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On the Geometry Arising in Some Meteorological Models in Two and Three Dimensions

  • Bertrand Banos
  • Volodya RoubtsovEmail author
  • Ian Roulstone
Chapter
Part of the Tutorials, Schools, and Workshops in the Mathematical Sciences book series (TSWMS)

Abstract

Using the formalism of Monge–Ampère operators, Roubtsov and Roulstone have shown in [15] that a complex geometry on phase space arises naturally in some two-dimensional Hamiltonian models of nearly geostrophic flows in hydrodynamics. The aim of this note is to show how a similar approach describes the geometry associated with a variety of semi-geostrophic and quasi-geostrophic models in two and three dimensions.

Notes

Acknowledgements

V.R. and I. R. express their deep thanks to organizers of the Summer School “Wisla 2018” and personally to Jerzy Szmit for a very stimulating summer school and for excellent working conditions. We are grateful to all participants for useful and fruitful discussions and inspiring atmosphere during the School.

During preparation of the material, V. R was partly supported by support of the Russian Foundation for Basic Research under the Grants RFBR 18-01-00461 and 19-51-53014 GFEN.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Bertrand Banos
    • 1
  • Volodya Roubtsov
    • 2
    • 3
    Email author
  • Ian Roulstone
    • 4
  1. 1.Faculté des sciences et sciences de l’ingénieur Bureau B125 - Sciences IIUniversité de Bretagne SudLorientFrance
  2. 2.Maths DepartmentUniversity of AngersAngersFrance
  3. 3.Theory Division, Math. Physics LabITEPMoscowRussia
  4. 4.Department of MathematicsUniversity of SurreyGuildfordUnited Kingdom

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