Introduction to Turbulence

Turbulence is the most dominant flow form in most technical and natural flows. The goal of the module is to obtain a view of the fundamental physical phenomena of turbulent flows.

General Informations

The students are going to learn the regularities for the statistic description of turbulence, based on the Navier-Stokes equations. These are in particular the two- and multi-point correlation equations as well as a set of special forms of these equations as in particular the Karman-Howarth equation for isotropic turbulence. Basic definitions for turbulent parameters such as length and time scales must be learned and understood. It follows the important Kolmogorov theory and turbulent energy spectra as well as extensions for higher correlations, which must be acquired and deduced by the students. With this basic knowledge the students learn a multiplicity of classical flow forms e.g. near-wall or free turbulent flows. These must be able to be outlined by the students and the respective scale laws must be able to be specified. Finally, approximation equations are dealt with. The different RANS concepts are introduced as well as the associated modelling concepts are described. The students must know the different model classes, distinguish them on the basis of their dis- and advantages as well as outline and clarify the main modelling concepts. The Large Eddy Simulation forms the conclusion of the approximation methods. The students must be able to describe the substantial ideas on the basis of equations, demonstrate advantages as well as carry out a delimitation of the RANS models. Finally the students should be able to evaluate the possibilities and limitations of all calculation methods.


1) Technical fluid dynamics or fundamentals of fluid mechanics,

2) ordinary and partial differential equation

Contents: Origin of turbulence and introduction of stability theory; introduction to turbulence and its statistical description; Reynolds decomposition, filtering and averaging the basic equations; correlation equations (one- and multi point); isotropic turbulence and the Karman-Howarth equation; turbulent decay; turbulent length-scales; Kolmogorov theory; energy spectrum; deeper investigations of isotropic turbulence (Intermittency); turbulent wall bounded flows; boundary and turbulent scaling laws; free shear flows; detached turbulent flows.

Regular cycle: Each Summer Semester


See Tucan

Office hours

By arrangement with Prof. Dr.-Ing. Martin Oberlack

Lecture Notes

See Moodle


Oral exams by arrangement with Prof. Dr.-Ing. Martin Oberlack

Lecturer | Assistant

Prof. Dr.-Ing. Martin Oberlack | Tim Gebler, M.Sc.


  • Pope: Turbulent Flows, Cambridge Universtity press 2000;
  • Davidson: Turbulence: an introduction for scientist and engineers;
  • Teenekes and Lumley: A first Course in turbulence;
  • Tsinober: An informal introduction to turbulence;
  • Rotta: Turbulente Strömungen, Teubner Verlag 1972.