Turbulence

Slides from the first lecture. Note that exercises only start on March 7. Next week (Feb 28) we will use all four hours for lectures.
Since I don not have the resources to  record each lecture [as we do in our undergrad course ME-280] I will give you access to a recording of the course from a few years ago - in 2021 the course was held entirely online due to the health situation. 

 

Dear All - Sorry, I completely forgot about uploading the slides and the exercises. Since you now don't have time to look at them before class, we will postpone the discussion until next week and instead only have lectures on Friday - that's better than pushing you to look at the exercises until tomorrow afternoon.

This week, we discuss statistical tools and methods

This week we will start with the discussion of actual turbulence theory. Specifically, we will look at two experimental facts about high-Re turbulence. One of these facts will become an input of the theory and the other one, we try to derive. As I said in class, try to follow the logic of the derivation!

Since we pushed through all of the statistical methods last week (4h !!!!) and skipped exercises, we will do 2 hours of exercises this week. That means: Lecture 10-12 / Exercises 13-15. The topic will be exercise sheets 2 and 3, but please also bring any other questions you might have. The purpose of the exercises is for you to think and ask questions! See you on Friday!

This week we will continue the core of K41 turbulence theory. Specifically we

• Derive the Karman-Howarth-Monin relation that allows us to connect the energy flux term to the third order structure function
• This will get us almost to the famous 4/5 law... we will do the final step in the next class 

This week we finally derive Kolmogorov's famous four-fifth law and thereby "Declare Victory!!!"

This week, we will finish our formal discussion of the derivation of K41 theory and start interpreting the results physically - that means, we will discuss phenomenology. 

This week, we will finish our formal discussion of the derivation of K41 theory and start interpreting the results physically - that means, we will start discussing phenomenology. 

In addition, Omid will discuss more Chaos theory - and specifically the role of periodic orbits in chaos. 

Note that we uploaded both exercise sheets 5 and 6 including their solutions. Those will be discussed next Monday - so please have a look and if you have questions, bring them on Monday!

This week, we will release the course project. Moreover, we will discuss the solutions of the last 2 exercise sheets. That means, the schedule for the 4 hours is: 

• The Kolmogorov Cascade and Decaying Turbulence
  
• Intro: Course project 
  
• Discussion exercise sheets 5 and 6
  

Welcome back everyone!! This week, we have three exciting topics to discuss. These are (1) decaying turbulence (2) introduction of the course project and (3), we will have the first of two lectures on an alternative modern dynamical systems approach to study turbulence and chaos. 

The schedule for May 2nd  thus is: 

• 10-11h30: Lecture 
• 11h30 - 12h00: Introduction of the course project
• 13h00 - 15h00: Chaos Theory - Part 1 

Note that we will not discuss any exercise sheet this week!

The schedule for May 9th  thus is: 

• 10-12h00: Lecture 
• 13h00 - 15h00: Chaos Theory - Part 2
  

Reminder: This week we have no classes but only a Q&A session on (a) the project and (b) exercise sheet 7. We will meet from 10-12 in the regular room but cancel the afternoon session so that you can work on your project.

EXTRA Q&A Monday, May 26th 17h15: As promised, we are organizing an extra opportunity to ask questions about the project. Just come to ME A2 495, on Monday, between 17h15 and 18h45. Some of us will be available to answer questions. Unfortunately, I personally can't be there but my team members also know - don't worry!!

Also remember: The online submission deadline is on Friday - but there will not be a class for obvious reasons. 

For those of you, who I won't see during the exam session and summer: Have a great summer break!!!

Tobias Schneider

As discussed on Feb 21 2025 i am giving you access to the 2021 recordings. Due to the health situation the course was completely online - either live or I prerecorded lectures. Note that some aspects of the course are specific to 2021. Consequently, these recordings are not a replacement for showing up in class. If you have to miss a class, maybe the best option is to (a) get notes from your friends & (b) watch the video that covers roughly the same material. Hopefully these videos are still useful for you.