# MEK9350 – Stochastic and Nonlinear Ocean Waves

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## 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.

## Prerequisites

### Recommended previous knowledge

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

## Overlapping courses

10 credits overlap with MEK4350 – Stochastic and Nonlinear Ocean Waves

## Teaching

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

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 oral or written examination. The form of examination will be announced by the teaching staff by 15 October/15 March for the autumn semester and the spring semester respectively.

In addition, each PhD student is expected to give a one hour oral presentation on a topic of relevance chosen in cooperation with the lecturer. The presentation has to be approved by the lecturer for the student to be admitted to the final exam.

### Examination support material

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

Information about approved calculators (Norwegian only)

### 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:

### Withdrawal from an examination

It is possible to take the exam up to 3 times. If you withdraw from the exam after the deadline or during the exam, this will be counted as an examination attempt.

### Special examination arrangements

Application form, deadline and requirements for special examination arrangements.

## Evaluation

The course is subject to continuous evaluation. At regular intervals we also ask students to participate in a more comprehensive evaluation.

10

PhD

### Teaching

Autumn 2018

Autumn 2017

Autumn 2016

Autumn 2015

Autumn 2014

Autumn. Taught according to demand and resources. If you want to attend the course, please send an e-mail to studieinfo@math.uio.no.

### Examination

Autumn 2018

Autumn 2017

Autumn 2016

Autumn 2015

Autumn 2014

According to demand and resources.

### Teaching language

English

The course is given in English. If no students have asked for the course in English within the first lecture, it may be given in Norwegian.

## Contact

Department of Mathematics