Turbulence and dynamos for astrophysicists (1/5)

This is a 5 part black board lecture on Turbulence by Prof. Anvar Shukurov. This lecture was presented already in 2016 and had a very positiv resonance among our students. We are glad that Prof. Shukurov willing to hold this lecture again, this year with an additional part on dimensional analysis.

The lecture will be presented in hybrid format and also include some exercises and problems.

Lecture hours have been extended with additional sessions so that the material can be presented in a more understandable and less rushed manner.

The extended times for the lecture are now

Monday, 10-12 and 15-16

Tuesday, 09-11 and 15:30-16:30

Wednesday 10-12 and 13-14

Thursday, 10-12 and 13-14

Friday, 14-17

Please regsiter in advance so we get an overview how many participants we can expect!

Syllabus (tentative)

Introduction

• Turbulence and its defining features
• Significance of turbulence

Elements of random functions

• Ensemble, volume and time averaging
• The Reynolds rules of averaging
• Correlation and structure functions
• Stationary random functions
• Spectral representation
• Correlation versus statistical dependence

Dimensional analysis [New]

Phenomenology of fluid turbulence

• Energy conservation
• Spectral energy transfer
• The Reynolds number
• Kolmogorov's theory
• Turbulent diffusion

Interstellar turbulence

• Energy sources
• Turbulence driven by supernovae
• Observational signatures
• Parameters of interstellar turbulence
• The role of turbulence in galaxies

Magnetohydrodynamic turbulence

• Isotropic Alfven wave turbulence
• Anisotropic Alfven wave turbulence

Turbulent dynamos

• The induction equation
• The necessity of dynamo action in astrophysics
• Fast and slow dynamos
• Turbulent dynamos
• Mean-field dynamos in galaxies
• Fluctuation dynamos
• Seed magnetic fields