Turbulence in rotating, stratified and electrically conducting fluids:
Gespeichert in:
1. Verfasser: | |
---|---|
Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2013
|
Ausgabe: | 1. publ. |
Schlagworte: | |
Online-Zugang: | Klappentext Inhaltsverzeichnis |
Beschreibung: | XVII, 681 S. Ill., graph. Darst. |
ISBN: | 9781107026865 |
Internformat
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250 | |a 1. publ. | ||
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Datensatz im Suchindex
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adam_text | Contents
Preface
page
xv
1
The interplay of waves and turbulence: a preview
1
1.1
Three types of wave
1
1.2
Waves and turbulence
11
1.3
Turbulence in geophysical and astrophysical flows
17
PART I FROM FLUID MECHANICS TO
MAGNETOHYDRODYNAMICS
2
Elementary fluid dynamics
27
2.1
The Navier-Stokes equation
27
2.2
The dissipation of energy in a viscous fluid
31
2.3
The
vortici
ty
equation
33
2.4
Burgers vortex
36
2.5
Kelvin s theorem and Helmholtz s laws
39
2.6
Conservation of
helicity
41
2.7
The dynamics of a localised vorticity distribution
43
3
Motion in a rotating fluid
50
3.1
The Coriolis force
51
3.2
The Taylor-Proudman theorem
52
3.3
Inerţial
waves and the formation of Taylor columns
53
3.3.1
Inerţial
waves
53
3.3.2
The spontaneous growth of Taylor columns
57
3.3.3
The helical structure of
inerţial
waves
61
3.4
Waves and stability
62
3.5
Rossby waves: an example of quasigeostrophic flow
64
3.6
Rotating, shallow-water flow
66
3.6.1
The shallow-water equations and potential vorticity conservation
66
3.6.2
Small disturbances:
Poincaré
waves and geostrophic adjustment
69
3.6.3
Small disturbances near a boundary: Kelvin waves
72
viu
Contents
Ъ.1
Quasigeostrophic, shallow-water flow
74
3.7.1
The quasigeostrophic shallow-water (QGSW) equations
74
3.7.2
The QGSW equations from potential vorticity conservation
75
3.7.3
The QGSW equations with bottom topography and the /f-plane
77
3.7.4
Rossby waves revisited
78
3.8
The boundary layers of
Karman,
Bödewadt
and
Ekman
HO
4
Motion in a stratified fluid
92
4.1
The Boussinesq approximation and the suppression of vertical motion
92
4.2
Blocking: the analogue of Taylor columns
97
4.3
Lee waves: the analogue of stationary inertia! waves 1
01
4.4
Internal gravity waves
104
4.4.1
Linear gravity waves
104
4.4.2
Waves in rotating, stratified fluids 1
07
4.5
Potential vorticity revisited
107
4.6
Valley winds: the analogue of
Ekman
layers I 1
2
5
The equations of electrodynamics
1
1
7
5.1
Maxwell s equations
117
5.2
Integral versions of Ampere s and Faraday s laws
120
5.3
An evolution equation for the magnetic field
123
5.4
The
Lorentz
force, Maxwell s stresses and Faraday s tension
124
5.5
The exchange of energy between the magnetic field and velocity field
126
6
Motion in a conducting fluid: magnetohydrodynamics
129
6.1
The equations of
MHD
and key dimensionless groups
129
6.2
Kinematics
132
6.2.1
Ideal fluids:
Alfvén s
theorem and magnetic
helicity
132
6.2.2
Diffusive effects: stretched flux tubes and flux expulsion
135
6.3
Magnetic damping at low magnetic Reynolds number
138
6.3.1
Simplifications at low Rm
138
6.3.2
Energy destruction and momentum conservation
139
6.3.3
Damping of a vortex
140
6.4
The damping of turbulence at arbitrary Rm (a preview)
144
6.5
Dynamics at high magnetic Reynolds number
146
6.5.1
Alfvén
waves and
Ełsasser
variables
] 46
6.5.2
Magnetostrophic waves
148
6.5.3
Conservation of cross
helicity
150
7
Instabilities and transition to turbulence
157
7.1
The instabilities of Rayleigh, Taylor and
Benard
157
7.1.1
Rayleigh s centrifugal instability and Taylor-Couette flow
157
7.1.2
Rayleigh-Bénard
convection, with and without a magnetic field
161
Contents ix
7.2
Stability of a stratified shear flow
166
7.2.1
Shear flow in the absence of stratification: Rayleigh s
inflection-point theorem
167
7.2.2
The Kelvin-Helmholtz instability
169
7.2.3
A necessary condition for instability of a stratified shear flow
173
7.3
Stability of
MHD
equilibria in ideal fluids
175
7.3.1
The stability of static equilibria
175
7.3.2
The stability of non-static equilibria
179
7.3.3
A Hamiltonian approach to stability: the role of the Lagrangian
182
7.3.4
An aside: the Kelvin-Arnold variational principle for
Euler
flows
185
7.3.5
The Chandrasekhar-Velikhov instability (or
MRI) (i):
a model problem
187
7.3.6
The
MRI
(ii):
the case of rotation plus an azimuthal field
190
7.3.7
The
MRI
(iii):
the case of rotation plus an axial field
191
PART II TURBULENCE IN THE ABSENCE OF
BODY FORCES
8
Elementary properties of turbulence
197
8.1
Transition to turbulence: some common themes
198
8.2
The need for a statistical approach and the closure problem of
turbulence
204
8.3
Different scales in a turbulent flow and the zeroth law of turbulence
206
8.4
Richardson s energy cascade and Kolmogorov s microscales
209
8.5
Enstrophy production in a turbulent flow
216
9
The language of turbulence: kinematics and statistics
220
9.1
Velocity correlation functions and structure functions
220
9.1.1
Correlation functions
221
9.1.2
Structure functions
227
9.1.3
Skewness and flatness
230
9.2
Fourier space
233
9.2.1
The Fourier transform as a filter
233
9.2.2
The spectral tensor and the energy spectrum
236
9.3
The simplifications of isotropy
243
9.3.1
Correlation functions and structure functions in
isotropie
turbulence
244
9.3.2
The spectral tensor in
isotropie
turbulence
247
9.3.3
Relating the second-order structure function to the
energy spectrum
250
9.3.4
Isotropie
turbulence with
helicity
253
9.3.5
Axisymmetric turbulence
254
x
Contents
10 Hydrodynamic
turbulence
I: classical theories
259
10.1
The phenomenology of Richardson and Kolmogorov
259
10.1.1
Richardson s cascade (reprise)
259
10.1.2
Kolmogorov s theory of the small scales
266
10.1.3
The Kolmogorov-Obukhov-Corrsin model of passive
scalar mixing
277
10.1.4
Yaglom s four-thirds law and Corrsin s integral in scalar mixing
281
10.2
Vortex and material line stretching
283
10.2.1
The enstrophy budget
283
10.2.2
Enstrophy production and the skewness factor: Betchov s theory
286
10.2.3
The stretching of material lines
290
10.2.4
Richardson s law of two-particle diffusion
293
10.3
The Karman-Howarth equation and its immediate consequences
297
10.3.1
The Karman-Howarth equation
297
10.3.2
Kolmogorov s four-fifths law
300
10.3.3
The skewness factor and enstrophy production (reprise)
301
10.3.4
Dynamics of the third-order correlations and the problem
of closure
303
10.3.5
Dynamics in spectral space
305
10.4
Kolmogorov s refined model of the small scales
307
11
Hydrodynamic turbulence II: steps towards rotating, stratified and
MHD
turbulence
318
11.1
The evolution of the large scales
319
11.1.1 Isotropie
turbulence: Saffman versus Batchelor turbulence
319
11.1.2
Long-range interactions in Saffman and Batchelor turbulence
325
11.1.3
The decay laws of Kolmogorov and Saffman for
isotropie
turbulence
328
11.1.4
Saffman s analysis of anisotropic turbulence
330
11.1.5
A proof of the
invariance
of the Saffman integrals Ly in
anisotropic turbulence
335
11.1.6
Axisymmetric Saffman turbulence
338
11.1.7
The role of angular momentum conservation in
isotropie
Batchelor turbulence: Landau s theory
343
11.1.8
Problems with Landau s theory of Batchelor turbulence
345
11.1.9
A consistent theory of the large scales in Batchelor turbulence
348
11.2
Two-dimensional turbulence
349
11.2.1
Vortex dynamics in two dimensions
350
11.2.2
The classical theory of Batchelor
355
11.2.3
The role of the coherent vortices
360
11.2.4
The governing equations in statistical form
362
11.2.5
Batchelor revisited
366
11.2.6
Statistical invariants associated with the large scales
368
Contents xi
PART III TURBULENCE IN THE PRESENCE OF
BODY FORCES
12
Rapidly rotating turbulence
381
12.1
The early experimental observations
382
12.2
Structure formation through wave propagation
386
12.2.1
The shaping of a single eddy by linear
inerţial
wave radiation
387
12.2.2
Implications for homogeneous turbulence: some more
linear theory
391
12.2.3 Anisotropie
structuring via non-linear wave interactions:
resonant triads
394
12.3
Recent experimental evidence
398
12.4
The cyclone, anticyclone asymmetry
404
12.5
The rate of decay of energy
405
12.5.1
A Saffman-like invariant for rapidly rotating turbulence
406
12.5.2
Speculative decay laws
409
13
Towards geophysics: shallow-water, rapidly rotating turbulence
414
13.1
Governing equations
414
13.2
Statistical invariants
416
13.3
Turbulence on the /3-plane: waves versus turbulence
419
13.4
Zonal flows in
β
-plane turbulence
423
13.5
Spectra in
β
-plane turbulence
428
14
Homogeneous stratified turbulence
435
14.1
Governing equations and dimensionless groups
435
14.2
Scalings, regimes and structures
439
14.3
A spectral description of stratified turbulence
444
14.4
The experimental and numerical evidence
446
14.5
Open questions and speculative spectral scalings
450
14.6
The rate of energy decay
453
14.6.1
A Saffman-like invariant
453
14.6.2
Possible decay laws
455
14.7
An alternative approach: the inhomogeneous turbulent cloud
457
15
Stratified shear flows and the atmospheric boundary layer
463
15.1
Neutral shear flows
463
15.1.1
The log-law of the wall for momentum and temperature
463
15.1.2
The k~l and ln(r/z) laws
470
15.2
The equations of stratified shear flow and the flux Richardson
number
479
15.3
The atmospheric boundary layer
484
15.3.1
The structure of the ABL and the diurnal cycle
485
15.3.2
Prandtl s theory for weak mean shear
487
15.3.3
The Monin-Obukhov theory
489
xii Contents
15.3.4
Spectral
measurements: near-neutral and stable conditions
492
15.3.5
More spectral measurements: the unstable ABL
496
16
MHD
turbulence at low magnetic Reynolds number
502
16.1
Governing equations
503
16.2
Angular momentum conservation, the growth of anisotropy and the
decay of energy
504
16.3
The evolution of individual eddies
507
16.4
From angular momentum conservation to statistical invariants
513
16.5
A Loitsyansky-like invariant for homogeneous
MHD
turbulence
516
16.6
The numerical evidence for a Loitsyansky-like invariant
5
1
9
16.7
A Saffman-like invariant for homogeneous
MHD
turbulence
522
16.8
Possible decay laws for fully developed E(k
-*- 0) —
k2 and
E(k
-* 0)
~ kA turbulence
522
16.9
The numerical evidence for freely decaying E(k
-+ 0)
~ k4
turbulence
525
17
Turbulence in the core of the Earth: the geodynamo
528
17.1
The need for a geodynamo theory
528
17.2
The structure of the Earth and the geomagnetic field
530
17.3
Some elementary ideas in dynamo theory
535
17.4
Anti-dynamo theories and necessary bounds
546
17.4.1
A minimum value of Rm is needed
546
17.4.2
Cowling s theorem and its relatives
547
17.5
Parker s model of the geodynamo
549
17.6
Two-scale theories of the geodynamo
553
17.7
The Taylor constraint
556
17.8
The numerical simulations
557
17.9
Other planetary dynamos
561
18
MHD
turbulence at high magnetic Reynolds number
573
18.1
Two-dimensional
MHD
turbulence
573
18.1.1
Governing equations, ideal invariants and cascade directions
573
18.1.2
The evidence of the numerical simulations
578
18.2
Free decay and the Landau-Loitsyansky and Saffman
invariants revisited
582
18.3
The spontaneous growth of a seed field and the importance of Prm
585
18.4
Magnetic field generation in non-helical forced turbulence
587
18.4.1
The magnetic
microscale,
ηλ,
of a seed field
588
18.4.2
Kazantsev s kinematic model
589
18.4.3
Saturation of the magnetic field
593
18.5
Helical turbulence and selective decay
595
18.5.1
Ideal invariants revisited
595
Contents xiii
18.5.2 Taylor
relaxation
596
18.5.3
Alfvénic
states and dynamic alignment
597
18.6
The governing equations for two-point statistics in
MHD
turbulence
601
18.6.1
Evolution equations for the two-point correlations
602
18.6.2
Third-order structure function laws in the
inerţial
range
606
18.7
Spectral theories of
Alfvénic
turbulence
608
18.7.1
The phenomenology of Iroshnikov
&
Kraichnan:
weak turbulence
608
18.7.2
The phenomenology of
Goldreich &
Sridhar: critical balance
612
19
Turbulent astrophysical flows
615
19.1
Accretion discs
615
19.1.1
Why discs form
617
19.1.2
Elementary properties of accretion discs
618
19.1.3
Accretion in binary star systems and protostellar discs
621
19.1.4
The standard model of accretion discs
625
19.1.5
The role of instabilities and turbulence in accretion discs
628
19.2
The turbulent Sun
631
19.2.1
The structure of the Sun
632
19.2.2
The
11
-year solar cycle
634
19.2.3
The tachocline and the solar dynamo
638
19.2.4
The turbulent photosphere and solar flares
644
19.3
The solar wind
647
19.3.1
The discovery of the solar wind
648
19.3.2
A simple model of the solar wind
650
19.3.3
Turbulence in the wind
653
Epilogue
659
References
663
Index
675
Turbulence
in Rotating, Stratified
and Electrically Conducting Fluids
There are two recurring themes in astrophysical and
geophysical fluid mechanics: waves and turbulence. This book
investigates how turbulence responds to rotation, stratification
or magnetic fields, identifying common themes, where they
exist, as well as the essential differences which inevitably arise
between different classes of flow.
The discussion is developed from first principles, making
the book suitable for graduate students as well as professional
researchers. The author focusses first on the fundamentals and
then progresses to such topics as the atmospheric boundary
layer, turbulence in the upper atmosphere, turbulence in the
core of the Earth, zonal winds in the giant planets, turbulence
within the interior of the Sun, the solar wind, and turbulent
flows in accretion discs. The book will appeal to engineers,
geophysicists, astrophysicists and applied mathematicians
who are interested in naturally occurring turbulent flows.
P. A. DAVIDSON is Professorof Fluid Mechanics in the
Department of Engineering at the University of Cambridge.
|
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format | Book |
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id | DE-604.BV041651628 |
illustrated | Illustrated |
indexdate | 2024-07-10T01:01:50Z |
institution | BVB |
isbn | 9781107026865 |
language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027092230 |
oclc_num | 885224787 |
open_access_boolean | |
owner | DE-634 DE-19 DE-BY-UBM DE-703 |
owner_facet | DE-634 DE-19 DE-BY-UBM DE-703 |
physical | XVII, 681 S. Ill., graph. Darst. |
publishDate | 2013 |
publishDateSearch | 2013 |
publishDateSort | 2013 |
publisher | Cambridge Univ. Press |
record_format | marc |
spelling | Davidson, P. A. 1957- Verfasser (DE-588)173480845 aut Turbulence in rotating, stratified and electrically conducting fluids P. A. Davidson 1. publ. Cambridge Cambridge Univ. Press 2013 XVII, 681 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Magnetohydrodynamik (DE-588)4130803-7 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 s Turbulente Strömung (DE-588)4117265-6 s Magnetohydrodynamik (DE-588)4130803-7 s DE-604 Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027092230&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Klappentext Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027092230&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Davidson, P. A. 1957- Turbulence in rotating, stratified and electrically conducting fluids Turbulente Strömung (DE-588)4117265-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd |
subject_GND | (DE-588)4117265-6 (DE-588)4077970-1 (DE-588)4130803-7 |
title | Turbulence in rotating, stratified and electrically conducting fluids |
title_auth | Turbulence in rotating, stratified and electrically conducting fluids |
title_exact_search | Turbulence in rotating, stratified and electrically conducting fluids |
title_full | Turbulence in rotating, stratified and electrically conducting fluids P. A. Davidson |
title_fullStr | Turbulence in rotating, stratified and electrically conducting fluids P. A. Davidson |
title_full_unstemmed | Turbulence in rotating, stratified and electrically conducting fluids P. A. Davidson |
title_short | Turbulence in rotating, stratified and electrically conducting fluids |
title_sort | turbulence in rotating stratified and electrically conducting fluids |
topic | Turbulente Strömung (DE-588)4117265-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd Magnetohydrodynamik (DE-588)4130803-7 gnd |
topic_facet | Turbulente Strömung Strömungsmechanik Magnetohydrodynamik |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027092230&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027092230&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
work_keys_str_mv | AT davidsonpa turbulenceinrotatingstratifiedandelectricallyconductingfluids |