OCEN 675
Nonlinear Wave-Wave Interaction In Ocean Waves & Its Implication To Ocean Engineering
Fall 2007
Lectures Time & Location MWF 11:30 am -12:20 pm
Lecturer:
Dr. Jun Zhang
CE/TTI 808E
CE 137
E-mail: jun-zhang@tamu.edu
Telephone: 845-2168
Textbook: Notes of “Nonlinear Wave-Wave Interaction In Ocean Waves & Its Implication To Ocean
Engineering”, by Jun Zhang
References:
1. Electronic Class Notes (E-notes), J. Zhang, 2007. Website: http://ceprofs.tamu.edu
2. The Applied Dynamics of Ocean Surface Waves, C.C. Mei, 1983, Wiley-Interscience.
3. The Dynamics of the Upper Ocean, O.M. Phillips, 1977, Second Edition, Cambridge University Press.
4. Ocean Waves-The Stochastic Approach, M.K. Ochi, 1998, Cambridge University Press.
5. Water Waves, J.J. Stoker, 1957, Interscience.
Course Description
Nonlinear wave-wave interactions in steep ocean waves significantly affect wave properties and long-term wave
evolution, which is crucial to many ocean scientific and engineering practices. This course introduces the
concepts of strong and weak wave interactions and physically and mathematically explains how they affect ocean
waves. To quantify and predict the effects of wave interactions, various perturbation methods, in particular Mode
Coupling Method (MCM) and Phase Modulation Method (PMM) are studied for deriving the solutions for wave
interactions. Applications of the knowledge on nonlinear wave interactions are demonstrated in using Hybrid
Wave Models to analyze wave measurements.
Tentative Course Outline
Week
Topics
1st Week
Introduction, Governing Equations
Review of Linear Spectral Wave Theory
2nd Week
Periodic Waves and Perturbation method
(Stokes Expansion)
3rd Week
Finite Amplitude Wave Theory;
Irregular Waves and Wave-Wave Interactions
.
Strong and Weak Interactions, Free and Bound Waves
Resultant and Free Wave Spectra
4th Week
5th Week
Mode Coupling Method and Phase Modulation Method,
Solution for Three-Wave Interaction up to Third Order
6th Week
Narrow-Band Assumption and Schrodinger Equations,
Side-Band Instability and Wave Instability
7th Week
Weak (resonance) Wave Interaction
WAM Model and Long-Term Wave Evolutions
Text Assignment
Ref. 1. Ch 1,
Ref. 2, Ch. 1,Ref. 4 Ch 1.
Ref. 1 Ch 2
Notes Ch. 1
Notes, Ch. 2
Notes Ch4.3
Ref. 2, Ch. 12
Notes Ch.6
8th Week
Phase Modulation Method,
Solution for Three-Wave Interaction up to Third Order
Notes Ch 7.
9th Week
Convergence Criteria,
Nonlinear Decomposition
Notes Ch. 8
Week
10th Week
Topics
Hybrid Wave Model (HWM), Wave Band Divisions
Text Assignment
Notes Ch.8
11th Week
Unidirectional HWM, Applications of UHWM
12th Week
1st project due, Short Crest Ocean Waves,
Data-Adaptive Method (Maximum Likelihood Method)
Notes Ch. 6.2
Notes Ch. 6.3
13th Week
Directional Hybrid Wave Model
Double and Single Summation
Notes Ch. 6.4
14th Week
Application of DHWM to Data Analysis of
Field Measurements*
15th Week
2nd Project Due, Review
Dec. 12
10:30 am – 12:30 pm Final Exam
Note Ch, 8
Notes Ch. 7.4-6
*These topics may or may not be offered, depending on the class progress.
Homework: Homework assignments must be handed in by the due date before the end of the class. Late
homework will be penalized unless you have strong reasons.
Projects: Two written projects will be signed and due respectively at the mid and end of the semester.
Exams: Only final exam will be given. Its grading will be based on both the approach and the final answer.
Course Grade: The final grade in the course is based on our best assessment of your understanding of the
material and participation during the semester. The final exam 40%, two written projects 30% and homework
30%. However, other factors, such as interaction with the teacher, participation in lecture and recitation, etc. can
make a significant difference in the final grade. The process of assigning the final grade also involves a careful
review of the final exam to look "behind the numbers" to understand better the kinds of mistakes that were made.
Letter grades will be assigned from your total course score according to 90% _A_100%,
80% _ B < 90%, 70% _ C < 80%, 60% _ D < 70%, and F < 60%.
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learning environment that provides for reasonable accommodation of their disabilities. If you believe you have a disability requiring an
accommodation, please contact the Department of Student Life, Services for Students with Disabilities, in Cain Hall or call 845-1637.