Turbulence in neutral Fluids und Plasmas

This module gives an introduction into turbulence research. It encompasses experimental observations as well was as intuitive model-based and theoretical approaches to describe turbulent processes. Starting point is the physics of low-dimensional chaotic systems. After a brief introduction into the basics of neutral fluids and magnetized plasmas the most important linear instabilities will be discussed before the influence of different types of nonlinearities on the dynamics of the fluid is demonstrated. Next fully developed turbulence will be treated for three- and two-dimensional fluids with an emphasis on magnetized plasmas. The different concepts will be illustrated with examples from astrophysics, fusion research and engineering sciences.  The lectures will be accompanied by computer exercises using numerical techniques to analyze time traces from turbulence experiments. This includes Fourier and wavelet techniques as well as non-linear methods such as bicoherence analyses.

After successful completion of this module the student is able to

1. explain the basic properties of turbulence
2. name the characteristic differences between chaos and turbulence
3. explain the important mechanisms leading to linear instabilities
4. describe experimental techniques to investigate turbulence
5. apply the basic numerical techniques to analyze turbulent time traces

Lectures up to the Bachelor level

The modul consists of a lecture and exercise classes.

In classroom lectures the teaching and learning content is presented by black board teaching and overhead slides in a didactical, structured, and comprehensive form. This includes basic knowledge as well as selected current topics from a very broad research field. Crucial facts are conveyed by involving the students in scientific discussions to develop their intellectual power and to stimulate their analytic thinking on physics problems. Regular attendance of the lectures is therefore recommended. Regular self-study of personal notes from the lectures and of textbooks are an important part of the learning process by the students. Such post-processing and practicing of the teaching content is indispensable to achieve the intended learning results that the students develop the ability of explaining and applying the learned knowledge independently.

In the exercise the learning content is deepened and exercised using problem examples and state of the art analysis programs. Thus the students are able to apply the learned physics knowledge independently.

Blackboard lecture, overhead presentations (powerpoint), discussion, complentary internet page, complentary literature, exercises in idividual and group workpractise sheets

• P.A. Davidson: Turbulence: An Introduction for Scientists and Engineers, Oxford University Press, (2004)
• U. Frisch: Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, (1995)
• S.B. Pope: Turbulent Flows, Cambridge University Press, (2000)
• U. Stroth: Plasmaphysik: Phänomene, Grundlagen, Anwendungen, Springer, (2017)

There will be an oral exam of 25 minutes duration. Therein the achievement of the competencies given in section learning outcome is tested exemplarily at least to the given cognition level using comprehension questions, sample calculations, discussion and sketches.

For example an assignment in the exam might be:

• Describe the turbulent cascade in two and three-dimensional turbulence
• Write down the Navier-Stokes and Hasegawa-Wakatani equations. Compare the different terms of both equations sets against each other.
• Discuss what determines the dissipation rate in turbulent systems
• Characterize different kinds of intermittent behavior
• Assess advantages and disadvantages of the conditional average technique.
• Explain the interchange instability and drift-wave and compare them against each other.

In the exam no learning aids are permitted.