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The Resource Non-linear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang

Non-linear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang

Label
Non-linear dynamics and statistical theories for basic geophysical flows
Title
Non-linear dynamics and statistical theories for basic geophysical flows
Statement of responsibility
Andrew J. Majda, Xiaoming Wang
Creator
Contributor
Subject
Language
eng
Cataloging source
UKM
http://library.link/vocab/creatorDate
1949-
http://library.link/vocab/creatorName
Majda, Andrew
Dewey number
551.01532051
Illustrations
illustrations
Index
index present
LC call number
QC809.F5
LC item number
M35 2006
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/relatedWorkOrContributorName
Wang, Xiaoming
http://library.link/vocab/subjectName
  • Geophysics
  • Fluid mechanics
  • Fluid dynamics
  • Geophysics
  • Statistical mechanics
  • Strömungsmechanik
  • Geophysik
  • Nichtlineares mathematisches Modell
Label
Non-linear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 33
  • 201
  • 6.6
  • An application of the maximum entropy principle to geophysical flows with topography
  • 204
  • 6.7
  • Application of the maximum entropy principle to geophysical flows with topography and mean flow
  • 211
  • 7
  • Equilibrium statistical mechanics for systems of ordinary differential equations
  • 219
  • 1.4
  • 7.2
  • Introduction to statistical mechanics for ODEs
  • 221
  • 7.3
  • Statistical mechanics for the truncated Burgers-Hopf equations
  • 229
  • 7.4
  • The Lorenz 96 model
  • 239
  • 8
  • Barotropic geophysical flows in a channel domain -- an important physical model
  • Statistical mechanics for the truncated quasi-geostrophic equations
  • 256
  • 8.2
  • The finite-dimensional truncated quasi-geostrophic equations
  • 258
  • 8.3
  • The statistical predictions for the truncated systems
  • 262
  • 8.4
  • Numerical evidence supporting the statistical prediction
  • 44
  • 264
  • 8.5
  • The pseudo-energy and equilibrium statistical mechanics for fluctuations about the mean
  • 267
  • 8.6
  • The continuum limit
  • 270
  • 8.7
  • The role of statistically relevant and irrelevant conserved quantities
  • 285
  • 1.5
  • 9
  • Empirical statistical theories for most probable states
  • 289
  • 9.2
  • Empirical statistical theories with a few constraints
  • 291
  • 9.3
  • The mean field statistical theory for point vortices
  • 299
  • 9.4
  • Variational derivatives and an optimization principle for elementary geophysical solutions
  • Empirical statistical theories with infinitely many constraints
  • 309
  • 9.5
  • Non-linear stability for the most probable mean fields
  • 313
  • 10
  • Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview
  • 317
  • 10.2
  • Basic issues regarding equilibrium statistical theories for geophysical flows
  • 50
  • 318
  • 10.3
  • The central role of equilibrium statistical theories with a judicious prior distribution and a few external constraints
  • 320
  • 10.4
  • The role of forcing and dissipation
  • 322
  • 10.5
  • Is there a complete statistical mechanics theory for ESTMC and ESTP?
  • 324
  • 1.6
  • 11
  • Predictions and comparison of equilibrium statistical theories
  • 328
  • 11.2
  • Predictions of the statistical theory with a judicious prior and a few external constraints for beta-plane channel flow
  • 330
  • 11.3
  • Statistical sharpness of statistical theories with few constraints
  • 346
  • 11.4
  • More equations for geophysical flows
  • The limit of many-constraint theory (ESTMC) with small amplitude potential vorticity
  • 355
  • 12
  • Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
  • 361
  • 12.2
  • Meta-stability of equilibrium statistical structures with dissipation and small-scale forcing
  • 362
  • 12.3
  • Crude closure for two-dimensional flows
  • 52
  • 385
  • 12.4
  • Remarks on the mathematical justifications of crude closure
  • 405
  • 13
  • Predicting the jets and spots on Jupiter by equilibrium statistical mechanics
  • 411
  • 13.2
  • The quasi-geostrophic model for interpreting observations and predictions for the weather layer of Jupiter
  • 417
  • 1
  • 2
  • 13.3
  • The ESTP with physically motivated prior distribution
  • 419
  • 13.4
  • Equilibrium statistical predictions for the jets and spots on Jupiter
  • 423
  • 14
  • The statistical relevance of additional conserved quantities for truncated geophysical flows
  • 427
  • 14.2
  • The response to large-scale forcing
  • A numerical laboratory for the role of higher-order invariants
  • 430
  • 14.3
  • Comparison with equilibrium statistical predictions with a judicious prior
  • 438
  • 14.4
  • Statistically relevant conserved quantities for the truncated Burgers-Hopf equation
  • 440
  • A.1
  • Spectral truncations of quasi-geostrophic flow with additional conserved quantities
  • 59
  • 442
  • 15
  • A mathematical framework for quantifying predictability utilizing relative entropy
  • 452
  • 15.1
  • Ensemble prediction and relative entropy as a measure of predictability
  • 452
  • 15.2
  • Quantifying predictability for a Gaussian prior distribution
  • 459
  • 2.2
  • 15.3
  • Non-Gaussian ensemble predictions in the Lorenz 96 model
  • 466
  • 15.4
  • Information content beyond the climatology in ensemble predictions for the truncated Burgers-Hopf model
  • 472
  • 15.5
  • Further developments in ensemble predictions and information theory
  • 478
  • 16
  • Non-linear stability with Kolomogorov forcing
  • Barotropic quasi-geostrophic equations on the sphere
  • 482
  • 16.2
  • Exact solutions, conserved quantities, and non-linear stability
  • 490
  • 16.3
  • The response to large-scale forcing
  • 510
  • 16.4
  • Selective decay on the sphere
  • 62
  • 516
  • 16.5
  • Energy enstrophy statistical theory on the unit sphere
  • 524
  • 16.6
  • Statistical theories with a few constraints and statistical theories with many constraints on the unit sphere
  • 536
  • 2.3
  • Stability of flows with generalized Kolmogorov forcing
  • 76
  • 3
  • Barotropic geophysical flows and two-dimensional fluid flows: elementary introduction
  • The selective decay principle for basic geophysical flows
  • 80
  • 3.2
  • Selective decay states and their invariance
  • 82
  • 3.3
  • Mathematical formulation of the selective decay principle
  • 84
  • 3.4
  • Energy-enstrophy decay
  • 1
  • 86
  • 3.5
  • Bounds on the Dirichlet quotient, [Lambda](t)
  • 88
  • 3.6
  • Rigorous theory for selective decay
  • 90
  • 3.7
  • Numerical experiments demonstrating facets of selective decay
  • 95
  • 1.2
  • A.1
  • Stronger controls on [Lambda](t)
  • 103
  • A.2
  • The proof of the mathematical form of the selective decay principle in the presence of the beta-plane effect
  • 107
  • 4
  • Non-linear stability of steady geophysical flows
  • 115
  • 4.2
  • Some special exact solutions
  • Stability of simple steady states
  • 116
  • 4.3
  • Stability for more general steady states
  • 124
  • 4.4
  • Non-linear stability of zonal flows on the beta-plane
  • 129
  • 4.5
  • Variational characterization of the steady states
  • 8
  • 133
  • 5
  • Topographic mean flow interaction, non-linear instability, and chaotic dynamics
  • 138
  • 5.2
  • Systems with layered topography
  • 141
  • 5.3
  • Integrable behavior
  • 145
  • 1.3
  • 5.4
  • A limit regime with chaotic solutions
  • 154
  • 5.5
  • Numerical experiments
  • 167
  • 6
  • Introduction to information theory and empirical statistical theory
  • 183
  • 6.2
  • Conserved quantities
  • Information theory and Shannon's entropy
  • 184
  • 6.3
  • Most probable states with prior distribution
  • 190
  • 6.4
  • Entropy for continuous measures on the line
  • 194
  • 6.5
  • Maximum entropy principle for continuous fields
Control code
62532870
Dimensions
26 cm
Extent
xii, 551 pages
Isbn
9780521834414
Isbn Type
(hbk.)
Lccn
2006295890
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other control number
9780521834414
Other physical details
illustrations
System control number
(OCoLC)62532870
Label
Non-linear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • 33
  • 201
  • 6.6
  • An application of the maximum entropy principle to geophysical flows with topography
  • 204
  • 6.7
  • Application of the maximum entropy principle to geophysical flows with topography and mean flow
  • 211
  • 7
  • Equilibrium statistical mechanics for systems of ordinary differential equations
  • 219
  • 1.4
  • 7.2
  • Introduction to statistical mechanics for ODEs
  • 221
  • 7.3
  • Statistical mechanics for the truncated Burgers-Hopf equations
  • 229
  • 7.4
  • The Lorenz 96 model
  • 239
  • 8
  • Barotropic geophysical flows in a channel domain -- an important physical model
  • Statistical mechanics for the truncated quasi-geostrophic equations
  • 256
  • 8.2
  • The finite-dimensional truncated quasi-geostrophic equations
  • 258
  • 8.3
  • The statistical predictions for the truncated systems
  • 262
  • 8.4
  • Numerical evidence supporting the statistical prediction
  • 44
  • 264
  • 8.5
  • The pseudo-energy and equilibrium statistical mechanics for fluctuations about the mean
  • 267
  • 8.6
  • The continuum limit
  • 270
  • 8.7
  • The role of statistically relevant and irrelevant conserved quantities
  • 285
  • 1.5
  • 9
  • Empirical statistical theories for most probable states
  • 289
  • 9.2
  • Empirical statistical theories with a few constraints
  • 291
  • 9.3
  • The mean field statistical theory for point vortices
  • 299
  • 9.4
  • Variational derivatives and an optimization principle for elementary geophysical solutions
  • Empirical statistical theories with infinitely many constraints
  • 309
  • 9.5
  • Non-linear stability for the most probable mean fields
  • 313
  • 10
  • Assessing the potential applicability of equilibrium statistical theories for geophysical flows: an overview
  • 317
  • 10.2
  • Basic issues regarding equilibrium statistical theories for geophysical flows
  • 50
  • 318
  • 10.3
  • The central role of equilibrium statistical theories with a judicious prior distribution and a few external constraints
  • 320
  • 10.4
  • The role of forcing and dissipation
  • 322
  • 10.5
  • Is there a complete statistical mechanics theory for ESTMC and ESTP?
  • 324
  • 1.6
  • 11
  • Predictions and comparison of equilibrium statistical theories
  • 328
  • 11.2
  • Predictions of the statistical theory with a judicious prior and a few external constraints for beta-plane channel flow
  • 330
  • 11.3
  • Statistical sharpness of statistical theories with few constraints
  • 346
  • 11.4
  • More equations for geophysical flows
  • The limit of many-constraint theory (ESTMC) with small amplitude potential vorticity
  • 355
  • 12
  • Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
  • 361
  • 12.2
  • Meta-stability of equilibrium statistical structures with dissipation and small-scale forcing
  • 362
  • 12.3
  • Crude closure for two-dimensional flows
  • 52
  • 385
  • 12.4
  • Remarks on the mathematical justifications of crude closure
  • 405
  • 13
  • Predicting the jets and spots on Jupiter by equilibrium statistical mechanics
  • 411
  • 13.2
  • The quasi-geostrophic model for interpreting observations and predictions for the weather layer of Jupiter
  • 417
  • 1
  • 2
  • 13.3
  • The ESTP with physically motivated prior distribution
  • 419
  • 13.4
  • Equilibrium statistical predictions for the jets and spots on Jupiter
  • 423
  • 14
  • The statistical relevance of additional conserved quantities for truncated geophysical flows
  • 427
  • 14.2
  • The response to large-scale forcing
  • A numerical laboratory for the role of higher-order invariants
  • 430
  • 14.3
  • Comparison with equilibrium statistical predictions with a judicious prior
  • 438
  • 14.4
  • Statistically relevant conserved quantities for the truncated Burgers-Hopf equation
  • 440
  • A.1
  • Spectral truncations of quasi-geostrophic flow with additional conserved quantities
  • 59
  • 442
  • 15
  • A mathematical framework for quantifying predictability utilizing relative entropy
  • 452
  • 15.1
  • Ensemble prediction and relative entropy as a measure of predictability
  • 452
  • 15.2
  • Quantifying predictability for a Gaussian prior distribution
  • 459
  • 2.2
  • 15.3
  • Non-Gaussian ensemble predictions in the Lorenz 96 model
  • 466
  • 15.4
  • Information content beyond the climatology in ensemble predictions for the truncated Burgers-Hopf model
  • 472
  • 15.5
  • Further developments in ensemble predictions and information theory
  • 478
  • 16
  • Non-linear stability with Kolomogorov forcing
  • Barotropic quasi-geostrophic equations on the sphere
  • 482
  • 16.2
  • Exact solutions, conserved quantities, and non-linear stability
  • 490
  • 16.3
  • The response to large-scale forcing
  • 510
  • 16.4
  • Selective decay on the sphere
  • 62
  • 516
  • 16.5
  • Energy enstrophy statistical theory on the unit sphere
  • 524
  • 16.6
  • Statistical theories with a few constraints and statistical theories with many constraints on the unit sphere
  • 536
  • 2.3
  • Stability of flows with generalized Kolmogorov forcing
  • 76
  • 3
  • Barotropic geophysical flows and two-dimensional fluid flows: elementary introduction
  • The selective decay principle for basic geophysical flows
  • 80
  • 3.2
  • Selective decay states and their invariance
  • 82
  • 3.3
  • Mathematical formulation of the selective decay principle
  • 84
  • 3.4
  • Energy-enstrophy decay
  • 1
  • 86
  • 3.5
  • Bounds on the Dirichlet quotient, [Lambda](t)
  • 88
  • 3.6
  • Rigorous theory for selective decay
  • 90
  • 3.7
  • Numerical experiments demonstrating facets of selective decay
  • 95
  • 1.2
  • A.1
  • Stronger controls on [Lambda](t)
  • 103
  • A.2
  • The proof of the mathematical form of the selective decay principle in the presence of the beta-plane effect
  • 107
  • 4
  • Non-linear stability of steady geophysical flows
  • 115
  • 4.2
  • Some special exact solutions
  • Stability of simple steady states
  • 116
  • 4.3
  • Stability for more general steady states
  • 124
  • 4.4
  • Non-linear stability of zonal flows on the beta-plane
  • 129
  • 4.5
  • Variational characterization of the steady states
  • 8
  • 133
  • 5
  • Topographic mean flow interaction, non-linear instability, and chaotic dynamics
  • 138
  • 5.2
  • Systems with layered topography
  • 141
  • 5.3
  • Integrable behavior
  • 145
  • 1.3
  • 5.4
  • A limit regime with chaotic solutions
  • 154
  • 5.5
  • Numerical experiments
  • 167
  • 6
  • Introduction to information theory and empirical statistical theory
  • 183
  • 6.2
  • Conserved quantities
  • Information theory and Shannon's entropy
  • 184
  • 6.3
  • Most probable states with prior distribution
  • 190
  • 6.4
  • Entropy for continuous measures on the line
  • 194
  • 6.5
  • Maximum entropy principle for continuous fields
Control code
62532870
Dimensions
26 cm
Extent
xii, 551 pages
Isbn
9780521834414
Isbn Type
(hbk.)
Lccn
2006295890
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other control number
9780521834414
Other physical details
illustrations
System control number
(OCoLC)62532870

Library Locations

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      201 Geological Sciences, Columbia, MO, 65211, US
      38.947375 -92.329062
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