Nonlinear Dynamics of Rotating Shallow Water: Methods and Advances, Volume 2

1st Edition

Series Volume Editors: Vladimir Zeitlin
Hardcover ISBN: 9780444522580
eBook ISBN: 9780080489469
Imprint: Elsevier Science
Published Date: 3rd April 2007
Page Count: 400
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Table of Contents


  1. V. Zeitlin, Introduction: fundamentals of rotating shallow water model in the geophysical fluid dynamics perspective
  2. G. Reznik and V. Zeitlin, Asymptotic methods with applications to the fast-slow splitting and the geostrophic adjustment
  3. S. Medvedev, The method of normal forms and fast-slow splitting
  4. F. Bouchut, Efficient numerical finite-volume schemes for shallow-water models
  5. V. Zeitlin, Nonlinear wave phenomena in rotating shallow water with applications to geostrophic adjustment
  6. A. Stegner, Experimental reality of geostrophic adjustment


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.

Key Features

· Incorporates analytical, numerical and experimental approaches in the geophysical fluid dynamics context · Combination of essentials in GFD, of the description of analytical, numerical and experimental methods (tutorial part), and new results obtained by these methods (original part) · Provides the link between GFD and mechanics (averaging method, the method of normal forms); GFD and nonlinear physics (shocks, solitons, modons, anomalous transport, periodic nonlinear waves)


Meteorology/Oceanography, Fluid dynamics, Applied mathematics/computational physics, Nonlinear physics


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© Elsevier Science 2007
Elsevier Science
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About the Series Volume Editors

Vladimir Zeitlin Series Volume Editor

Being trained as theoretical physicists (thesis on quantum field theory and elementary particles) switched to geophysical fluid dynamics (GFD) in early 1980s. Worked at the Institute of Atmospheric Physics (Moscow) on vortex dynamics, wave-vortex interactions and turbulence. After moving to France joined Laboratory of Dynamical Meteorology and got professorship at Paris VI. Teaching GFD for years. Last years lead research focused on fundamental problems in GFD. Much in this direction was done using the simplest conceptual rotating shallow water model or its multi-layer versions -reported in the book.

Affiliations and Expertise

University P. And M. Curie (Paris VI) – Ecole Normale Superieure