Falk Feddersen: SIOC 211A Linear Waves (Winter 2017)

Linear Ocean Waves

SIOC 211A Section 888045
Professor Falk Feddersen
falk at coast.ucsd.edu
Phone: 858.534.4345
Office: 2nd floor CCS - blue door with sticker that says Quit Beefin, Eat Lobstah

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 first part of the course will then proceed through ocean-related waves in (mostly) homogenous media. The second part of the course will proceed through wave in inhomogenous media which will involve refraction, caustics, and many other interesting phenomena. The class will principally draw on two sets of lecture notes. The first are a set of lecture notes for 211A inspired by Rick Salmon that I am editing and revising. The second are lecture notes presented to Myrl Hendershott by his former students David Chapman and Paola Malanotte-Rizzoli. In addition, sections of various books will be assigned reading. Lectures will be at the level of SIO214 (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 three projects. The first two you will use data from surface gravity and internal waves. The third project is an in situ surfzone lab. The goal is 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

Basics and Review

  • Lecture 1: Classic Wave Equations: Linear superposition, plane waves, phase speed, standing vs. propagating (FF: Chapter 1)

Homogenous Media

  • Lecture 2: Surface Gravity Waves A. Linearization, Derivation, Disperison Relationship (FF: Chapter 2, MCH: 1.1-1.3, 3.1-3.5, KUNDU: 7.1, 7.2)
  • Lecture 3: 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)
  • Lecture 4: Surface Gravity Waves C. Dispersion, group velocity, stationary phase (FF Chapter 4 MCH: 1.4 and 1.5, KUNDU 7.5)
  • Lecture 5: Acoustic Waves A. Perfect fluid and derivation of acoustic wave equation (FF: Chapter 5, KUNDU 1.8,1.9, 15.2)
  • Lecture 6: Acoustic Waves B. Energy conservation, reflection, transmission (FF: Chapter 6)
  • Lecture 7: Bousinesq Approximation (FF: Chapter 7, Vallis 2.4.2)
  • Lecture 8: 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)
  • Lecture 9: Internal Gravity Waves B. Energy conservation (FF: Chapter 9)
  • Lecture 10: Internal Gravity Waves C. Normal modes (FF: Chapter 10, MCH 4.3 PROJECT 2)
  • Lecture 11: Internal Gravity Waves D. Reflection on a slope and surface expression
  • Lecture 12: Linear shallow water equations: no rotation. wave equation, plane waves, dispersion relationship, diffraction, seiches
  • Lecture 13: Linear shallow water equations with Rotation A. inertial-gravity waves, Kelvin waves, tides, and Rossby waves
  • Lecture 14: Linear shallow water equations with Rotation B. edge waves, shelf waves

    Non-homogeneous Media

    • Lecture 16: Ray theory, Snells law,
    • Lecture 17: Action Conservation
    • Lecture 18: Wave-current interaction
    • Lecture 19: Internal Gravity Waves: non-constant N, critical layers
    • Lecture 20: Synthesis

    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.