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Multi-scale Methods for Geophysical Flows

  • Christian L. E. Franzke
  • Marcel OliverEmail author
  • Jens D. M. Rademacher
  • Gualtiero Badin
Chapter
Part of the Mathematics of Planet Earth book series (MPE, volume 1)

Abstract

Geophysical flows comprise a broad range of spatial and temporal scales, from planetary- to meso-scale and microscopic turbulence regimes. The relation of scales and flow phenomena is essential in order to validate and improve current numerical weather and climate prediction models. While regime separation is often possible on a formal level via multi-scale analysis, the systematic exploration, structure preservation, and mathematical details remain challenging. This chapter provides an entry to the literature and reviews fundamental notions as background for the later chapters in this collection and as a departure point for original research in the field.

Notes

Acknowledgements

We thank Sergey Danilov for helpful advice on several aspects of this paper, and Federica Gugole and Gözde Özden for careful proof reading of parts of the manuscript. CF was supported by the German Research Foundation (DFG) through the Cluster of Excellence CliSAP (EXC177) at the University of Hamburg and DFG grant FR3515/3-1. GB was partially supported by DFG grants FOR1740 and BA5068/8-1.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Christian L. E. Franzke
    • 1
  • Marcel Oliver
    • 2
    Email author
  • Jens D. M. Rademacher
    • 3
  • Gualtiero Badin
    • 1
  1. 1.Center for Earth System Research and Sustainability (CEN), Universität HamburgHamburgGermany
  2. 2.Jacobs UniversityBremenGermany
  3. 3.Fachbereich MathematikUniversität BremenBremenGermany

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