**Falk Feddersen: SIOC 211A Linear Waves (Winter 2018)**

## Linear Ocean Waves

SIOC 211A Section 921976Professor 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 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

- 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 PROJECT 2)
- Internal Gravity Waves D. Ray Tracing with non-constant N and Reflection on a slope (FF: Chapter 11)
- Internal Gravity Waves E. Combined Internal and Surface Gravity Waves (FF: Chapter 12)
- Acoustic Waves A. Perfect fluid and derivation of acoustic wave equation (FF: Chapter 5)
- Acoustic Waves B. Energy conservation, reflection, transmission (FF: Chapter 6)
- Linear shallow water equations: Derivation (FF: Chapter 13)
- Linear shallow water equations no rotation. (FF: Chapter 14)
- Linear shallow water equations with Rotation A. inertial-gravity waves, Kelvin waves, tides (FF: Chapter 15)
- Linear shallow water equations with Rotation B. edge waves, shelf waves
- Slowly Varying WKB Theory
- Wave Action Conservation - Wave Current Interaction
- Synthesis

**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
- Gill A, Atmosphere/Ocean Dynamics. Available electronically from UCSD library E-BOOK and direct from PUBLISHER
- 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
- Internal Wave Beam Generation on a Slope VIDEO
- 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.
- Cole et al., Observations of Tidal Internal Wave Beams at Kauai Channel, Hawaii, JPO, doi: 10.1175/2008JPO3937.1, 2009, link

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