Physics of buoyant flows: from instabilities to turbulence
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey
World Scientific
[2018]
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| Online-Zugang: | Inhaltsverzeichnis Klappentext |
| Beschreibung: | xxiv, 327 Seiten Illustrationen, Diagramme |
| ISBN: | 9789813237797 |
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| 100 | 1 | |a Verma, Mahendra K. |d 1966- |e Verfasser |0 (DE-588)1165899922 |4 aut | |
| 245 | 1 | 0 | |a Physics of buoyant flows |b from instabilities to turbulence |c Mahendra K Verma, Indian Institute of Technology Kanpur, India |
| 264 | 1 | |a New Jersey |b World Scientific |c [2018] | |
| 300 | |a xxiv, 327 Seiten |b Illustrationen, Diagramme | ||
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| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 653 | 0 | |a Buoyant ascent (Hydrodynamics) | |
| 653 | 0 | |a Fluid dynamics | |
| 653 | 0 | |a Buoyant convection | |
| 653 | 0 | |a Turbulence | |
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Datensatz im Suchindex
| _version_ | 1804178822338183168 |
|---|---|
| adam_text | Contents
Reviews
Foreword
Preface
Acknowledgments
Notation
Basic Formulation, Patterns, and Chaos 1
1. Introduction 3
2. Basic Framework 7
2.1 Equations in terms of density variation......................... 7
2.2 Equations in terms of temperature............................... 9
2.3 Rayleigh-Bénard convection....................................... 13
2.4 Justification of Oberbeck-Boussinesq approximation .............. 13
2.5 Equations for the stably stratified flows simplified............. 15
2.6 Boundary conditions, Box geometry ............................... 16
2.7 Nondimensionalized RBC equations................................. 17
2.8 Kinetic and potential energies, entropy.......................... 20
2.9 Heat transport and Nusselt number in RBC......................... 23
3. Fourier Space Description 27
3.1 Definitions...................................................... 27
3.2 Energy and entropy............................................... 29
3.3 Reality condition................................................ 31
3.4 Free-slip basis functions for RBC................................ 32
3.5 No-slip boundary condition for RBC............................... 39
XIX
XX
Physics of Buoyant Flows: Prom Instabilities to Turbulence
3.6 Craya-Herring decomposition........................................ 40
3.7 Craya-Herring basis for 2D flows................................... 43
3.8 Craya-Herring for 3D vector field revisited........................ 47
3.9 Helical decomposition ............................................. 48
3.9.1 The helical mode u+ ...................................... 49
3.9.2 The helical mode u_ ....................................... 50
3.9.3 Mixture of u+ and u_...................................... 51
3.10 Helical waves...................................................... 52
3.11 Helicity under parity transformation............................... 54
4. Energy Transfers in Buoyancy-Driven Flows 57
4.1 Mode-to-Mode energy transfers in RBC .............................. 57
4.2 Energy transfers in stably stratified flows........................ 64
4.3 Energy flux due to nonlinear interactions.......................... 64
4.4 Shell-to-shell energy transfers.................................... 68
4.5 Pseudo-spectral method............................................. 69
5. Waves in Stably Stratified Flows 73
5.1 Internal gravity waves............................................. 73
5.2 Derivation of waves in Craya-Herring basis......................... 77
6. Instabilities in Thermal Convection 79
6.1 Thermal instability for Free-slip boundary condition............... 79
6.2 Linearized version of Rayleigh-Bénard convection................... 84
6.3 Boundary conditions for RBC instabilities.......................... 85
6.4 Thermal instability for the no-slip boundary condition ....... 87
6.5 Thermal instability in Craya-Herring basis......................... 89
6.6 Rayleigh-Taylor instability........................................ 90
6.7 Schwarzschild criterion for convective instability................. 94
7. Nonlinear Saturation 99
7.1 Lorenz equations................................................... 99
7.2 Stationary solution of Lorenz equations and nonlinear saturation . 102
7.3 Bifurcation analysis...............................................105
7.4 Amplitude equation ................................................107
7.5 Nonlinear interactions in stably stratified flows..................109
8. Patterns and Chaos in Buoyancy-Driven Flows 111
8.1 Seven-mode model of RBC............................................Ill
8.1.1 Derivation of the seven-mode model........................Ill
8.1.2 Generation of secondary modes..............................114
8.2 Patterns and chaos in moderate and large-Pr RBC....................117
Contents
xxi
8.3 Patterns and chaos in small-Pr RBC............................120
8.4 Understanding patterns using amplitude equation...............121
9. Boundary Layer, Bulk, and Exact Relations in Thermal Convection 125
9.1 Viscous and thermal boundary layers...........................125
9.2 Temperature profile in RBC.....................................127
9.3 Exact relations of RBC.........................................130
9.4 Conservation laws..............................................132
Turbulent Buoyant Flows 135
10. A Survey of Hydrodynamic Turbulence 137
10.1 Kolmogorov’s theory for 3D hydrodynamic turbulence.............137
10.2 Kraichnan’s theory for 2D hydrodynamic turbulence..............142
10.3 Energy spectrum in the dissipation wavenumber regime...........143
10.4 Passive scalar turbulence......................................144
10.4.1 Formalism of passive scalar turbulence ...............144
10.4.2 Passive-scalar turbulence for various regime..........146
11. Scaling of Large-Scale Quantities in RBC 149
11.1 Preliminary models for scaling of Peclet and Nusselt numbers ... 149
11.1.1 Scaling of Peclet number..............................149
11.1.2 Scaling of Nusselt number..............................151
11.2 Modified scaling arguments for the Peclet number and ©.........152
11.3 Relative strengths of various forces in RBC ...................158
11.4 Nusselt number scaling.........................................160
11.4.1 Arguments of Kraichnan.................................161
11.4.2 Arguments based on correlations........................161
11.4.3 Arguments based on boundary layers.....................163
11.4.4 Analytical bounds on Nu by Doering et al...............165
11.4.5 Arguments of Grossmann and Lohse.......................167
11.5 Scaling of viscous dissipation rate............................167
11.6 Comparison between the dissipation rates in the bulk and boundary
layer..........................................................169
11.7 Scaling of entropy dissipation rate ...........................171
11.8 Grossmann-Lohse model for the scaling of Nusselt and Peclet
numbers........................................................172
11.8.1 Grossmann-Lohse model .................................172
11.8.2 Comparison between GL model and that of Pandey and
Verma..................................................175
11.9 Scaling of large-scale quantities for free-slip RBC............176
XXII
Physics of Buoyant Flows: From Instabilities to Turbulence
11.10 Onset of ultimate regime?......................................178
12. Phenomenology of Stably Stratified Turbulence 181
12.1 Various regimes of SST.........................................181
12.2 SST with moderate buoyancy.....................................182
12.2.1 Classical Bolgiano-Obukhov scaling for SST .............182
12.2.2 BO phenomenology revisited..............................184
12.2.3 Numerical verification of BO scaling....................185
12.3 SST with weak buoyancy ........................................187
12.4 SST with strong buoyancy.......................................188
12.5 SST in 2D......................................................190
12.6 Experimental and observational results.........................193
13. Phenomenology for Turbulent Thermal Convection 195
13.1 Energy flux based phenomenological arguments for turbulent
convection.....................................................195
13.2 Numerical demonstration of Kolmogorov-like scaling for RBC . . . 197
13.3 Entropy spectrum of RBC........................................200
13.4 Turbulence in zero- and small-Pr RBC...........................202
13.5 Turbulence for infinite and large-Pr RBC ......................202
13.6 Structure functions for RBC....................................204
13.7 Taylor’s frozen-in hypothesis for RBC?.........................205
13.8 Experimental results on RBC spectrum ..........................208
13.8.1 Results from PIV measurements...........................208
13.8.2 Results from local field measurements...................208
13.9 Numerical results on RBC.......................................210
13.10 Turbulence in the boundary layers of RBC.......................211
13.11 Turbulence in two-dimensional RBC..............................211
13.12 Simulation of turbulent convection in a periodic box ..........212
13.13 Field theoretic treatment of RBC...............................213
14. Turbulence Phenomenology of Other Buoyancy-Driven Flows 215
14.1 Rayleigh-Taylor turbulence (RTT) ..............................215
14.2 Unstably stratified turbulence.................................217
14.3 Taylor-Couette turbulence......................................218
14.4 Bubbly turbulence..............................................220
14.5 Turbulence in thermally-driven hemisphere .....................220
15. Anisotropy in Thermally-Driven Turbulence 223
15.1 Anisotropy quantification in real space........................223
15.1.1 Flow visualisation......................................223
15.1.2 Structure function, EUi±/((D — l)EUy ), and Lj_/L .... 224
Contents
xxiii
15.2 Anisotropy quantification in Fourier space.........................225
15.2.1 EU!±(k)/(2Eu n(k)) 225
15.2.2 Ring spectrum for spherical rings .........................226
15.2.3 Ring spectrum for cylindrical rings........................227
15.3 Measures of Energy transfers ......................................228
15.3.1 Ring-to-ring energy transfers..............................228
15.3.2 Energy exchange between u and u_l in RBC.............228
15.3.3 Energy exchange between u and u_l in stably stratified
flows .....................................................230
15.4 Numerical results on the anisotropy in RBC.........................230
15.5 Numerical results on anisotropy in stably stratified flows.........233
16. Shell Models for Buoyancy-Driven Turbulence 235
16.1 Shell model for turbulent convection...............................236
16.2 Shell model for stably stratified turbulence.......................238
16.3 Shell-model results for turbulent convection.......................238
16.4 Shell model results for stably stratified turbulence ..............240
16.5 Other shell models of buoyancy-driven flows........................241
17. Structures and Flow Reversals in RBC 243
17.1 Structures and Large-scale circulation in RBC......................243
17.2 LSC and its reversal in 2D closed box .............................244
17.2.1 Nonlinear interactions among the large-scale Fourier modes 245
17.2.2 Nusselt number fluctuations during a reversal..............248
17.2.3 Symmetries of Fourier modes................................249
17.2.4 Reversals under variations of Prandtl number and
geometries.................................................251
17.3 LSC and flow reversals in 3D Cartesian box.........................252
17.4 LSC and its reversal in a cylindrical annulus or 2D periodic RBC . 255
17.5 LSC and flow reversals in a cylinder ..............................256
17.5.1 Rotation-led reversals.....................................257
17.5.2 Cessation-led reversals....................................258
17.6 Reversals in dynamo and Kolmogorov flow............................260
17.7 Flow reversals: Low-dimensional or stochastic?.....................261
17.8 Summary of flow reversal studies...................................262
17.9 Structures in turbulence with and without walls....................263
17.10 Two-dimensionalization of large-Pr RBC............................263
Buoyant Flows with Rotation and Magnetic Field 267
18. Rotating Flows
269
xxiv Physics of Buoyant Flows: From Instabilities to Turbulence
18.1 Taylor-Proudman theorem...........................................269
18.2 Inertial wave ....................................................270
19. Buoyant and Rotating Flows 275
19.1 Stably stratified flow with rotation..............................275
19.2 Rotating convection ..............................................276
19.3 Some important results of rotating convection....................280
20. Magnetohydrodynamics and Rotating Flows 283
20.1 Alfvén waves......................................................284
20.2 Alfvén wave in rotating fluids....................................285
21. Buoyant Flows Under Magnetic Field 287
21.1 Stably stratified flows under magnetic field.....................287
21.2 Magnetoconvection.................................................288
22. Buoyant and Rotating Flows Under Magnetic Field 293
22.1 Stably stratified and rotating flow under magnetic field.........293
22.2 Magnetoconvection with rotation...................................294
23. Double Diffusive Convection 297
23.1 Linear instability analysis of double diffusive convection........297
24. Conclusions 301
Appendix A Thermal Parameters of Common Fluids 303
Appendix B Phase and Group Velocities of a Wave Packet 305
Appendix C Proper Orthogonal Decomposition of RBC 307
C.l Proper Orthogonal Decomposition (POD) ............................ 307
C.2 POD vs. Fourier modes ..............................................307
Bibliography 311
Index 323
Physics of Buoyant Flows
From Instabilities to Turbulence
Buoyancy drives fluids everywhere including those in the atmospheres and interiors
of planets and stars. Prime examples of such flows are in mantle convection,
atmospheres, solar convection, dynamos, heat exchangers, airships and hot air
balloons. Buoyancy also brings in extremely rich phenomena including waves and
instabilities, patterns, chaos, and turbulence. The book discusses these features
in the context of stable and and unstable stratification.
In the book we focus on buoyancy-driven turbulence, both in stably stratified flow
and in thermal convection. We discuss the spectral theory including energy flux
and show that thermally-driven turbulence is similar to hydrodynamic turbulence.
We also describe nonlinear saturation and pattern formation in Rayleigh-Bénard
convection, scaling of large-scale quantities like Reynolds and Nusselt numbers,
flow anisotropy, and the dynamics of flow structures, namely flow reversals. We
extend this analysis to include rotation and magnetic field.
This book presents all the major aspects of the buoyancy-driven flows in a coherent
and unified manner that would appeal to advanced graduate students and
researchers.
|
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| id | DE-604.BV045149978 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T08:10:05Z |
| institution | BVB |
| isbn | 9789813237797 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030539668 |
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| spelling | Verma, Mahendra K. 1966- Verfasser (DE-588)1165899922 aut Physics of buoyant flows from instabilities to turbulence Mahendra K Verma, Indian Institute of Technology Kanpur, India New Jersey World Scientific [2018] xxiv, 327 Seiten Illustrationen, Diagramme txt rdacontent n rdamedia nc rdacarrier Konvektion (DE-588)4117572-4 gnd rswk-swf Turbulente Strömung (DE-588)4117265-6 gnd rswk-swf Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Buoyant ascent (Hydrodynamics) Fluid dynamics Buoyant convection Turbulence Strömungsmechanik (DE-588)4077970-1 s Konvektion (DE-588)4117572-4 s Turbulente Strömung (DE-588)4117265-6 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=030539668&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 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=030539668&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Verma, Mahendra K. 1966- Physics of buoyant flows from instabilities to turbulence Konvektion (DE-588)4117572-4 gnd Turbulente Strömung (DE-588)4117265-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4117572-4 (DE-588)4117265-6 (DE-588)4077970-1 |
| title | Physics of buoyant flows from instabilities to turbulence |
| title_auth | Physics of buoyant flows from instabilities to turbulence |
| title_exact_search | Physics of buoyant flows from instabilities to turbulence |
| title_full | Physics of buoyant flows from instabilities to turbulence Mahendra K Verma, Indian Institute of Technology Kanpur, India |
| title_fullStr | Physics of buoyant flows from instabilities to turbulence Mahendra K Verma, Indian Institute of Technology Kanpur, India |
| title_full_unstemmed | Physics of buoyant flows from instabilities to turbulence Mahendra K Verma, Indian Institute of Technology Kanpur, India |
| title_short | Physics of buoyant flows |
| title_sort | physics of buoyant flows from instabilities to turbulence |
| title_sub | from instabilities to turbulence |
| topic | Konvektion (DE-588)4117572-4 gnd Turbulente Strömung (DE-588)4117265-6 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Konvektion Turbulente Strömung Strömungsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030539668&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=030539668&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
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