### Timetable

### Description

Master’s Programme in Atmospheric Sciences is responsible for the course.

Module where the course belongs 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

The course is available to students from other degree programmes.

- Basics of dynamics of Newtonian fluids. Suitable course at the University of Helsinki is the BSc level course FYS2073 Virtausilmiöt (Fluid Phenomena).
- Basic knowledge on differential calculus (e.g. partial differential equations, tensors, etc).
- Other courses related to time-series analysis (ATM310 Time Series Analysis in Geosciences) may be useful.

Recommended optional studies are:

Can be taken in the early or later stages of studies. The course will be offered every second year in the spring term.

- 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.

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

Weekly lectures and exercises (individual work).

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.

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