The Resource Nonlinear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang
Nonlinear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang
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The item Nonlinear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Nonlinear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Extent
 xii, 551 pages
 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 BurgersHopf 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 quasigeostrophic equations
 256
 8.2
 The finitedimensional truncated quasigeostrophic 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 pseudoenergy 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
 Nonlinear 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 betaplane channel flow
 330
 11.3
 Statistical sharpness of statistical theories with few constraints
 346
 11.4
 More equations for geophysical flows
 The limit of manyconstraint theory (ESTMC) with small amplitude potential vorticity
 355
 12
 Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
 361
 12.2
 Metastability of equilibrium statistical structures with dissipation and smallscale forcing
 362
 12.3
 Crude closure for twodimensional 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 quasigeostrophic 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 largescale forcing
 A numerical laboratory for the role of higherorder invariants
 430
 14.3
 Comparison with equilibrium statistical predictions with a judicious prior
 438
 14.4
 Statistically relevant conserved quantities for the truncated BurgersHopf equation
 440
 A.1
 Spectral truncations of quasigeostrophic 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
 NonGaussian ensemble predictions in the Lorenz 96 model
 466
 15.4
 Information content beyond the climatology in ensemble predictions for the truncated BurgersHopf model
 472
 15.5
 Further developments in ensemble predictions and information theory
 478
 16
 Nonlinear stability with Kolomogorov forcing
 Barotropic quasigeostrophic equations on the sphere
 482
 16.2
 Exact solutions, conserved quantities, and nonlinear stability
 490
 16.3
 The response to largescale 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 twodimensional 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
 Energyenstrophy 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 betaplane effect
 107
 4
 Nonlinear 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
 Nonlinear stability of zonal flows on the betaplane
 129
 4.5
 Variational characterization of the steady states
 8
 133
 5
 Topographic mean flow interaction, nonlinear 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
 Isbn
 9780521834414
 Label
 Nonlinear dynamics and statistical theories for basic geophysical flows
 Title
 Nonlinear dynamics and statistical theories for basic geophysical flows
 Statement of responsibility
 Andrew J. Majda, Xiaoming Wang
 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
 StrÃ¶mungsmechanik
 Geophysik
 Nichtlineares mathematisches Modell
 Label
 Nonlinear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang
 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 BurgersHopf 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 quasigeostrophic equations
 256
 8.2
 The finitedimensional truncated quasigeostrophic 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 pseudoenergy 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
 Nonlinear 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 betaplane channel flow
 330
 11.3
 Statistical sharpness of statistical theories with few constraints
 346
 11.4
 More equations for geophysical flows
 The limit of manyconstraint theory (ESTMC) with small amplitude potential vorticity
 355
 12
 Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
 361
 12.2
 Metastability of equilibrium statistical structures with dissipation and smallscale forcing
 362
 12.3
 Crude closure for twodimensional 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 quasigeostrophic 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 largescale forcing
 A numerical laboratory for the role of higherorder invariants
 430
 14.3
 Comparison with equilibrium statistical predictions with a judicious prior
 438
 14.4
 Statistically relevant conserved quantities for the truncated BurgersHopf equation
 440
 A.1
 Spectral truncations of quasigeostrophic 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
 NonGaussian ensemble predictions in the Lorenz 96 model
 466
 15.4
 Information content beyond the climatology in ensemble predictions for the truncated BurgersHopf model
 472
 15.5
 Further developments in ensemble predictions and information theory
 478
 16
 Nonlinear stability with Kolomogorov forcing
 Barotropic quasigeostrophic equations on the sphere
 482
 16.2
 Exact solutions, conserved quantities, and nonlinear stability
 490
 16.3
 The response to largescale 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 twodimensional 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
 Energyenstrophy 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 betaplane effect
 107
 4
 Nonlinear 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
 Nonlinear stability of zonal flows on the betaplane
 129
 4.5
 Variational characterization of the steady states
 8
 133
 5
 Topographic mean flow interaction, nonlinear 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
 Nonlinear dynamics and statistical theories for basic geophysical flows, Andrew J. Majda, Xiaoming Wang
 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 BurgersHopf 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 quasigeostrophic equations
 256
 8.2
 The finitedimensional truncated quasigeostrophic 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 pseudoenergy 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
 Nonlinear 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 betaplane channel flow
 330
 11.3
 Statistical sharpness of statistical theories with few constraints
 346
 11.4
 More equations for geophysical flows
 The limit of manyconstraint theory (ESTMC) with small amplitude potential vorticity
 355
 12
 Equilibrium statistical theories and dynamical modeling of flows with forcing and dissipation
 361
 12.2
 Metastability of equilibrium statistical structures with dissipation and smallscale forcing
 362
 12.3
 Crude closure for twodimensional 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 quasigeostrophic 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 largescale forcing
 A numerical laboratory for the role of higherorder invariants
 430
 14.3
 Comparison with equilibrium statistical predictions with a judicious prior
 438
 14.4
 Statistically relevant conserved quantities for the truncated BurgersHopf equation
 440
 A.1
 Spectral truncations of quasigeostrophic 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
 NonGaussian ensemble predictions in the Lorenz 96 model
 466
 15.4
 Information content beyond the climatology in ensemble predictions for the truncated BurgersHopf model
 472
 15.5
 Further developments in ensemble predictions and information theory
 478
 16
 Nonlinear stability with Kolomogorov forcing
 Barotropic quasigeostrophic equations on the sphere
 482
 16.2
 Exact solutions, conserved quantities, and nonlinear stability
 490
 16.3
 The response to largescale 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 twodimensional 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
 Energyenstrophy 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 betaplane effect
 107
 4
 Nonlinear 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
 Nonlinear stability of zonal flows on the betaplane
 129
 4.5
 Variational characterization of the steady states
 8
 133
 5
 Topographic mean flow interaction, nonlinear 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
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