Myrl Hendershott and Falk Feddersen: SIOC 211A Linear Waves (Winter 2019)

Linear Ocean Waves

SIOC 211A Section 921976
Professors Myrl Hendershott and Falk Feddersen
mhendershott@ucsd.edu, ffeddersen@ucsd.edu
Phone: 858.534.4345
Office: Sverdrup (MH) and DSD West (FF) Meetings
Class: Monday/Wednsday time 12:30-13:50 : IGPP 4301 Revelle Conference Room
Office Hours: Friday 10am

Description Most of the class is concerned with linear wave theory as it applies to the ocean. The emphasis is on gravity waves of various types but other waves will also be discussed. The course will begin with an introduction/review of the wave equation and relevant principles that should be familiar from Fourier analysis. The class will principally draw on two sets of lecture notes (see below). In addition, sections of various books will be assigned reading. Lectures will be at the level of SIOC 214 (fluids) and SIO 203A (math A) and make use of material covered in both. You will also make use of tools developed in data analysis.

Course Requirements Students should enroll in four (4) units. First year students should register as letter. Others can register as S/U. Students are expected to complete all the assigned homework, quizes, projects, and a final exam. There will be regularly assigned homework. Homework is expected to be done in LaTeX. There will be occasional short class quizzes as with GFD. There will be a short quiz due on the first day of class that does not count toward your grade. There will be two projects on surface gravity and internal waves with a goal to either confirm or reject the theoretical constructs you're learning. The final grade will be based 1/2 on problem sets (HW + quizes), 1/4 on projects and 1/4 on final exam.

Syllabus

  1. (FF) Classic Wave Equations: Linear superposition, plane waves, phase speed, standing vs. propagating (FF: Chapter 1)
  2. (FF) Surface Gravity Waves A. Linear Derivation, Disperison Relationship (FF: Chapter 2, MCH: 1.1-1.3, 3.1-3.5, KUNDU: 7.1, 7.2)
  3. (FF) Surface Gravity Waves B. Flux-conservation equations, wave energy, energy flux, group velocity (YOUTUBE: Waves across the Pacific, FF Chapter 3, MCH 3.8, KUNDU 7.5), (PROJECT 1)
  4. (MH) Surface Gravity Waves C. Dispersion, group velocity, stationary phase (FF Chapter 4 MCH: 1.4 and 1.5, KUNDU 7.5)
  5. (MH) Surface Gravity Waves D: Ray theory, Snells law (FF: Chapter 16)
  6. (MH) Acoustic Waves A. Perfect fluid and derivation of acoustic wave equation (FF: Chapter 5)
  7. (MH)Acoustic Waves B. Energy conservation, reflection, transmission (FF: Chapter 6)
  8. (FF) Perfect fluid and Boussinesq approximation (FF: 5.1-5.2, Chapter 7, KUNDU 1.8,1.9, 15.2)
  9. (FF) Internal Gravity Waves A. Wave equation derivation, solutions and dispersion relationship (FF Chapter 8, KUNDU 7.8, MCH: 4.1 and 4.2, Pedlosky Waves Lecture 7)
  10. (FF) Internal Gravity Waves B. Energy conservation (FF: Chapter 9)
  11. (FF) Internal Gravity Waves C. Normal modes (FF: Chapter 10, MCH 4.3 PROJECT 2)
  12. (MH) Internal Gravity Waves D. Ray Tracing with non-constant N and Reflection on a slope (FF: Chapter 11)
  13. (FF) Internal Gravity Waves E. Combined Internal and Surface Gravity Waves (FF: Chapter 12)
  14. (MH) Linear shallow water equations: Derivation (FF: Chapter 13)
  15. (MH) Linear shallow water equations no rotation. (FF: Chapter 14)
  16. (MH)Linear shallow water equations with Rotation A. inertial-gravity waves, Kelvin waves, tides (FF: Chapter 15)
  17. (MH) Linear shallow water equations with Rotation B. Rossby Waves
  18. Synthesis/Review

Lecture notes
The two principal lecture note sources are the following Other Books These books that have relvant material in them. These include YOUTUBE VIDEOS AND WEBSITES BACKGROUND TO FOURIER ANALYSIS PAPERS
Surface Gravity Waves Ocean Acoustic Waves Internal Waves

If you have any questions or comments, please contact me at falk@coast.ucsd.edu.