This special issue grew out of the symposium “Mathematics, waves and geophysical flow”, which took place in Bremen, 15–16 December 2016, and the workshop on “Geometric methods for geophysical fluid dynamics and climate modelling”, held in Hamburg, 5–7 June 2017. For all intents and purposes, the two symposia served as the kick-off to the mathematical part of the Collaborative Research Center TRR 181 “Energy Transfers in Atmosphere and Ocean” funded by the German Research Foundation; the second workshop also served as a complementary and methodological initiative within the excellence cluster “Integrated Climate System Analysis and Prediction” (CliSAP).
The TRR 181 aims at improving the energetic consistency of ocean and atmosphere models with the hope to further reduce biases and to increase the skill of those models. The research topics range from observations, understanding and modelling of physical processes to fundamental questions about coarse-graining, parameterisations, and numerical methods. CliSAP encompasses an even broader range of questions from climate variability and predictability to climate impacts.
Fundamentally, these activities root in mathematical descriptions of nature and employ mathematical tools at almost every step. Yet, mathematics proper, the art of deducing firm conclusions from a clearly stated set of assumptions through a chain of rigorous and irrefutable arguments, is frequently out of sync with the complexities of geophysical flow and earth system models. Complexity arises from multiple physics, multiple scales, the sheer number of essential degrees of freedom, and the fact that much of our knowledge, beyond observation, comes from numerical simulation with its own set of limitations and biases.
Thus, “mathematics” in the context of geophysical fluid dynamics – especially regarding the particular circle of questions raised – often contributes by looking at the subject with a mathematical mind: what are useful fundamental concepts and paradigms, what are limit cases, what are the fundamental trade-offs between different modelling strategies? Perhaps most importantly, mathematics tries to challenge the state of the art by questioning, or even identifying, the underlying assumptions.
The papers in this issue illustrate the diverse interactions when mathematical minds are confronted with challenges of geophysical fluid dynamics and earth system modelling. The papers revolve along three major themes: geometry, stochastic modelling, and (in)stability.
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