Course content

The course covers advanced topics in turbulence. The primary purpose of the course is to ensure that students have a working knowledge of contemporary problems in turbulence as well as a thorough understanding of what is considered canonical knowledge. This begins by studying Kolmogorov's original work and its implications, and then touches on various advanced topics in turbulence by addressing canonical turbulent flows (periodic box turbulence, grid turbulence, channel flows, pipe flows, and boundary layers). This course is taught in the autumn of odd numbered years; e.g., autumn 2025, autumn 2027, and so on. It will not be taught in autumn 2024.

Learning outcome

Knowledge: •

• Turbulent cascade •
• Turbulent kinetic energy equation •
• Turbulence spectra, structure functions, and scalings of both
• Kolmogorov's laws and similarity hypotheses •
• Expectations for the evolution and decay of turbulent kinetic energy in different flows •
• Common non-dimensionalisations in turbulence and their significance •
• Correlations in turbulent flows •
• Relevant length, velocity and time scales in different flows •
• Considerations for setting up simulations (e.g., DNS, LES) •
• Law-of-the-wall •
• Velocity and variance profiles for wall-bounded flows •
• Limitations on high Reynolds number experiments and simulations

Skills: •

• Identify turbulent spectrum, correlation, and structure functions by appearance. •
• Understand the relevant non-dimensionalisation of turbulent parameters in different scenarios. •
• Understand the limitations on both experiments and simulations, and how to optimise conditions within them.

General competence: •

• Prepare short presentations in a group. •
• Read journal articles and discuss their content. •
• Discuss and formulate pointed questions on advanced scientific topics. •
• Understand the scientific and paper-publishing process.

Learning methods and activities

The general structure of the course is that there are classes that occur once every 2 weeks. Classes are approximately 3 hours. During a class, there is a short lecture period, and the remainder is made-up of student presentations and discussion. Students are assigned a task (sometimes in groups) based on a set of readings for each class. This task is then shared with the group, and a discussion follows. Participation in student tasks and attendance are optional, however, given this is the primary form of content delivery, it would be very difficult to pass the exam without attending the majority of the classes. All meetings are conducted in English.

Required previous knowledge

A strong foundation in fluid mechanics and an introduction to turbulence (including the Reynolds Averaged Navier-Stokes equations).

Course materials

Notes are to be taken in class based on the lectures, student assignments and group discussions. Example readings from previous years are (students are not necessarily expected to read this entire list):

• Kolmogorov (Dokl Akad Nauk SSSR, 1941a,b,c)
• Comte-Bellot & Corrsin (J Fluid Mech, 1966)
• Kim, Moin & Moser (J Fluid Mech, 1987)
• Lumley (Phys Fluids, 1992)
• Jiménez (Arbor, 2004)
• Smits, McKeon, Marusic (Ann Rev Fluid Mech, 2011)
• Valente & Vassilicos (J Fluid Mech, 2011)
• Krogstad & Davidson (J Fluid Mech, 2011)
• Marusic, Monty, Hultmark & Smits (J Fluid Mech, 2013)
• Hearst & Lavoie (J Fluid Mech, 2014)
• Vassilicos (Ann Rev Fluid Mech, 2015)
• Cardesa, Vela-Martín & Jiménez (Science, 2017)

In addition, the following textbook is highly recommended for anyone who intends to continue their education in turbulence, however, no readings or assignments are directly drawn from it:

• Pope (2000) Turbulent Flows, Cambridge University Press, UK.

Credit reductions