http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems. The simplifications often result in models that are amenable to solution both analytically and numerically. This volume and its companion explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations. They show how geometry and analysis facilitate solution strategies. -- Amazon.
Vol. 1. ANALYTICAL METHODS AND NUMERICAL MODEL: A view of the equations of meteorological dynamics and various approximations / A. A. White -- Extended-geostrophic Euler-Poincare models for mesoscale oceanographic flow / J. S. Allen, D. D. Holm and P. A. Newberger -- Fast singular oscillating limits of stably-stratified 3D Euler and Navier-Stokes equations and ageostrophic wave fronts / A. Babin, A. Mahalov and B. Nicolaenko -- New mathematical developments in atmosphere and ocean dynamics, and their application to computer simulations / M. J. P. Cullen -- Rearrangements of functions with applications to meteorology and ideal fluid flow / R. J. Douglas -- Statistical methods in atmospheric dynamics: probability metrics and discrepancy measures as a means of defining balance / S. Baigent and J. Norbury.
Vol. 2. GEOMETRIC METHODS AND MODELS: Balanced models in geophysical fluid dynamics: Hamiltonian formulation, constraints and formal stability / O. Bokhove -- The swinging spring: a simple model of atmospheric balance / P. Lynch -- On the stationary spectra for an ensemble of plane weakly nonlinear internal gravity waves / P. Caillol and V. Zeitlin -- Hamiltonian description of shear flow / N. J. Balmforth and P. J. Morrison -- Some applications of transformation theory in mechanics / M. J. Sewell -- Legendre-transformable semi-geostrophic theories / R. James Purser -- The Euler-Poincare equations in geophysical fluid dynamics / D. D. Holm, J. E. Marsden and T. Ratiu -- Are there higher-accuracy analogues of semi-geostrophic theory? / M. E. McIntyre and I. Roulstone.
edited by John Norbury and Ian Roulstone.
"[These] volumes are the result of the stimulus provided by the programme on The Mathematics of Atmosphere and Ocean Dynamics held at the Isaac Newton Institute for Mathematical Sciences in 1996, together with a follow-up meeting there in December 1997"--Preface.