Dynamique des fluides astrophysiques: 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics
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Amsterdam [u.a.]
North-Holland
1993
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| Series: | École d'Été de Physique Théorique <LesHouches>: Session
47 |
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| Online Access: | Inhaltsverzeichnis |
| Item Description: | Bd.-zählung der Serie auf der Haupttitelseite fälschlicherweise 67 |
| Physical Description: | XXXIV, 615 S. Ill., graph. Darst. |
| ISBN: | 0444817972 |
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| 084 | |a PHY 927f |2 stub | ||
| 245 | 1 | 0 | |a Dynamique des fluides astrophysiques |b 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics |c éd. par J.-P. Zahn ... |
| 246 | 1 | 1 | |a Astrophysical fluid dynamics |
| 264 | 1 | |a Amsterdam [u.a.] |b North-Holland |c 1993 | |
| 300 | |a XXXIV, 615 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a École d'Été de Physique Théorique <LesHouches>: Session |v 47 | |
| 500 | |a Bd.-zählung der Serie auf der Haupttitelseite fälschlicherweise 67 | ||
| 650 | 0 | 7 | |a Astrophysik |0 (DE-588)4003326-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Strömungsmechanik |0 (DE-588)4077970-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)1071861417 |a Konferenzschrift |y 1987 |z Les Houches |2 gnd-content | |
| 689 | 0 | 0 | |a Strömungsmechanik |0 (DE-588)4077970-1 |D s |
| 689 | 0 | 1 | |a Astrophysik |0 (DE-588)4003326-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Zahn, Jean-Paul |e Sonstige |4 oth | |
| 830 | 0 | |a École d'Été de Physique Théorique <LesHouches>: Session |v 47 |w (DE-604)BV000022608 |9 47 | |
| 856 | 4 | 2 | |m Digitalisierung TU Muenchen |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006185330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
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| adam_text | CONTENTS
Lecturers
Participants
Préface
Preface
Contents
xv
Course
1.
Astrophysical fluid dynamics, by E.A. Spiegel
1.
Kinematics of the continuum
2.
Fluid dynamics
2.1.
Conservation laws
2.2.
Baroclinic flows
3.
Atmospheric waves
3.1.
Simple static states
3.2.
Linear theory
4.
Cosmology s fictitious forces
5.
Conclusion
6.
Further reading
6
11
Π
14
17
17
19
24
31
32
Course
2.
Hydrodynamic turbulence,
by
M. Le sieur
33
1.
Basic
equations and elementary vortex dynamics
37
1.1.
Qualitative introduction
to
turbulence
37
1.2.
The Navier-Stokes equation
38
1.2.1.
Notations
38
1.2.2.
The continuity equation
38
1.2.3.
The strain tensor
39
1.2.4.
The linear-momentum equation
40
1.2.5.
Thermodynamics
41
1.2.6.
The incompressibility assumption for the velocity
43
1.2.7.
The Boussinesq approximation
43
1.3.
The dynamics of vorticity
44
1.3.1.
The Kelvin theorem
45
1.3.2.
Potential vorticity
45
1.4.
The geostrophic approximation
47
1.4.1.
The geostrophic balance
47
1.4.2.
The quasi-geostrophic potential vorticity equation
48
2.
Transition to turbulence
48
2.1.
The Reynolds number
48
2.2.
How can turbulence develop in an irrotational flow?
49
2.3.
The linear-instability theory
50
2.3.1.
The Orr-Sommerfeld and the Rayleigh equation
50
2.3.2.
The mixing-layer instability
50
2.3.3.
The plane jet
52
2.3.4.
The boundary layer
54
2.4.
Secondary instabilities
54
2.4.1.
The Kelvin-Helmholtz billow
54
2.4.2.
The Tollmien—Schlichting wave
55
2.5.
Non-linear instabilities
56
2.5.1.
The plane Poiseuille flow
56
2.5.2.
The circular Poiseuille flow
56
2.6.
Turbulence in a fluid heated from below
56
2.7.
Rotating or stratified flows
57
xxiv
3.
Homogeneous turbulence viewed from Fourier space
58
3.1.
Statistical formalism
58
3.1.1.
Use of random functions
58
3.1.2.
Homogeneity, stationarity, isotropy
58
3.2.
Fourier representation
59
3.2.1.
The Navier-Stokes equation in Fourier space
59
3.2.2.
Craya representation
60
3.3.
Velocity correlation and spectral tensors
61
3.3.1.
Velocity correlation tensor
61
3.3.2.
Spectral tensor
61
3.4.
Projection of the spectral tensor in the Craya frame
62
3.5.
Some additional remarks about the spectra
64
4.
Phenomenological theories of turbulence
65
4.1.
Inhomogeneous turbulence
65
4.2.
Spectral interactions in
isotropie
turbulence
65
4.2.1.
Detailed conservation
66
4.2.2.
Kinetic energy flux
67
4.3.
The Kolmogorov theory
68
4.3.1.
Characteristic scales
68
4.3.2.
The Obukhov theory
69
4.3.3.
The second-order structure function
69
4.3.4.
The Richardson law
70
4.4.
The enstrophy blow-up
70
4.4.1.
The
Euler
equation and three-dimensional turbulence
70
4.4.2.
The skewness factor
70
4.4.3.
The enstrophy blow-up theorem
71
5.
Stochastic models of turbulence
73
5.1.
Introduction
73
5.2.
The closure problem in Fourier space
73
5.3.
The quasi-normal approximation
74
5.4.
Eddy-damped quasi-normal theory (EDQN)
75
5.5.
Eddy-damped quasi-normal Markovian theory (EDQNM)
76
5.6.
The stochastic models
76
5.7.
EDQNM results for
isotropie
turbulence
77
5.7.1.
Kinetic energy
77
5.7.2.
Passive scalar
77
5.7.3.
Anomalous scalar decay
78
5.8.
Non-local interactions
78
5.9.
The statistical-predictability theory
79
5.10.
Large-eddy simulations in spectral space
81
xxv
6.
Two-dimensional turbulence
81
6.1.
Two-dimensional flow
81
6.1.1.
The vorticity equation and stream function
81
6.1.2.
How can a real flow be two-dimensional?
83
6.2.
Two-dimensional
isotropie
turbulence
83
6.2.1.
Spectra
83
6.2.2.
Kinetic energy and enstrophy conservation
84
6.2.3.
The Fj0rtoft theorem
85
6.2.4.
Enstrophy cascade
85
6.2.5.
The inverse energy cascade
86
6.3.
EDQNM analysis of the enstrophy cascade
86
6.4.
Two-dimensional turbulence in mixing layers
87
6.5.
Conclusion
88
References
89
Course
3.
Generic instabilities and nonlinear dynamics,
by O. Thual
93
1.
Introduction
97
2.
Bifurcations in dissipative dynamical systems
98
2.1.
Examples of dissipative dynamical systems
98
2.1.1.
Definition
98
2.1.2.
Example: the
Lorenz
model
99
2.1.3.
Example: the
Liénard
oscillators
99
2.2.
Bifurcations of a fixed point
100
2.2.1.
Stability of a fixed point
100
2.2.2.
Real-eigenvalue crossing
100
2.2.3.
Complex conjugated eigenvalues
101
2.2.4.
Example: the
Lorenz
model
101
2.2.5.
Example: the
Liénard
oscillators
102
2.3.
Normal forms of the bifurcations
102
2.3.1.
Pitchfork bifurcation
102
2.3.2.
The
Hopf
bifurcation
103
2.4.
KBM method for the calculation of normal forms
105
2.4.1. Hopf
bifurcation
105
2.4.2.
Pitchfork bifurcation
106
2.4.3.
Application to the
Lorenz
model
107
2.4.4.
Application to the
Liénard
oscillators
109
3.
Generic
instabilities of spatial systems
110
3.1.
Stability of equilibrium in spatial systems
110
3.2.
2D Ray
leigh-Bénard
convection
110
3.2.1.
Small box 111
3.2.2.
Large box
113
3.2.3.
Family of solutions
114
3.3.
Spatially coupled oscillators
115
3.3.1.
Spatial coupling due to diffusion
115
3.3.2.
Small box
116
3.3.3.
Large box
116
3.4.
Simple model for a classification
117
3.4.1.
Four generic destabilizations
118
3.4.2.
Real eigenvalue destabilizing L (0)
119
3.4.3.
Real eigenvalue destabilizing L (kc) and
¿д(—
kc)
120
3.4.4.
Complex eigenvalues destabilizing
¿д(0)
120
3.4.5.
Complex eigenvalues destabilizing L (kc) and Lx(-kc)
121
3.4.6.
Summary and supercritical cases
121
3.5.
Thermohaline convection
122
4.
Introduction to the phase equation theory
123
4.1.
Family of periodic structures
124
4.1.1.
A-type or B-type periodic structures
124
4.1.2.
Marginal mode
124
4.1.3.
Family of marginal modes
126
4.2.
Phase equation for the Landau equation
126
4.2.1.
Stability of the Wq s
127
4.2.2.
Derivation of the phase equation
128
4.3.
Phase equation for the Ginzburg-Landau equation
129
4.3.1.
Stability of Wo
130
4.3.2.
Phase equation derivation
131
4.4.
Phase equations for periodic structures
131
4.4.1.
B-type structures
131
4.4.2. Eckhaus
instability of B-type structures
132
4.4.3.
Zig-zag instability of B-type structures
132
4.4.4.
A-type
periodic structures
133
4.4.5. Eckhaus
instability of
A-type
structures
133
4.4.6.
Zig-zag instability of
A-type
structures
134
4.5.
Family of phase equations
134
4.5.1.
B-type
Eckhaus
nonlinear coefficients
134
4.5.2.
A-type zig-zag nonlinear coefficients
135
4.5.3.
Zig-zag nonlinear coefficients
135
5.
Conclusion
135
5.1.
Dynamical systems
135
5.2.
Spatially confined systems
136
5.3.
Spatially extended systems
136
5.4.
Supercritical or
subcriticai
instabilities
137
References
138
Course
4.
Magnetohydrodynamic turbulence,
by A. Pouquet
139
1. Magnetohydrodynamic turbulence
143
1.1.
Fundamental equations
143
1.1.1.
Introduction
143
1.1.2.
Coupling to the dynamics
145
1.2.
The
MHD
approximation
147
1.2.1.
The non-relativistic limit
147
1.2.2.
The parameters
148
1.2.3.
The incompressible case
149
1.2.4.
The
Elsässer
variables
150
1.2.5.
Discussion
151
1.3.
Joule dissipation
152
1.4.
Large magnetic Reynolds number
152
1.4.1.
The frozen field
152
1.4.2.
Hamiltonian dynamics
153
1.4.3.
Flux tubes
154
1.5.
Magnetohydrodynamical waves
154
1.6.
Discussion
156
2.
Observations and phenomenology
158
2.1.
Introduction
158
2.2.
Methods of observation
158
2.2.1.
The
Zeeman
effect
158
2.2.2.
Polarization observations
159
2.3.
The Earth as a planet
159
2.4.
The Sun as a star
160
2.5.
Beyond the Sun
161
2.6.
Radio jets
162
2.7.
A phenomenological analysis of
MHD
turbulence
163
3.
Large-scale behavior
165
3.1.
The invariants of the
MHD
equations
165
3.2.
An
MHD
fluid as a mechanical system
166
3.3.
The general state of minimal energy
169
3.4.
The two-dimensional case
171
3.5.
Oscillations in a radio jet
172
3.6.
Statistical mechanics of truncated systems
172
3.7.
Self-organization of flows
173
4.
Topology of magnetic field lines
173
4.1.
Knots are vital
173
4.2.
Magnetic
helicity
and linkage of field lines
174
4.3.
Magnetostatic equilibrium
177
4.3.1.
The derivation
177
4.3.2.
Stability properties
179
4.4.
Where does the energy go?
179
4.5.
Topological solitons 1
79
4.6.
The emerging dynamical picture
181
4.7.
Change of topology
182
5.
Transport coefficients
182
5.1.
Introduction
182
5.2.
The closure equations in
MHD
183
5.3.
Turbulent transport coefficients as non-local expansion of closures
190
5.4.
Destabilization effect of small-scale magnetic
helicity
191
5.4.1.
A phenomenological argument
191
5.4.2.
Closure results
192
5.5.
The inverse cascade of magnetic
helicity
193
5.5.1.
Characteristic times
193
5.5.2.
Numerical evidence for large-scale self-organization of
MHD
flows
194
5.6.
Two-scale analysis of non-linear
MHD
195
5.7.
The non-linear dynamo
196
6.
Low-dimensional
MHD
197
6.1.
The scalar model
198
6.2.
Dimensionality of the flow
201
6.3.
One-dimensional Burgers equation extended to
MHD
203
6.4.
Lack of singularity in two-dimensional inviscid
MHD
204
6.5.
The inverse cascade of the magnetic potential
207
6.6.
The development of current sheets
208
7.
The growth of velocity-magnetic field correlations
209
7.1.
Introduction
209
7.2.
Phenomenology of correlated flows
209
7.3.
Does the correlation coefficient really grow and why?
214
7.4.
Lack of universality of the
inerţial
ranges of correlated
MHD
flows
217
7.5.
Selective decay
219
7.6.
The emerging dynamical picture
221
7.7.
Conclusion
222
References
224
Course
5.
Dynamo theory, by P.H. Roberts
229
1.
Dynamo theory
233
1.1.
Introduction
233
1.2.
Basic theory
242
1.3.
Large magnetic Reynolds numbers
255
2.
Mean-field theory
260
2.1.
Reynolds stress
260
2.2.
Mean-field electrodynamics: first attack
270
2.3.
Theo-effect
275
2.3.1.
a2-dynamos
279
2.3.2.
αω
-dynamos
281
2.3.3.
αω
-dynamos
with meridional circulation
288
2.4.
Mean-field electrodynamics: second attack
288
3.
Magnetohydrodynamic dynamos
299
3.1.
Equilibration
299
3.2.
Magnetoconvection in rotating systems
311
3.3.
Conclusions
316
References
316
Appendix A. Notes added December,
1992 318
Appendix B. Recent literature
322
Course
6.
Thermal convection and penetration,
by J. Toomre
325
1.
Introduction
329
2.
Boussinesq convection in simple geometries
332
2.1.
Rayleigh-Bénard
convection
332
2.2.
Posing the problem
333
2.2.1.
Basic equations
333
2.2.2.
The Oberbeck-Boussinesq approximation
334
2.2.3.
Separating into mean and fluctuating parts
336
2.2.4.
Boundary conditions
338
2.3.
Modal expansions
338
2.3.1.
Single-mode equations
339
2.4.
Linear stability and the onset of convection
342
2.4.1.
Cartoon sketch of the instability
342
2.4.2.
Stability analysis with free boundaries
343
2.5.
Nonlinear solutions of single-mode equations with
Z
= 0 345
2.6.
Time-dependent solutions of multi-mode equations
348
2.7.
Low Prandtl numbers and vertical vorticity
352
3.
Anelastic modal convection
353
3.1.
The anelastic approximation
354
3.2.
Convection in simple polytropes
356
3.3.
Dynamical consequences of stratification
357
3.4.
Penetrative convection in piecewise polytropes
358
3.4.1.
Asymmetries in upward and downward solutions
360
3.4.2.
Penetration and its implications
362
3.5.
Dynamical coupling of convection zones in
A-type
stars
363
3.5.1.
Modeling the outer envelope
364
3.5.2.
Downward solution and countercells
364
3.5.3.
Upward solution and pronounced coupling of zones
366
3.5.4.
Lateral deflection of flows below the surface
367
4.
Two-dimensional fully compressible convection
369
4.1.
Formulating the problem
370
4.2.
Single unstable layer of convection
373
4.2.1.
Prominent asymmetries between uprlows and downflows
373
4.2.2.
Dynamical balance leading to asymmetries
375
4.3.
Convection penetrating into stable regions above and below
377
4.3.1.
Coupling between plumes and gravity waves
377
4.3.2.
Temporal signatures of coupling
378
4.3.3.
Time-averaged fluxes and penetration depth
381
4.4.
Penetration and mixing below a convection zone
383
4.4.1.
Measure of relative stabilities of layers
383
4.4.2.
Varying penetration depth
383
4.4.3.
Mixing of a passive scalar
386
5.
Three-dimensional fully compressible convection
387
5.1.
Unstable convection layer with simple physics
388
5.2.
Simulations of solar granulation
391
6. Final
reflections
393
References
394
Course
7.
Linear adiabatic stellar pulsation,
by
D.O.
Gough
399
1.
Introduction
403
1.1.
The fluid
406
1.2.
Equations of motion
408
2.
The equilibrium state
409
3.
Linearized equations
411
4.
Radial pulsations
413
4.1.
Linearized equations of motion
413
4.2.
Boundary conditions
415
4.2.1.
Oscillations of an isothermal atmosphere
418
4.3.
Orthogonality of eigenfunctions
421
4.4.
Some nomenclature
422
4.5.
Variational principle
422
4.6.
Lower bound to the pulsation frequency
423
4.7.
Elementary discussion of dynamical stability
424
4.8.
The Liouville-Green expansion of high-order modes
425
4.8.1.
Reduction to standard form
425
4.8.2.
Radial oscillations of the isothermal aimosphere revisited
427
4.8.3.
The JWKB approximation
428
4.8.4.
Form of the solution: wave trapping
429
4.8.5.
Bridging the transition: eigenvalue equation
429
5. Nonradial
oscillations about a spherically symmetric state
434
5.1.
The equations of motion
435
5.2.
Boundary conditions
436
5.3.
Variational principle
438
5.4.
The Cowling approximation: reduction to standard form
439
5.5.
Mode classification
440
5.6.
The
ƒ
mode
445
5.7.
Modes of high degree
449
5.7.1.
Subphotospheric modes
449
5.7.2.
Atmospheric modes
453
5.7.3.
Interior
д
modes
454
5.8.
Modes of high order
455
6.
Inversion of asymptotic formulae
464
7.
Perturbation
theory
469
7.1.
Spherically symmetric perturbations
470
7.2.
Aspherical scalar perturbations: degenerate perturbation theory
475
7.3.
Advection by rotation
479
7.4.
Internal magnetic field
483
7.5.
Adding perturbations
485
7.6.
Horizontal inhomogeneity
488
8.
Asymptotic representation by locally plane waves
492
8.1.
The adiabatic wave equation in standard form
493
8.2.
The three-dimensional Liouville-Green expansion
495
8.3.
The eikonal equation
496
8.4.
EBK quantization
498
8.5.
Evaluation of the quantization conditions
505
8.6.
Construction of the eigenfunction
507
8.6.1.
The phases
508
8.6.2.
The amplitudes
511
8.6.3.
The eigenfunction
512
8.7.
Aspherical perturbation theory
514
8.7.1.
The principle of least action
514
8.7.2.
The perturbed eigenfrequency
516
8.7.3.
Sound-speed perturbations
517
8.7.4.
Frequency perturbations by a deeply buried magnetic field
520
8.7.5.
Rotational splitting
522
8.8.
On the averaging of (solar) frequency data
522
9.
Concluding remarks
526
Appendix
1.
The plane-parallel envelope
530
Appendix
2.
Reality of eigenfrequencies below the critical cutoff
533
Appendix
3.
The Roche stellar model and its radial pulsations
534
Appendix
4.
JWKB expansion of the damped oscillator equation
537
Appendix
5.
Causal adiabatic oscillations of an isothermal atmosphere
540
Appendix
6.
The oscillation of a plane-parallel polytrope supporting an isother¬
mal atmosphere
546
Appendix
7.
Acoustic oscillations of an isothermal sphere
551
Appendix
8.
The scaling factor in the Abel sound-speed inversion
552
Appendix
9.
Invariants from eikonal equations under symmetries in a sphere
553
Appendix
10.
Asymptotic associated Legendre functions
556
References
559
Course
8.
Instabilities and turbulence in rotating stars,
by J.-P.
Zahn 561
1.
Rotating objects
565
1.1.
Equilibrium configurations
565
1.1.1.
Uniform rotation
567
1.1.1.1.
Constant density
567
1.1.1.2.
The Roche model
568
1.1.2.
Differential rotation
569
1.2.
The dynamics
571
2.
Baroclinic instabilities
573
2.1.
Buoyancy and related instabilities
574
2.1.1.
Varying chemical composition
574
2.1.2.
Effect of dissipation
575
2.1.3.
Double-diffusive instability
575
2.2.
The Coriolis force and related instabilities
576
2.3.
The baroclinic state and thermal wind
577
2.4.
Axisymmetric baroclinic instability
578
2.4.1.
Effect of dissipation
579
2.5.
Non-axisymmetric baroclinic instability
580
3.
Shear instabilities
583
3.1.
The critical Reynolds number
583
3.2.
Stabilization by the buoyancy force
584
3.3.
Shear instabilities in a rotating flow
586
3.4.
Turbulence in rotating flows
589
4.
Thermal imbalance and meridional circulation in rotating stars
592
4.1. Von
Zeipel s theorem
593
4.2.
The energy generation rate in a barotropic star
594
4.3.
The meridional circulation
597
5.
Turbulence in rotating stars
600
5.1.
Horizontal turbulence
601
5.1.1.
Inhibition of the meridional advection of chemicals
601
5.1.2.
Parametrization
602
5.2.
The turbulent transport in the vertical direction
605
5.2.1.
Turbulence produced by the vertical shear
606
5.2.2.
Turbulence produced by the horizontal shear
606
5.3.
The observational evidence
608
5.3.1.
The solar tachocline
608
5.3.2.
Transport of lithium versus transport of angular momentum
610
5.4.
Towards a coherent picture
611
References
613
|
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| genre | (DE-588)1071861417 Konferenzschrift 1987 Les Houches gnd-content |
| genre_facet | Konferenzschrift 1987 Les Houches |
| id | DE-604.BV009295100 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:34:30Z |
| institution | BVB |
| isbn | 0444817972 |
| language | Undetermined |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006185330 |
| oclc_num | 644582812 |
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| owner_facet | DE-12 DE-91G DE-BY-TUM DE-83 |
| physical | XXXIV, 615 S. Ill., graph. Darst. |
| publishDate | 1993 |
| publishDateSearch | 1993 |
| publishDateSort | 1993 |
| publisher | North-Holland |
| record_format | marc |
| series | École d'Été de Physique Théorique <LesHouches>: Session |
| series2 | École d'Été de Physique Théorique <LesHouches>: Session |
| spelling | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics éd. par J.-P. Zahn ... Astrophysical fluid dynamics Amsterdam [u.a.] North-Holland 1993 XXXIV, 615 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier École d'Été de Physique Théorique <LesHouches>: Session 47 Bd.-zählung der Serie auf der Haupttitelseite fälschlicherweise 67 Astrophysik (DE-588)4003326-0 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf (DE-588)1071861417 Konferenzschrift 1987 Les Houches gnd-content Strömungsmechanik (DE-588)4077970-1 s Astrophysik (DE-588)4003326-0 s DE-604 Zahn, Jean-Paul Sonstige oth École d'Été de Physique Théorique <LesHouches>: Session 47 (DE-604)BV000022608 47 Digitalisierung TU Muenchen application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006185330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics École d'Été de Physique Théorique <LesHouches>: Session Astrophysik (DE-588)4003326-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4003326-0 (DE-588)4077970-1 (DE-588)1071861417 |
| title | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics |
| title_alt | Astrophysical fluid dynamics |
| title_auth | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics |
| title_exact_search | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics |
| title_full | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics éd. par J.-P. Zahn ... |
| title_fullStr | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics éd. par J.-P. Zahn ... |
| title_full_unstemmed | Dynamique des fluides astrophysiques 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics éd. par J.-P. Zahn ... |
| title_short | Dynamique des fluides astrophysiques |
| title_sort | dynamique des fluides astrophysiques 29 juin 31 juillet 1987 astrophysical fluid dynamics |
| title_sub | 29 juin - 31 juillet 1987 = Astrophysical fluid dynamics |
| topic | Astrophysik (DE-588)4003326-0 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Astrophysik Strömungsmechanik Konferenzschrift 1987 Les Houches |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006185330&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000022608 |
| work_keys_str_mv | AT zahnjeanpaul dynamiquedesfluidesastrophysiques29juin31juillet1987astrophysicalfluiddynamics AT zahnjeanpaul astrophysicalfluiddynamics |