Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances

Edited by

  • Vladimir Zeitlin, University P. And M. Curie (Paris VI) – Ecole Normale Superieure

The rotating shallow water (RSW) model is of wide use as a conceptual tool in geophysical fluid dynamics (GFD), because, in spite of its simplicity, it contains all essential ingredients of atmosphere and ocean dynamics at the synoptic scale, especially in its two- (or multi-) layer version. The book describes recent advances in understanding (in the framework of RSW and related models) of some fundamental GFD problems, such as existence of the slow manifold, dynamical splitting of fast (inertia-gravity waves) and slow (vortices, Rossby waves) motions, nonlinear geostrophic adjustment and wave emission, the role of essentially nonlinear wave phenomena. The specificity of the book is that analytical, numerical, and experimental approaches are presented together and complement each other. Special attention is paid on explaining the methodology, e.g. multiple time-scale asymptotic expansions, averaging and removal of resonances, in what concerns theory, high-resolution finite-volume schemes, in what concerns numerical simulations, and turntable experiments with stratified fluids, in what concerns laboratory simulations. A general introduction into GFD is given at the beginning to introduce the problematics for non-specialists. At the same time, recent new results on nonlinear geostrophic adjustment, nonlinear waves, and equatorial dynamics, including some exact results on the existence of the slow manifold, wave breaking, and nonlinear wave solutions are presented for the first time in a systematic manner.
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Meteorology/Oceanography, Fluid dynamics, Applied mathematics/computational physics, Nonlinear physics


Book information

  • Published: April 2007
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-52258-0

Table of Contents

Preface1. V. Zeitlin, Introduction: fundamentals of rotating shallow water model in the geophysical fluid dynamics perspective2. G. Reznik and V. Zeitlin, Asymptotic methods with applications to the fast-slow splitting and the geostrophic adjustment3. S. Medvedev, The method of normal forms and fast-slow splitting4. F. Bouchut, Efficient numerical finite-volume schemes for shallow-water models5. V. Zeitlin, Nonlinear wave phenomena in rotating shallow water with applications to geostrophic adjustment6. A. Stegner, Experimental reality of geostrophic adjustment