MEK9350 – Stochastic and Nonlinear Ocean Waves
Course description
Schedule, syllabus and examination date
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.
Admission to the course
PhD candidates from the Faculty of Mathematics and Natural Sciences at 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.
Recommended previous knowledge
- Should be taken in the same semester as or after MEK4100 – Mathematical Methods in Mechanics or 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.
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 or final oral exam, which counts 100 % towards the final grade.
The form of examination will be announced by the lecturer by 1 October/1 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. Information about approved calculators in Norwegian.
Oral examination: No examination support material is allowed.
Language of examination
Courses taught in English will only offer the exam paper in English. You may submit your response in Norwegian, Swedish, Danish or English.
Grading scale
Grades are awarded on a pass/fail scale. Read more about the grading system.
Resit an examination
This course offers both postponed and resit of examination. Read more:
More about examinations at UiO
- Use of sources and citations
- Special exam arrangements due to individual needs
- Withdrawal from an exam
- Illness at exams / postponed exams
- Explanation of grades and appeals
- Resitting an exam
- Cheating/attempted cheating
You will find further guides and resources at the web page on examinations at UiO.