# MEK9350 – Stochastic and Nonlinear Ocean Waves

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## Changes in the course due to coronavirus

Autumn 2020 we plan for teaching and examinations to be conducted as described in the course description and on semester pages. However, changes may occur due to the corona situation. You will receive notifications about any changes at the semester page and/or in Canvas.

Spring 2020: Teaching and examinations was digitilized. See changes and common guidelines for exams at the MN faculty spring 2020.

## Course content

An introduction is given to stochastic description of ocean waves, wave spectrum, wave statistics, and definition of freak waves. An introduction is also given to nonlinear wave resonance, free and bound waves, models for nonlinear wave evolution, and modulational instability.

## Learning outcome

After completing the course you will :

• know how to compute the Fourier transform, Fourier series and DFT (Discrete Fourier Transform) by hand and on computer, and account for the relationship between Fourier series and DFT, aliasing, Nyquist frequency and Parsevals theorem;
• know how to describe ocean waves as a stochastic process, and have knowledge of relevant properties for stochastic processes for ocean waves such as stationary and weakly stationary process, ergodic process and narrow band process;
• have knowledge of elementary wave statistics including skewness and kurtosis. Relevant distributions including normal distribution and Rayleigh distribution;
• be able to explain what we mean by Gaussian sea, wave height, significant wave height, crest height and freak waves;
• know how to compute the wave spectrum as the Fourier transform of the auto correlation function and use the Fourier transform to estimate spectrum;
• know about spectrum in several dimensions, including wave vector spectrum, wavenumber spectrum, frequency spectrum and directional spectrum;
• know how to explain the meaning of nonlinear wave resonance for gravity waves, and distinguish between free and bound waves;
• have basic knowledge of the difference between linear and nonlinear statistical distributions for crest heights and wave heights;
• have knowledge of simple models for nonlinear evolution of wave trains, and corresponding nonlinear phenomena such as modulational instability of Stokes waves.

PhD candidates from the University of Oslo should apply for classes and register for examinations through Studentweb.

If a course has limited intake capacity, priority will be given to PhD candidates who follow an individual education plan where this particular course is included. Some national researchers’ schools may have specific rules for ranking applicants for courses with limited intake capacity.

PhD candidates who have been admitted to another higher education institution must apply for a position as a visiting student within a given deadline.

Should be taken in the same semester as or after MEK4100 – Mathematical Methods in Mechanics or MEK4320 – Hydrodynamic Wave Theory/MEK9320 – Hydrodynamic Wave Theory.

## Teaching

4 hours of lectures/exercises per week throughout the semester.

The course may be taught in Norwegian if the lecturer and all students at the first lecture agree to it.

Upon the attendance of three or fewer students, the lecturer may, in conjunction with the Head of Teaching, change the course to self-study with supervision.

## Examination

Final written exam 4 hours or final oral exam, which counts 100 % towards the final grade.

The form of examination will be announced by the lecturer by 15 October/15 March for the autumn semester and the spring semester respectively.

This course has 2 mandatory assignments that must be approved before you can sit the final exam.

In addition, each PhD candidate is expected to give an oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer before you can sit the final exam.

It will also be counted as one of the three attempts to sit the exam for this course, if you sit the exam for one of the following courses:MEK4350 – Stochastic and Nonlinear Ocean Waves

### Examination support material

Written examination: Rottmann´s formula list and approved calculator.

Oral examination: No examination support material is allowed.

### Language of examination

Subjects taught in English will only offer the exam paper in English.

You may write your examination paper in Norwegian, Swedish, Danish or English.

### Resit an examination

This course offers both postponed and resit of examination. Read more:

### Special examination arrangements, use of sources, explanations and appeals

See more about examinations at UiO

Last updated from FS (Common Student System) Sep. 23, 2020 4:18:58 PM

Credits
10
Level
PhD
Teaching
Autumn

Taught according to demand and resources. Contact studieinfo@math.uio.no if you are interested in this course.

Examination
Autumn
Teaching language
Norwegian (English on request)

## Contact

Department of Mathematics