(Vol. 14 from series Handbook of Numerical Analysis). Elsevier,
Amsterdam, London, New York, 2009, 777 pp. - ISBN:
978-0-444-51893-4
The development of the mode form of atmospheric sciences is generally traced back to John von Neumann and the meteorological school that he founded in the late 1950s and early 1960s. With such a prestigious background, there are well-established traditions of scientific interactions between specialists of atmospheric and oceans sciences and applied and computational mathematicians. The task is not easy, however, as each of the fields has considerably developed independently: specific problems, specific tools, specific methodologies, and often different languages. Nevertheless, interactions are indispensable. The demands for predictions are numerous, and the interests at task are considerable, from weather predictions for agriculture and many other economical motivations, or evolution of pollution, to large-scale problems like global warming.
Computational mathematicians, applied and numerical analysts, have a different approach. They tend to develop tools that are appropriate for the computational solution of various sorts of problems and equations. It is, therefore, natural to confront these new tools to the formidable problems of atmospheric and oceanic sciences. Mathematicians can also check the well posedness of certain problems and contribute to validate or set aside certain models and certain approaches. So the general purpose of this volume is to bring useful and important geophysical problems to the attention of mathematicians, and to present useful tools developed by mathematicians.
Contents.
Finite-Volume Methods in Meteorology – (Bennert Machenhauer, Eigil Kaas, Peter Hjort Lauritzen).
Computational Keel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations – (Alexander F. Shchepetkin, James С McWilliams).
Bifurcation Analysis of Ocean, Atmosphere, and Climate Models – (Eric Simonnet, HenkA. Dijkstra, Michael Ghil).
Time-Periodic Flows in Geophysical and Classical Fluid Dynamics – (R.M.Samelson).
Momentum Maps for Lattice EPDiff – (Colin J. Cotter, Darryl D. Holm).
Numerical Generation of Stochastic Differential Equations in Climate Models – (Brian Ewald, Cecile Penland).
Large-eddy Simulations for Geophysical Fluid Dynamics – (Marcel Lesieur, Olivier Metais).
Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions – (Pablo Mininni, Annick Pouquet, Peter Sullivan).
Data Assimilation for Geophysical Fluids – (Jacques Blum, Frangois-Xavier Le Dimet, I. Michael Navon).
Energetic Consistency and Coupling of the Mean and Covariance Dynamics – (Stephen E. Cohn).
Boundary Value Problems for the Inviscid Primitive Equations in Limited Domains – (Antoine Rousseau, Roger M. Temam, Joseph J. Tribbia).
Some Mathematical Problems in Geophysical Fluid Dynamics – (Madalina Petcu, Roger M. Temam, Mohammed Ziane).
The development of the mode form of atmospheric sciences is generally traced back to John von Neumann and the meteorological school that he founded in the late 1950s and early 1960s. With such a prestigious background, there are well-established traditions of scientific interactions between specialists of atmospheric and oceans sciences and applied and computational mathematicians. The task is not easy, however, as each of the fields has considerably developed independently: specific problems, specific tools, specific methodologies, and often different languages. Nevertheless, interactions are indispensable. The demands for predictions are numerous, and the interests at task are considerable, from weather predictions for agriculture and many other economical motivations, or evolution of pollution, to large-scale problems like global warming.
Computational mathematicians, applied and numerical analysts, have a different approach. They tend to develop tools that are appropriate for the computational solution of various sorts of problems and equations. It is, therefore, natural to confront these new tools to the formidable problems of atmospheric and oceanic sciences. Mathematicians can also check the well posedness of certain problems and contribute to validate or set aside certain models and certain approaches. So the general purpose of this volume is to bring useful and important geophysical problems to the attention of mathematicians, and to present useful tools developed by mathematicians.
Contents.
Finite-Volume Methods in Meteorology – (Bennert Machenhauer, Eigil Kaas, Peter Hjort Lauritzen).
Computational Keel Algorithms for Fine-Scale, Multiprocess, Longtime Oceanic Simulations – (Alexander F. Shchepetkin, James С McWilliams).
Bifurcation Analysis of Ocean, Atmosphere, and Climate Models – (Eric Simonnet, HenkA. Dijkstra, Michael Ghil).
Time-Periodic Flows in Geophysical and Classical Fluid Dynamics – (R.M.Samelson).
Momentum Maps for Lattice EPDiff – (Colin J. Cotter, Darryl D. Holm).
Numerical Generation of Stochastic Differential Equations in Climate Models – (Brian Ewald, Cecile Penland).
Large-eddy Simulations for Geophysical Fluid Dynamics – (Marcel Lesieur, Olivier Metais).
Two Examples from Geophysical and Astrophysical Turbulence on Modeling Disparate Scale Interactions – (Pablo Mininni, Annick Pouquet, Peter Sullivan).
Data Assimilation for Geophysical Fluids – (Jacques Blum, Frangois-Xavier Le Dimet, I. Michael Navon).
Energetic Consistency and Coupling of the Mean and Covariance Dynamics – (Stephen E. Cohn).
Boundary Value Problems for the Inviscid Primitive Equations in Limited Domains – (Antoine Rousseau, Roger M. Temam, Joseph J. Tribbia).
Some Mathematical Problems in Geophysical Fluid Dynamics – (Madalina Petcu, Roger M. Temam, Mohammed Ziane).