Content:

Mathematics plays a central role in the development and analysis of models for weather and climate prediction. Controlled physical experiments are out of the question, so that the only way we can study Earth’s weather and climate is through mathematical models, computational experiments, and data analysis.

Fluctuations in daily weather are tightly connected to turbulence, and turbulence represents a challenge for the predictability of weather. No general solution for the equations of fluid motion is known, and specifically no general solutions to flow problems involving turbulence are available. Instead, scientists rely on conceptual models, complex computer simnulations, and advanced statistics and time series analysis to understand the essence of the daily weather and how it feeds back onto the climate.

This course/seminar focuses on techniques of mathematical modeling that assist scientists in exploring the listed issues systematically.

The course will cover a selection from the following topics

1. Conservation laws and governing equations,

2. Numerical methods for geophysical flow simulations,

3. Dynamical systems and bifurcation theory,

4. Data-based characterization of atmospheric flows

Literaturhinweise werden anfangs des Semesters in Abhängigkeit von
der Themenauswahl gegeben.  

Interessante Startpunkte, die einen ersten Einstieg in obige drei
Hauptpunkte erlauben, sind  

Klein R.,
Scale-Dependent Asymptotic Models for Atmospheric Flows,
Ann. Rev. Fluid Mech., vol. 42, 249-274 (2010)

D. Durran, 
Numerical Methods for Fluid Dynamics with Applications to Geophysics, 
Springer, Computational Science and Engineering Series, (2010)

Metzner Ph., Putzig L., Horenko I.,
Analysis of persistent nonstationary time series and applications
Comm. Appl. Math. & Comput. Sci., vol. 7, 175-229 (2012)

Tennekes and Lumley, A first course in Turbulence, MIT Press (1974)