Global atmospheric and oceanic modelling : fundamental equations

著者

    • Staniforth, Andrew N.

書誌事項

Global atmospheric and oceanic modelling : fundamental equations

Andrew N. Staniforth

Cambridge University Press, 2022

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注記

Includes bibliographical references and index

内容説明・目次

内容説明

Combining rigorous theory with practical application, this book provides a unified and detailed account of the fundamental equations governing atmospheric and oceanic fluid flow on which global, quantitative models of weather and climate prediction are founded. It lays the foundation for more accurate models by making fewer approximations and imposing dynamical and thermodynamical consistency, moving beyond the assumption that the Earth is perfectly spherical. A general set of equations is developed in a standard notation with clearly stated assumptions, limitations, and important properties. Some exact, non-linear solutions are developed to promote further understanding and for testing purposes. This book contains a thorough consideration of the fundamental equations for atmospheric and oceanic models, and is therefore invaluable to both theoreticians and numerical modellers. It also stands as an accessible source for reference purposes.

目次

  • Preface. Notation and acronyms. Part I. Foundations: 1. Introduction
  • 2. Governing equations for motion of a dry atmosphere: Vector form
  • 3. Governing equations for motion of a cloudy atmosphere: Vector form
  • 4. Governing equations for motion of geophysical fluids: Vector form
  • 5. Orthogonal curvilinear coordinate systems
  • 6. Governing equations for motion of geophysical fluids: Curvilinear form
  • 7. Representation of gravity: Basic theory and spherical planets
  • 8. Representation of gravity: Further theory and spheroidal planets
  • 9. Thermodynamic potentials and thermodynamical consistency
  • 10. Moist thermodynamics
  • 11. Ocean thermodynamics
  • 12. Geopotential coordinates for modelling planetary atmospheres and oceans
  • 13. Vertical coordinates and boundary conditions
  • 14. Variational methods and Hamilton's principle of stationary action
  • 15. Conservation. Part II. Dynamically Consistent Equation Sets: 16. Deep and shallow equation sets in 3D
  • 17. Quasi-shallow equation sets in 3D
  • 18. Shallow water equation sets in 2D
  • 19. A barotropic potential vorticity (BPV) equation for flow over a spheroidal planet. Part III. Exact Steady and Unsteady Nonlinear Solutions: 20. Exact steady solutions of the global shallow water equations
  • 21. Exact 3D steady solutions of global equation sets
  • 22. Exact unsteady solutions of the barotropic potential vorticity equation over an ellipsoid
  • 23. Exact unsteady solutions in 3D over an ellipsoidal planet. Appendix. References. Index.

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