**Falk Feddersen: SIOC 202A Fundamentals of Wave Physics (Winter 2018)**

## Fundamentals of Wave Physics (Part 1)

SIOC 202A Section 921970Professor 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**This is part one of the Fundamentals of Wave Physics course and it lasts 5 weeks. Bill Kuperman will teach part 2 which will focus on Acoustics. This is a required course for first year AOS students. Part one of this course is concerned with linear wave theory as it applies to the ocean, particularly surface gravity waves and internal waves. 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 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 SIOC 202A (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. If you are required to take this course, you 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 one project and surface gravity waves. 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 a final exam for this portion of the class.

## Syllabus

- Classic Wave Equations: Linear superposition, plane waves, phase speed, standing vs. propagating (FF: Chapter 1)
- 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)
- 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)
- Surface Gravity Waves C. Dispersion, group velocity, stationary phase (FF Chapter 4 MCH: 1.4 and 1.5, KUNDU 7.5)
- Surface Gravity Waves D: Ray theory, Snells law (FF: Chapter 16)
- Perfect fluid and Boussinesq approximation (FF: 5.1-5.2, Chapter 7, KUNDU 1.8,1.9, 15.2)
- 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)
- Internal Gravity Waves B. Energy conservation (FF: Chapter 9)
- Internal Gravity Waves C. Normal modes (FF: Chapter 10, MCH 4.3)
- Internal Gravity Waves D. Ray Tracing with non-constant N and Reflection on a slope (FF: Chapter 11)

**Lecture notes**

The two principal lecture note sources are the following

- Feddersen Wave Lecture Notes (30 Jan 2018 version, revised Chapter 16, not final, denoted FF above)
- Myrl's Wave Lecture Notes by Chapman and Mallanote-Rizzoi (denoted MCH above)

**Other Books**These books that have relvant material in them. These include

- Kundu, Cohen, Dowling,
*Fluid Mechanics:*Chapter 7 on Gravity Waves (same book as SIOC 214 - denoted KUNDU) - Pedlosky, J. Waves in the Ocean and Atmosphere. Introduction to Wave Dynamics. (in class reserves)
- Vallis, Atmospheric and Oceanic Fluid Dynamics, Electronic Resource (same book as SIOC 212A - denoted Vallis)
- Rick Salmon's Undergraduate Waves Textbook is also a nice resource. It is light on fluid dynamics but strong on inspiration and Fourier analysis
- Mei, CC, The Applied Dynamics of Surface Gravity Waves (in CCS basement). Note that this book is also available electronically from UCSD library: E-BOOK
- Pedlosky, J. Geophysical Fluid Dynamics (should be in course reserves)
- Myrl's chapter on Ocean Tides
- Lighthill, Waves in Fluids (in class reserves)
- Whitham, Linear and Nonlinear waves (in class reserves)

**YOUTUBE VIDEOS AND WEBSITES**

- MIT Opencourseware Lecture 4.5 on Evolution of a Slowly Varying Wave Packet
- MIT Opencourseware Lecture 4.6 on Evolution of a Slowly Varying Wave Packet
- Stormsurf Wave Model Web Site
- CDIP Web Site
- Waves Across the Pacific
- Internal Waves Generated from a cylinder: VIDEO 1, VIDEO 2
- Kraig Winters (SIO): Internal Tide impinging on a slope: Full nonlinear solutions Kraig winters lab
- Linear internal wave generation from seamount: VIDEO
- Internal Tide Generation Luzon Strait YOUTUBE

**BACKGROUND TO FOURIER ANALYSIS**

- Signals and Systems by Oppenheimer and Willsky. This is the best intro book on Fourier particularly the chapter on "Fourier Analysis for Conintous Time Signals and Systems".
- MIT CourseWare on Signals and Systems: In particular see the lectures 7, 8, 9 at https://ocw.mit.edu/resources/res-6-007-signals-and-systems-spring-2011/lecture-notes/
- YOUTUBE playlist of MIT course lectures

**PAPERS**

*Surface Gravity Waves*

- Snodgrass, Hasselman, Munk et al., Propagation of ocean swell across the pacific, Phil. Trans. Royal Soc A, doi:10.1098/rsta.1966.0022, 1966.
- Rascle et al., A global wave parameter database for geophysical applications. Part 1: Wave-current, Ocean Modeling, 25, 154-171, doi:10.1016/j.ocemod.2008.07.006, 2008.
- Okihiro et al., Excitation of Seiche Observed in a Small Harbor, JGR, 1993.
- Ferrari and Wunsch, The distribution of eddy kinetic and potential energies in the global ocean, Tellus, doi:10.1111/j.1600-0870.2009.00432.x 2010. link

*Ocean Acoustic Waves*

- Dushaw et al., A decade of acoustic thermometry in the North Pacific Ocean, JGR, doi:10.1029/2008JC005124, 2009

*Internal Waves*

- Alford et al., Near-Inertial Internal Gravity Waves in the Ocean, Annual Rev Marine Sci, 2016. [READ SECTIONS 1, 2, 3]
- Zhao et al. Global Observations of open-ocean mode-one M2 Internal TidesJ. Physical Oceanography, 2016.
- Alford, Sustained, Full-Water-Column Observations of Internal Waves and Mixing near Mendocino Escarpment, J. Physical Oceanography 2010.
- Nikurashin and Ferrari, Global energy conversion rate from geostrophic flows into internal lee waves in the deep ocean, Geophysical Research Letters, 2011.
- Alford Redistribution of energy available for ocean mixing by long-range propagation of internal waves, Nature 2003.
- Alford The formation and fate of internal waves in the South China SeaNature 2015 (super nonlinear waves)
- Garret and Kunze, Internal Tide Generaion in the Deep Ocean, Annual Review of Fluid Mechanics, 2007.

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