Geophysical and astrophysical convection
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Geophysical and astrophysical convection / ed. by Fox P.A., Kerr R.M. - Amsterdam: Gordon and Breach, 2000. - 390 p. - (Fluid mechanics of astrophysics and geophysics; vol.8). - ISBN 90-5699-258-9.
 
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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
    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 Entrainment 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 Belmonte 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 Image 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 Werne
    11.1 Introduction ...................................................... 221
    11.2 Nonrotating Rayleigh-Benard convection ............................ 222
    11.3 Turbulent convection theories ..................................... 223
         11.3.1 Priestley's theory ......................................... 223
         11.3.2 Kadanoff, Zaleski and Zanetti's theory ..................... 223
         11.3.3 Shraiman and 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
         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 Illustrative 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


Вверх Geophysical and astrophysical convection / ed. by Fox P.A., Kerr R.M. - Amsterdam: Gordon and Breach, 2000. - 390 p. - (Fluid mechanics of astrophysics and geophysics; vol.8). - ISBN 90-5699-258-9.

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