This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.
• Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics
• Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences
• Contributions uniquely address central problems and provide a survey of the frontier of research
1. 1 Introduction 2. 2 Transport schemes in one and two dimensions 3. 3 FV models 4. 4 Summary 5. 5 Acknowledgments 6. Computational Kernel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations 7. Nonlinear Methods (Part 2) 8. Bifurcation Analysis of Ocean, Atmosphere, and Climate Models 9. Time-Periodic Flows in Geophysical and Classical Fluid Dynamics 10. Momentum Maps for Lattice EPDiff 11. Numerical Generation of Stochastic Differential Equations in Climate Models 12. Turbulence (Part 3) 13. Large-eddy Simulations for Geophysical Fluid Dynamics 14. Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions 15. Data Assimilation (Part 4) 16. Data Assimilation for Geophysical Fluids 17. Energetic Consistency and Coupling of the Mean and Covariance Dynamics 18. Analysis (Part 5) 19. Boundary Value Problems for the Inviscid Primitive Equations in Limited Domains 20. Abstract 21. 1 Introduction 22. 2 Two-dimensional x – z case 23. 3 Space dimension 2.5 24. 4 The full 3D linear case 25. 5 Conclusion 26. 6 Acknowledgments 27. Some Mathematical Problems in Geophysical Fluid Dynamics 28. Abstract 29. 1 Introduction 30. 2 The PEs: weak formulation, existence of weak solutions 31. 3 Strong solutions of the PEs in dimensions 2 and 3 32. 4 Regularity for the elliptic linear problems in geophysical fluid dynamics 33. 5 Acknowledgments 34. Index 35. Color Plate Section
This book provides a survey of the frontiers of research in the numerical modeling and mathematical analysis used in the study of the atmosphere and oceans. The details of the current practices in global atmospheric and ocean models, the assimilation of observational data into such models and the numerical techniques used in theoretical analysis of the atmosphere and ocean are among the topics covered.
• Truly interdisciplinary: scientific interactions between specialties of atmospheric and ocean sciences and applied and computational mathematics
• Uses the approach of computational mathematicians, applied and numerical analysts and the tools appropriate for unsolved problems in the atmospheric and oceanic sciences
• Contributions uniquely address central problems and provide a survey of the frontier of research
1. 1 Introduction 2. 2 Transport schemes in one and two dimensions 3. 3 FV models 4. 4 Summary 5. 5 Acknowledgments 6. Computational Kernel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations 7. Nonlinear Methods (Part 2) 8. Bifurcation Analysis of Ocean, Atmosphere, and Climate Models 9. Time-Periodic Flows in Geophysical and Classical Fluid Dynamics 10. Momentum Maps for Lattice EPDiff 11. Numerical Generation of Stochastic Differential Equations in Climate Models 12. Turbulence (Part 3) 13. Large-eddy Simulations for Geophysical Fluid Dynamics 14. Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions 15. Data Assimilation (Part 4) 16. Data Assimilation for Geophysical Fluids 17. Energetic Consistency and Coupling of the Mean and Covariance Dynamics 18. Analysis (Part 5) 19. Boundary Value Problems for the Inviscid Primitive Equations in Limited Domains 20. Abstract 21. 1 Introduction 22. 2 Two-dimensional x – z case 23. 3 Space dimension 2.5 24. 4 The full 3D linear case 25. 5 Conclusion 26. 6 Acknowledgments 27. Some Mathematical Problems in Geophysical Fluid Dynamics 28. Abstract 29. 1 Introduction 30. 2 The PEs: weak formulation, existence of weak solutions 31. 3 Strong solutions of the PEs in dimensions 2 and 3 32. 4 Regularity for the elliptic linear problems in geophysical fluid dynamics 33. 5 Acknowledgments 34. Index 35. Color Plate Section
