Turbulence in Fluids (NS-376B) (2022)

Bachelor program Physics, University of Utrecht

A level 3 course given by Anna von der Heydt and Aarnout van Delden

Tutorials by Edoardo Bellincioni and Sacha Sinet

The course is given in period 3 (February-April),

Lectures and tutorials every Monday and Wednesday morning

Information about the course on Osiris: link

Content
Instabilities of flows and their transition to turbulent behaviour are widespread phenomena in engineering, geophysical and astrophysical flows. Turbulence has become one of the most important unsolved problems in classical physics. This course offers the basic knowledge on turbulent fluid flows and their (numerical) modelling. The problem has two aspects: one is to understand why a fluid system becomes turbulent, i.e. shows complex structures both spatially and temporally; the other aspect has the goal to develop a potentially universal model of the transport properties of the flow in different scales. In this course both aspects will be covered using methods from dynamical systems theory (including bifurcation, chaos and fractals) and statistical physics. Exercises will introduce the student to numerical simulation of (turbulent) flows.

Learning outcomes
1. Able to distinguish between laminar and turbulent flows and characterise basic properties of each.
2. Able to perform linear stability analysis of basic examples of fluid flows.
3. Able to analyse basic instabilities and turbulence in fluid flows using key mathematical techniques: bifurcations and chaos, stochastic events, probabilistic description of turbulent flows.
4. Understand the physical mechanisms associated with fluid instabilities, such as the Kelvin Helmholtz instability and hydrostatic instability, leading to steady cellular flow patterns and many times to turbulent flow patterns.Understand how and why these flow patterns modify the background state, such as the basic therma stratification.
5. Understand basic theories on turbulent flows, such as dimensional and scaling arguments, conserved quantities, spectral cascade of turbulent energy, Kolmogorov theory and be able to apply their principles for geometrically simple flow conditions.
6. Have basic knowledge on intermittency and other corrections to the simplest theory and understand examples of how to model them numerically.
7. Able to calculate transport properties of basic turbulent flows.
8. Employment skills and knowledge
8a. Critically analyse practical problems and express them in physical/mathematical terms.
8b. Manage time efficiently and prioritise activities.

Schedule

See Osiris: link

Lectures

1. Introduction: refresher on hydrodynamics (Monday of week 7) : Anna von der Heydt

2. Statistical concepts and probability distributions (Wednesday of week 7) : Anna von der Heydt

3. Mean flow equations, Reynolds stresses (Monday of week 8) : Anna von der Heydt

4. Introduction to dynamical systems (Wednesday of week 8) : Anna von der Heydt

5. The advection equation (Monday of week 9) : Aarnout van Delden (Lecture5[TurbulenceFluids]_AdvectionEquation.pdf)

6. Thermal convection and hydrodynamic stability (Wednesday week 9) : Aarnout van Delden (Lecture6[TurbulenceFluids]_ThermalConvection].pdf)

7. Nonlinear thermal convection: the Lorenz (1963) model (Monday of week 10) : Aarnout van Delden (Lecture7[TurbulenceFluids]_ThermalConvection].pdf)

8. Chaos and predictability in the Lorenz model (Wednesday of week 10) : Aarnout van Delden (Lecture8[TurbulenceFluids]_Chaos&Predictability.pdf)

9. Nonlinear scale selection and spectral transfer of energy in two-dimensional convection (Monday of week 11) : Aarnout van Delden (Lecture9[TurbulenceFluids]_NonLinearScaleSelection.pdf)

10. Three-dimensional convection: horizontal planform selection (Wednesday of week 11) : Aarnout van Delden (Lecture10[TurbulenceFluids]_ConvectionPatterns.pdf)

11. Turbulent free shear flows I (Monday of week 12) : Anna von der Heydt

12. Turbulent free shear flows II (Wednesday of week 12) : Anna von der Heydt

13. Fully developed turbulence I ()(Monday of week 13) : Anna von der Heydt

14. Fully developed turbulence II (Wednesday of week 13) : Anna von der Heydt

15. Summary and questions (Wednesday of week 14) : Anna von der Heydt and Aarnout van Delden

Exercises

See the slides and lectures notes above

Exam

11 April 2022, 8:30-10:30h EDUC-AlFA - first half is analytical; second half is digital (bring your laptop)

a.j.vandelden@uu.nl (room 615 BBG)