© 2019

Energy Transfers in Atmosphere and Ocean

  • Carsten Eden
  • Armin Iske


  • Gives a coherent and up-to-date overview over highly relevant interdisciplinary research activities between applied mathematics, meteorology, and physical oceanography, being funded by Deutsche Forschungsgemeinschaft via a collaborative research center

  • Covers a wide range of highly relevant topics relying on novel concepts from mathematical modelling and numerical simulation, wave processes, large-scale and balanced processes

  • Offers the reader to prepare themselves for research activities in this interdisciplinary area


Part of the Mathematics of Planet Earth book series (MPE, volume 1)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Christian L. E. Franzke, Marcel Oliver, Jens D. M. Rademacher, Gualtiero Badin
    Pages 1-51
  3. Jin-Song von Storch, Gualtiero Badin, Marcel Oliver
    Pages 53-85
  4. Dirk Olbers, Carsten Eden, Erich Becker, Friederike Pollmann, Johann Jungclaus
    Pages 87-125
  5. Christian Mertens, Janna Köhler, Maren Walter, Jin-Song von Storch, Monika Rhein
    Pages 127-143
  6. Sergey Danilov, Stephan Juricke, Anton Kutsenko, Marcel Oliver
    Pages 145-192
  7. Alexa Griesel, Julia Dräger-Dietel, Kerstin Jochumsen
    Pages 193-224
  8. Almut Gassmann, Richard Blender
    Pages 225-244
  9. Knut Klingbeil, Hans Burchard, Sergey Danilov, Claus Goetz, Armin Iske
    Pages 245-286
  10. Harald Garcke, Michael Hinze, Christian Kahle
    Pages 287-307
  11. Back Matter
    Pages 309-312

About this book


This book describes a recent effort combining interdisciplinary expertise within the Collaborative Research Centre “Energy transfers in atmosphere and ocean” (TRR-181), which was funded by the German Research Foundation (DFG). Energy transfers between the three dynamical regimes – small-scale turbulence, internal gravity waves and geostrophically balanced motion – are fundamental to the energy cycle of both the atmosphere and the ocean. Nonetheless, they remain poorly understood and quantified, and have yet to be adequately represented in today’s climate models.

Since interactions between the dynamical regimes ultimately link the smallest scales to the largest ones through a range of complex processes, understanding these interactions is essential to constructing atmosphere and ocean models and to predicting the future climate. To this end, TRR 181 combines expertise in applied mathematics, meteorology, and physical oceanography.

This book provides an overview of representative specific topics addressed by TRR 181, ranging from  

- a review of a coherent hierarchy of models using consistent scaling and approximations, and revealing the underlying Hamiltonian structure 
 - a systematic derivation and implementation of stochastic and backscatter parameterisations 
 - an exploration of the dissipation of large-scale mean or eddying balanced flow and ocean eddy parameterisations; and 
 - a study on gravity wave breaking and mixing, the interaction of waves with the mean flow and stratification, wave-wave interactions and gravity wave parameterisations

to topics of a more numerical nature such as the spurious mixing and dissipation of advection schemes, and direct numerical simulations of surface waves at the air-sea interface.

In TRR 181, the process-oriented topics presented here are complemented by an operationally oriented synthesis focusing on two climate models currently being developed in Germany. In this way, the goal of TRR 181 is to help reduce the biases in and increase the accuracy of atmosphere and ocean models, and ultimately to improve climate models and climate predictions.


mathematical modelling . numerical simulation energy transfers small-scale turbulence internal gravity waves geostrophically balanced motion ocean atmosphere atmosphere circulation eddy-parameterisation gravity wave-parameterisation stochastic-parameterisation backscatter-parameterisation balanced flow unbalanced flow

Editors and affiliations

  • Carsten Eden
    • 1
  • Armin Iske
    • 2
  1. 1.Center for Earth System Research and Sustainability (CEN)University of HamburgHamburgGermany
  2. 2.Department of MathematicsUniversity of HamburgHamburgGermany

About the editors

Carsten Eden is a full professor of theoretical oceanography at Universität Hamburg, Germany. He works on understanding the dynamics of the ocean circulation from the smallest to the largest scale and on parameterisations for ocean models.

Armin Iske is a full professor of mathematics at the University of Hamburg, Germany. His research interests include multivariate numerical approximation and scattered data analysis with applications to the simulation-based sciences. He has edited several volumes on approximation theory and numerical methods for computational sciences and engineering.

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