Geophysical & Astrophysical Convection

392 Pages·2000·55.517 MB·\392

by  Peter A Fox (Editor), Robert M. Kerr (Editor)

GEOPHYSICAL AND ASTROPHYSICAL
CONVECTION
THE FLUID MECHANICS OF ASTROPHYSICS AND GEOPHYSICS
A series edited by ANDREW SOWARD,
University of Exeter, UK and
MICHAEL GHIL,
University of California, Los Angeles, USA
Founding Editor: PAUL ROBERTS,
University of California, Los Angeles, USA
Volume 1 SOLAR FLARE MAGNETOHYDRODYNAMICS
Edited by E.R. Priest
Volume 2 STELLAR AND PLANETARY MAGNETISM
Edited by AM. Soward
Volume 3 MAGNETIC FIELDS IN ASTROPHYSICS
Ya.B. Zeldovich, AA Ruzmaikin and D.D. Sokoloff
Volume 4 MANTLE CONVECTION: Plate Tectonics and Global Dynamics
Edited by w.R. Peltier
Volume 5 DIFFERENTIAL ROTATION AND STELLAR CONVECTION:
Sun and Solar-Type Stars
G. RUdiger
Volume 6 TURBULENCE, CURRENT SHEETS AND SHOCKS IN COSMIC
PLASMA
S.l Vaintshtein, AM. Bykov and IN. Toptygin
Volume 7 EARTH'S DEEP INTERIOR: The Doornbos Memorial Volume
Edited by D.l. Crossley
Volume 8 GEOPHYSICAL AND ASTROPHYSICAL CONVECTION
Edited by P.A. Fox and R.M. Kerr
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GEOPHYSICAL AND ASTROPHYSICAL
CONVECTION
Edited by
PETER A. FOX
National Center for Atmospheric Research
Boulder, Colorado, USA
and
ROBERT M. KERR
National Center for Atmospheric Research
Boulder, Colorado, USA
Contributions from a workshop sponsored by the Geophysical
Turbulence Program at the National Center for Atmospheric Research,
October 1995
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A catalogue record for this book is available from the British Library.
ISBN: 90-5699-258-9
ISSN: 0260-4353
Contents
List of Figures ix
List of Tables xii
Preface xiii
Acknowledgements xiv
1. Atmospheric Convection with Analogies in Astrophysics and the Laboratory 15
Robert M. Kerr
1.1 Introduction 15
1.2 Reynolds number and modeling 17
1.3 Dry convective scaling 20
1.4 Precipitating convection 23
1.5 Hierarchy of scales 27
1.6 Improving LES 30
1.7 Conclusion 32
2. Solar and Stellar Convection: A Perspective for Geophysical Fluid Dynamicists 37
Peter A. Gilman
2.1 Introduction 38
2.2 Solar motions 39
2.3 Global features of convection zone 43
2.3.1 Structure with radius 43
2.3.2 Influence of rotation 45
2.3.3 Upper boundary layer 45
2.3.4 Lower boundary layer 46
2.3.5 Waves and instabilities in and near the convection zone 47
2.4 Simulating solar convection 48
2.5 Summary of methods and results for compressible convection 49
2.6 Convection as driver of differential rotation 51
2.7 Interaction of the convection zone with the solar surfaces and the shear layer
at the base 52
2.8 Concluding remarks 54
3. Unsteady Non-Penetrative Thermal Convection From Non-Uniform Surfaces 59
Richard D. Keane, Noboyuki Fujisawa and Ronald J. Adrian
3.1 Introduction 59
3.2 Experimental apparatus and procedure 62
3.3 Results 65
3.3.1 Heat transfer characteristics 65
3.3.2 Existence of horizontal mean flow 67
3.3.3 Patterns of convection 67
3.4 Summary and conclusions 74
4. Astrophysical Convection and Dynamos 85
Axel Brandenburg, Ake Nordlund and Robert F. Stein
4.1 Introduction 85
4.2 Deep solar convection 87
4.3 Low Prandtl number effects 88
4.4 The entropy gradient 90
4.5 The thermal time scale problem 94
4.6 The formation of magnetic structures 97
4.7 Magnetic dynamo action 99
4.8 Downward pumping 100
4.9 Outstanding problems 101
5. Dynamics of Cumulus Entrainment 107
Wojciech W. Grabowski
5.1 Introduction 107
v
vi CONTENTS
5.2 Turbulent entrainment in cumulus clouds and in buoyancy-driven flows 111
5.3 Entrainment as a result of interfacial instabilities 113
5.4 Entraiument and buoyancy reversal 121
5.5 Conclusions 123
6. The 2/7 Law in Turbulent Thermal Convection 129
Stephane Zaleski
6.1 Introduction 129
6.2 Problem definition 130
6.3 Simple approaches to scaling 131
6.3.1 Similarity arguments based on dimensional analysis 131
6.3.2 Marginal stability and boundary layer similarity 132
6.4 Mechanistic approaches to scaling 133
6.4.1 Inviscid interior scaling 133
6.4.2 Plume theories with a single length scale 134
6.4.3 Plume theory with several length scales 135
6.4.4 2/7 scaling: Shraiman-Siggia theory 136
6.4.5 Range of validity 136
6.5 Comparison with experiments 138
6.6 Critique 139
6.7 Conclusion 140
7. Organization of Atmospheric Convection over the Tropical Oceans: The Role of Vertical
Shear and Buoyancy 145
Margaret A. LeMone
7.1 Introduction 145
7.2 Convection in the fair weather mixed layer 146
7.2.1 Larger aspect-ratio mixed-layer banded structures 149
7.3 Precipitating convection 152
7.3.1 Buoyancy 152
7.3.2 Shear 154
7.4 Conclusions 161
8. Images of Hard Turbulence: Buoyant Plumes in a Crosswind 165
Andrew Belrrwnte and Albert Libchaber
8.1 Introduction 165
8.2 Hard Turbulence 167
8.3 Experimental techniques 169
8.3.1 The convection cell 169
8.3.2 Visualization 170
8.3.3 bnage processing 172
8.4 Shadowgraph images 172
8.5 Intensity correlation measurements 177
8.6 Discussion 179
9. Convection in Cloud-Topped Atmospheric Boundary Layers 185
Christopher S. Bretherton
9.1 Introduction 185
9.2 Global distribution and importance of boundary layer cloud 186
9.3 Convective dynamics of CTBLs 190
9.4 Further observations and conclusions 195
10. Solar Granulation: A Surface Phenomenon 199
Mark Peter Rast
10.1 Introduction 200
10.2 Granular dynamics 201
10.3 Heat transport 207
10.4 Flow stability 211
10.5 Conclusion 216
11. Turbulent Convection: What has Rotation Taught Us? 221
Joseph Weme
11.1 Introduction 221
11.2 Nonrotating Rayleigh-Benard convection 222
11.3 Turbulent convection theories 223
CONTENTS vii
11.3.1 Priestley's theory 223
11.3.2 Kadanoff, Zaleski & Zanetti's theory 223
11.3.3 Shraiman & Siggia's theory 224
11.3.4 Cautionary comment on scaling theories 224
11.3.5 She's theory 225
11.3.6 Yakhot's theory 225
11.4 Rotating Rayleigh-Benard convection 226
11.5 Numerical simulation of rotating convection 226
11.5.1 Intermittent flow fields 227
11.5.2 Cyclonic plumes 227
11.5.3 Ekman pumping 227
11.5.4 Linear thermal Ekman layer 230
11.5.5 Nonlinear Ekman spirals 232
11.5.6 Plume-plume interactions 234
11.5.7 Rotating hard turbulence 235
11.6 Conclusions 236
12. Helical Buoyant Convection 241
Douglas Lilly
12.1 Rotating thunderstorms and tornadoes 241
12.2 Analysis and illustrations 244
12.3 Further discussion 250
13. Modeling Mantle Convection: A Significant Challenge in Geophysical Fluid Dynamics 257
David A. Yuen, S. Balachandar and U. Hansen
13.1 Introduction 258
13.2 Model and numerical techniques 259
13.2.1 Anelastic liquid model 260
13.2.2 Internal solid-state phase transitions 261
13.2.3 Thermal-chemical convection 262
13.2.4 Mantle rheology 263
13.2.5 Numerical methodologies 264
13.3 Past achievements and computational challenges 264
13.3.1 Sample past results 265
13.3.2 Computational requirements 268
13.4 Results 269
13.4.1 Viscous heating in mantle convection 269
13.4.2 High Rayleigh number thermal-chemical convection 271
13.5 Perspectives and future directions 273
14. Turbulent Transport in Rotating Compressible Convection 295
Nicholas H. Brummell
14.1 Introduction 295
14.2 Local modelling of rotating compressible convection 297
14.2.1 Turbulent transport of convective energy 299
14.2.2 Turbulent transport of (angular) momentum 302
14.3 Conclusions 306
15. Potential Vorticity, Resonance and Dissipation in Rotating Convective Turbulence 309
Peter Bartello
15.1 Background 310
15.2 Normal mode equations, conservation and resonance 312
15.2.1 The <GGG> interactions 314
15.2.2 The <AAA> interactions 314
15.2.3 The <GAA> interactions 314
15.2.4 The <GGA> interactions 314
15.3 Numerical Results 315
15.3.1 Metais et al. (1994) revisited 315
15.3.2 Simulations with large vertical dissipation 316
15.4 Conclusions 320
16. Numerical Simulations of Convection in Protostellar Accretion Disks 323
William Cabot
16.1 Introduction 323
16.1.1 What are protostellar accretion disks? 323
viii CONTENTS
16.1.2 Why is convection (potentially) important? 324
16.2 Properties of protostellar disks 326
16.2.1 General disk properties 326
16.2.2 Under what conditions do disks become convective? 326
16.2.3 Simplifying assumptions 327
16.3 Numerical hydrodynamic simulations 327
16.3.1 Further simplifying assumptions 327
16.3.2 Governing equations 329
16.3.3 Boundary conditions 330
16.3.4 Parameters 331
16.4 Simulation results 332
16.4.1 Incompressible simulations 332
16.4.2 Compressible simulations 332
16.5 Discussion 336
16.5.1 Why does disk convection generate inward transport of angular momentum? 339
16.5.2 What are the consequences? 340
16.5.3 What more needs to be done? 341
16.5.4 Conclusions 342
17. A New Model for Turbulence: Convection Rotation and 2D 345
V.M. Canuto, M.S. Dubovikov, A. Dienstfrey and D.J. Wielaard
17.1 Turbulent convection 345
17.1.1 New stochastic equations 345
17.1.2 Numerical results 347
17.1.3 Conclusions 347
17.2 Rotating turbulence 347
17 .2.1 Basic results 347
17.2.2 2D-3D states in rotating turbulence 352
17.2.3 Decaying turbulence 353
17.2.4 Conclusions 354
17.3 2D Turbulence 354
17.3.1 Basic features 354
17.3.2 Basic equations. Time evolution of the energy spectrum 354
17.3.3 Numerical results 355
17.3.4 Conclusions 357
18. Transport Using Transilient Matrices 363
Roland B. Stull and Jerzy Bartnicki
18.1 Introduction 363
18.2 A transilient turbulence parameterization 365
18.2.1 Mixing potential, Y, first estimate 366
18.2.2 Influences of nonlocal static stability 366
18.2.3 Convective overturning and subgrid turbulence 367
18.2.4 Unequal grid spacing 368
18.2.5 Transilient matrices 368
18.2.6 Use of transilient matrices 369
18.2.7 Turbulent flux and mixed-layer depth 369
18.3 Split time step and the destabilization problem 369
18.4 Calibration 371
18.5 lllustrative model 372
18.6 Simulation results for idealized scenarios 373
18.6.1 Neutral boundary layer 374
18.6.2 Unstable (free-convective) mixed layer 376
18.6.3 Mechanically mixed layer 377
18.6.4 Both buoyant and mechanically mixed layer 378
18.6.5 Stable boundary layer 378
18.6.6 Diurnal cycles of boundary layer forcings (including pollution dispersion) 380
18.6.7 Discussion 382
18.7 Conclusions 384
Index 389
List of Figures
1.1 Velocities from a Ra = 2 x 107, Prandtl number = 0.7, aspect ratio 6 direct
simulation of Rayleigh-Benard convection 16
1.2 Huid motion in Rayleigh-Benard convection in the hard turbulence regime 22
1.3 Deep convection results for CAPE in the boundary layer 25
1.4 Huid motions near a squall line (SL) that maintain precipitation 26
2.1 High resolution photograph of solar granulation 40
2.2 Full disk dopplergram from MDI instrument on SOHO 41
2.3 Differential rotation linear velocity and mean meridional flow 42
2.4 Structure of the solar convection zone 44
2.5 Schematic of angular momentum balance within the solar convection zone 53
3.1 Test-section schematic 62
3.2 Temperature history for the resistance wire thermometer 63
3.3 Nusselt number vs. flux Rayleigh number 66
3.4 How visualization of non-penetrative thermal convection 68
3.5 How visualization of non-penetrative thermal convection 69
3.6 Planform flow visualization of convection 70
3.7 Planform flow visualizations of convection 71
3.8 Sections of thermal plumes 73
3.9 Temperature distributions 77
3.10 Temperature distributions 78
3.11 Temperature distributions through a thermal plume 79
3.12 Temperature distributions through a thermal plume 80
3.13 Temperature distributions through a thermal plume 81
3.14 Temperature distributions through a thermal plume 82
3.15 Temperature distributions through a thermal plume 83
3.16 Temperature distributions through a thermal plume 84
4.1 Contours of horizontal slices of the density fluctuation and the vertical velocity 89
4.2 Profiles of entropy and convective flux 91
4.3 Profiles of entropy and convective flux 92
4.4 Evolution of two downdrafts shown in the entropy 93
4.5 Horizontal slices of the temperature through a downdraft 93
4.6 Histograms of cosines of angles between eigenvectors 96
4.7 Cosines of angles between different vector fields 97
4.8 Power spectra of the kinetic and magnetic energy, temperature fluctuation, and
kinetic and magnetic helicities 98
4.9 Snapshots of a strong magnetic flux tube 99
4.10 Evolution of magnetic and kinetic energy and magnetic Taylor microscale 100
4.11 Three-dimensional image of the magnetic energy density 101
4.12 Three-dimensional image of the enstrophy density 102
4.13 Three-dimensional visualisation of vorticity 103
5.1 Example of the lower-tropospheric sounding and analysis of convection 108
5.2 Results of the mixing analysis 110
5.3 Fields of the cloud water and the perturbation streamfunction 114
5.4 Three-dimensional perspective of the cloud water field 116
5.5 Profiles of the velocity tangential to the interface 117
5.6 Average buoyancy and shear production of perturbation kinetic energy 118
7.1 Structure of the fair weather tropical atmospheric boundary layer over the ocean 147
7.2 Radar-reflectivity patterns in the fair-weather boundary layer 148
7.3 Fair-weather banded structures over the tropical ocean 150
7.4 Schematic showing how mixed-layer convention induces gravity waves 151
7.5 Thermodynamic profiles for tropical convention 153
7.6 Updraft magnitudes over the tropical oceans 155
ix