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Table of Contents

1. Course title

Turbulence Theory


2. Course code


Aikaisemmat leikkaavat opintojaksot 535041 Turbulenssioppi, 5 op

3. Course status: compulsory/optional

-Which degree programme is responsible for the course?
Master's Programme in Atmospheric Sciences

-Which module does the course belong to?
ATM300 Advanced Studies in Atmospheric Sciences
compulsory for

  • Study Track in Geophysics of the Hydrosphere

optional for

  • Study Track in Biogeochemical Cycles
  • Study Track in Meteorology

-Is the course available to students from other degree programmes?

4. Course level (first-, second-, third-cycle/EQF levels 6, 7 and 8)


Master’s level, degree programmes in medicine, dentistry and veterinary medicine = secondcycle
degree/EQF level 7
Doctoral level = third-cycle (doctoral) degree/EQF level 8


-Does the course belong to basic, intermediate or advanced studies (cf. Government Decree
on University Degrees)?
Advanced studies

5. Recommended time/stage of studies for completion

Can be taken in the early or later stages of studies.

6. Term/teaching period when the course will be offered

The course will be offered every second year in the spring term.

7. Scope of the course in credits

5 cr

8. Teacher coordinating the course

Ivan Mammarella

9. Course learning outcomes

-Description of the learning outcomes provided to students by the course
- See the competence map (

10. Course completion methods

The course will consists of lectures and exercises, and at the end of the course there will be an exam.

11. Prerequisites


12. Recommended optional studies


Recommended optional studies are:

13. Course content


  • Introduction: the origin and nature of turbulence, methods of analysis, diffusivity of turbulence.
  • The statistical description of turbulent flow: the probability density functions, Fourier transforms and characteristic functions, correlation functions and spectra.
  • Mean flow equations for momentum and heat: Reynolds equations, Reynolds stress, turbulent heat transfer.
  • The dynamics of turbulence: mean and turbulent kinetic energy, vorticity, dynamics of turbulent fluctuations.
  • Free shear flows: turbulent wakes, jets and mixing layer.
  • Wall-bounded shear flows: flows in pipes and channels, boundary layers.
  • Turbulent Spectra and the scales of turbulent motion.
  • Examples of turbulent transport in geophysical fluids.

14. Recommended and required literature


  • Lecture notes;
  • Tennekes, H. & J.L. Lumley, 1972. A First Course in Turbulence. The MIT Press.

15. Activities and teaching methods in support of learning

Weekly lectures and exercises (individual work).

16. Assessment practices and criteria, grading scale


To pass the course, the students need to do 1/3rd of the exercises.

The exercises will contribute to 25% of the overall grade. The rest 75% will be determined by the final exam.

17. Teaching language