM 170 11.1.4 A LOWER BOUND ON THE
FUNDAMENTAL FREQUENCY . . 172 11.1.5 HOMOLOGY SCALING FOR THE
FUNDAMENTAL FREQUENCY OF STARS 172 11.2 NON-ADIABATIC RADIAL
OSCILLATIONS 173 11.2.1 PHYSICAL DISCUSSION OF DRIVING AND DAMPING . .
. 176 11.3 THE QUASI-ADIABATIC APPROXIMATION 178 12. NONRADIAL
OSCILLATIONS AND HELIOSEISMOLOGY 181 12.1 NONRADIAL MODES OF OSCILLATION
OF A STAR 181 12.2 MODE CLASSIFICATION 185 12.3 THE COWLING
APPROXIMATION 186 12.4 A SIMPLIFIED DISCUSSION OF NONRADIAL OSCILLATIONS
.... 187 12.5 A MORE GENERAL ASYMPTOTIC EXPRESSION 190 12.6
HELIOSEISMOLOGY: THE DUVALL LAW 193 12.7 TASSOUL S FORMULA 196 12.8
ASYMPTOTICS OF G MODES 198 CONTENTS XI 12.9 PROBING THE SUN S INTERNAL
ROTATION 199 APPENDIX A USEFUL CONSTANTS AND QUANTITIES 205 A.I
FUNDAMENTAL PHYSICAL CONSTANTS 205 A.2 ASTRONOMICAL QUANTITIES 205 A.3
CARTESIAN TENSORS: INDEX NOTATION AND SUMMATION CONVENTION 206 APPENDIX
B VECTOR CALCULUS IN SPHERICAL AND CYLINDRICAL POLAR COORDINATES 207 B.I
CYLINDRICAL POLAR COORDINATES (M, 207 B.2 SPHERICAL POLAR COORDINATES
{R,6,) 208 APPENDIX C SELF-ADJOINT EIGENVALUE PROBLEMS 209 C.I REALITY
OF EIGENVALUES 209 C.2 ORTHOGONALITY OF EIGENFUNCTIONS 210 C.3
EIGENFUNCTION EXPANSIONS 210 C.4 VARIATIONAL PRINCIPLE 211 APPENDIX D
THE JWKB METHOD 213 BIBLIOGRAPHY 217 INDEX 223
|
| adam_txt |
AN INTRODUCTION TO ASTROPHYSICAL FLUID DYNAMICS MICHAEL J THOMPSON
UNIVERSITY OF SHEFFIELD, UK IMPERIAL COLLEGE PRESS CONTENTS PREFACE V 1.
BASIC FLUID EQUATIONS 1 1.1 THE MATERIAL DERIVATIVE 2 1.2 THE CONTINUITY
EQUATION 3 1.3 THE MOMENTUM EQUATION 3 1.4 NEWTONIAN GRAVITY 6 1.5 THE
MECHANICAL AND THERMAL ENERGY EQUATIONS 7 1.6 A LITTLE MORE
THERMODYNAMICS 9 1.7 PERFECT GASES 11 1.8 THE VIRIAL THEOREM 12 1.9
VORTICITY 14 2. SIMPLE MODELS OF ASTROPHYSICAL FLUIDS AND THEIR MOTIONS
19 2.1 HYDROSTATIC EQUILIBRIUM FOR A SELF-GRAVITATING BODY . 20 2.1.1
SPHERICALLY SYMMETRIC CASE 20 2.1.2 PLANE-PARALLEL LAYER UNDER CONSTANT
GRAVITY . . . . 22 2.2 EQUATIONS OF STELLAR STRUCTURE 23 2.3 SMALL
PERTURBATIONS ABOUT EQUILIBRIUM 25 2.3.1 ISOTHERMAL FLUCTUATIONS 26
2.3.2 ADIABATIC FLUCTUATIONS 27 2.4 LAGRANGIAN PERTURBATIONS 28 2.5
SOUND WAVES 28 2.6 SURFACE GRAVITY WAVES 30 2.7 PHASE SPEED AND GROUP
VELOCITY 32 VIII ASTROPHYSICAL FLUID DYNAMICS 2.8 ORDER-OF-MAGNITUDE
ESTIMATES FOR ASTROPHYSICAL FLUIDS 33 2.8.1 TYPICAL SCALES 33 2.8.2
IMPORTANCE OF VISCOSITY 33 2.8.3 THE ADIABATIC APPROXIMATION 35 2.8.4
THE APPROXIMATION OF INCOMPRESSIBILITY 35 3. THEORY OF ROTATING BODIES
37 3.1 EQUATION OF MOTION IN A ROTATING FRAME 38 3.2 EQUILIBRIUM
EQUATIONS FOR A SLOWLY ROTATING BODY . 38 3.3 THE ROCHE MODEL 40 3.4
CHANDRASEKHAR-MILNE EXPANSION 41 3.5 DYNAMICS OF ROTATING STELLAR MODELS
45 3.6 SOLAR ROTATION 46 3.7 BINARY STARS 50 4. FLUID DYNAMICAL
INSTABILITIES 55 4.1 CONVECTIVE INSTABILITY 55 4.1.1 THE SCHWARZSCHILD
CRITERION 55 4.1.2 EFFECTS OF DISSIPATION 60 4.1.3 MODELLING CONVECTION:
THE BOUSSINESQ APPROXIMATION 61 4.2 THE RAYLEIGH-TAYLOR INSTABILITY 62
4.3 ROTATIONAL INSTABILITY 63 4.4 SHEAR AND THE KELVIN-HELMHOLTZ
INSTABILITY 64 4.4.1 THE KELVIN-HELMHOLTZ INSTABILITY 64 4.4.2 CRITICAL
RICHARDSON AND REYNOLDS NUMBERS . 67 4.4.3 TURBULENCE AND THE
KOLMOGOROV SPECTRUM . 68 5. MAGNETOHYDRODYNAMICS 71 5.1 MAXWELL'S
EQUATIONS AND THE MHD APPROXIMATION . 71 5.2 MHD WAVES 74 5.3 SOME MHD
APPLICATIONS 76 5.3.1 SOLAR PROMINENCES 76 5.3.2 DYNAMO THEORY 78 5.3.3
CORONAL HEATING 81 5.4 MHD INSTABILITIES 82 6. NUMERICAL COMPUTATIONS 85
CONTENTS IX 6.1 THE FORMULATION OF FINITE DIFFERENCES 86 6.2 THE VON
NEUMANN STABILITY ANALYSIS 87 6.3 VARIOUS FINITE-DIFFERENCE SCHEMES 89
6.3.1 THE LAX METHOD 89 6.3.2 UPWIND DIFFERENCING 89 6.3.3 THE STAGGERED
LEAPFROG METHOD 90 6.3.4 THE LAX-WENDROFF METHOD 90 6.3.5 IMPLICIT
SCHEMES: THE CRANK-NICHOLSON METHOD . 91 6.4 CONSIDERATIONS FOR MORE
COMPLEX SYSTEMS 92 6.5 OPERATOR SPLITTING 93 6.6 EXAMPLES OF
IMPLEMENTATIONS 95 6.6.1 1-D LAGRANGIAN SCHEME WITH ARTIFICIAL VISCOSITY
. 95 6.6.2 2-D SCHEME USING OPERATOR SPLITTING 98 6.6.3 CODES FOR
COMPUTING ASTROPHYSICAL FLOWS 100 6.7 SMOOTHED PARTICLE HYDRODYNAMICS
101 7. PLANETARY ATMOSPHERE DYNAMICS 107 4 7.1 THE IMPORTANCE OF
ROTATION: THE ROSSBY NUMBER . . . . 107 7.2 RELATIVE AND ABSOLUTE
VORTICITY 108 7.3 POTENTIAL VORTICITY 110 7.4 BAROCLINICITY AND THE
THERMAL WIND EQUATION 110 7.5 GEOSTROPHIC MOTION 112 7.6 SOME
APPROXIMATE MODELS 116 7.6.1 THE SHALLOW-WATER MODEL 117 7.6.2 /-PLANE
AND /3-PLANE MODELS 119 7.7 WAVES , . 120 7.8 EKMAN LAYERS 122 8.
ACCRETION, WINDS AND SHOCKS 127 8.1 BERNOULLI'S THEOREM 128 8.2 THE DE
LAVAL NOZZLE 129 8.3 THE BONDI PROBLEM 130 8.4 THE PARKER SOLAR-WIND
SOLUTION 134 8.5 NONLINEAR ACOUSTIC WAVES 134 8.6 SHOCK WAVES 139 8.7
BLAST WAVE FROM A SUPERNOVA 140 9. VISCOUS ACCRETION DISKS 143 X
ASTROPHYSICAL FLUID DYNAMICS 9.1 ROLE OF ANGULAR MOMENTUM AND ENERGETICS
OF ACCRETION 143 9.2 THIN ACCRETION DISKS 145 9.3 DIFFUSION EQUATION FOR
SURFACE DENSITY 147 9.4 STEADY DISKS 150 9.5 THE NEED FOR ANOMALOUS
VISCOSITY 153 10. JEANS INSTABILITY AND STAR FORMATION 155 10.1 LINKS TO
OBSERVATIONS 156 10.2 JEANS INSTABILITY 156 10.3 JEANS INSTABILITY WITH
ROTATION 158 10.3.1 JEANS INSTABILITY FOR A ROTATING SYSTEM 159 10.4
AMBIPOLAR DIFFUSION 161 10.5 FRAGMENTATION 162 10.6 SOME COMMENTS ON
STAR FORMATION 163 11. RADIAL OSCILLATIONS OF STARS 165 11.1 LINEAR
ADIABATIC WAVE EQUATION FOR RADIAL OSCILLATIONS 165 11.1.1 BOUNDARY
CONDITIONS 168 11.1.2 EIGENVALUE NATURE OF THE PROBLEM 169 11.1.3
SELF-ADJOINTNESS OF THE PROBLEM 170 11.1.4 A LOWER BOUND ON THE
FUNDAMENTAL FREQUENCY . . 172 11.1.5 HOMOLOGY SCALING FOR THE
FUNDAMENTAL FREQUENCY OF STARS 172 11.2 NON-ADIABATIC RADIAL
OSCILLATIONS \ 173 11.2.1 PHYSICAL DISCUSSION OF DRIVING AND DAMPING . .
. 176 11.3 THE QUASI-ADIABATIC APPROXIMATION 178 12. NONRADIAL
OSCILLATIONS AND HELIOSEISMOLOGY 181 12.1 NONRADIAL MODES OF OSCILLATION
OF A STAR 181 12.2 MODE CLASSIFICATION 185 12.3 THE COWLING
APPROXIMATION 186 12.4 A SIMPLIFIED DISCUSSION OF NONRADIAL OSCILLATIONS
. 187 12.5 A MORE GENERAL ASYMPTOTIC EXPRESSION 190 12.6
HELIOSEISMOLOGY: THE DUVALL LAW 193 12.7 TASSOUL'S FORMULA 196 12.8
ASYMPTOTICS OF G MODES 198 CONTENTS XI 12.9 PROBING THE SUN'S INTERNAL
ROTATION 199 APPENDIX A USEFUL CONSTANTS AND QUANTITIES 205 A.I
FUNDAMENTAL PHYSICAL CONSTANTS 205 A.2 ASTRONOMICAL QUANTITIES 205 A.3
CARTESIAN TENSORS: INDEX NOTATION AND SUMMATION CONVENTION 206 APPENDIX
B VECTOR CALCULUS IN SPHERICAL AND CYLINDRICAL POLAR COORDINATES 207 B.I
CYLINDRICAL POLAR COORDINATES (M, 207 B.2 SPHERICAL POLAR COORDINATES
{R,6,) 208 APPENDIX C SELF-ADJOINT EIGENVALUE PROBLEMS 209 C.I REALITY
OF EIGENVALUES 209 C.2 ORTHOGONALITY OF EIGENFUNCTIONS 210 C.3
EIGENFUNCTION EXPANSIONS 210 C.4 VARIATIONAL PRINCIPLE 211 APPENDIX D
THE JWKB METHOD 213 BIBLIOGRAPHY 217 INDEX 223 |
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| illustrated | Illustrated |
| index_date | 2024-07-02T19:14:51Z |
| indexdate | 2024-07-09T21:09:15Z |
| institution | BVB |
| isbn | 186094633X 1860946151 |
| language | English |
| lccn | 2006284172 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016229416 |
| oclc_num | 65284316 |
| open_access_boolean | |
| owner | DE-703 DE-11 DE-29T |
| owner_facet | DE-703 DE-11 DE-29T |
| physical | XI, 227 S. graph. Darst. |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | Imperial College Press |
| record_format | marc |
| spelling | Thompson, Michael J. Verfasser aut An introduction to astrophysical fluid dynamics Michael J. Thompson London Imperial College Press 2006 XI, 227 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Includes bibliographical references (p. 217-221) and index Astrofysica gtt Astrophysique Fluides, Dynamique des Reologie gtt Fluid dynamics Astrophysics Astrophysik (DE-588)4003326-0 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Astrophysik (DE-588)4003326-0 s Strömungsmechanik (DE-588)4077970-1 s DE-604 http://www.loc.gov/catdir/toc/fy0702/2006284172.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016229416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Thompson, Michael J. An introduction to astrophysical fluid dynamics Astrofysica gtt Astrophysique Fluides, Dynamique des Reologie gtt Fluid dynamics Astrophysics Astrophysik (DE-588)4003326-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4003326-0 (DE-588)4077970-1 |
| title | An introduction to astrophysical fluid dynamics |
| title_auth | An introduction to astrophysical fluid dynamics |
| title_exact_search | An introduction to astrophysical fluid dynamics |
| title_exact_search_txtP | An introduction to astrophysical fluid dynamics |
| title_full | An introduction to astrophysical fluid dynamics Michael J. Thompson |
| title_fullStr | An introduction to astrophysical fluid dynamics Michael J. Thompson |
| title_full_unstemmed | An introduction to astrophysical fluid dynamics Michael J. Thompson |
| title_short | An introduction to astrophysical fluid dynamics |
| title_sort | an introduction to astrophysical fluid dynamics |
| topic | Astrofysica gtt Astrophysique Fluides, Dynamique des Reologie gtt Fluid dynamics Astrophysics Astrophysik (DE-588)4003326-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Astrofysica Astrophysique Fluides, Dynamique des Reologie Fluid dynamics Astrophysics Astrophysik Strömungsmechanik |
| url | http://www.loc.gov/catdir/toc/fy0702/2006284172.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016229416&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT thompsonmichaelj anintroductiontoastrophysicalfluiddynamics |