AMS 227 SYLLABUS, Winter 2018
General Information
Class and Exams Schedule
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General Information
Tentative schedule (this will be updated as the course proceeds)
Class and Exams Schedule
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General Information
- Textbook: Unfortunately, there isn't a single textbook that covers all the material for this course at the level required. The instructor will provide you with a set of notes that will hopefully serve a similar purpose. There are, however, a number of excellent books on Waves or Instabilities, that are strongly recommended as further reading. These can be found in any good university library (and most of them are in my office, at the moment):
- Supplemental material:
- Waves in the Ocean and Atmosphere: Introduction to wave dynamics, by J. Pedlosky
- Introduction to hydrodynamic stability, by P. Drazin
- Fluid Dynamics by Michel Rieutord
- Fluid Mechanics by Kundu, Cohen and Dowling. This was the AMS217 textbook, a nice reference for an introduction to the subject.
- Applied Partial Differential Equations by R. Haberman. This was the AMS 212A textbook. Hopefully you're familiar with PDEs, however, otherwise you're in trouble.
- Linear and nonlinear waves, by G. Whitham. Probably the modern reference on the topic of waves, contains a lot more than we will cover, however.
- Hydrodynamic stability, by P. Drazin and W. Reid. The more comprehensive and more complete version of the "Intro" book listed above.
- Hydrodynamic and hydromagnetic stability, by S. Chandrasekhar. Any astrophysicist should have a copy of this. Most likely it contains that instability you thought you discovered. Consult before attempting to publish.
- Homework: Homework will be given every week. You are encouraged to do it in groups, though you should all hand in separate answers.
- Projects: Students will be required to present a class project in the very last week, applying some of the methods learned to their own research.
- Grading Policy:
- Homework: 50 % of total grade.
- Project: 50 % of total grade.
Tentative schedule (this will be updated as the course proceeds)
- Week 1 (January):
- General introduction to the equations of fluid dynamics
- Week 2:
- Jan 15: Holiday
- Pressure waves (the basics)
- Week 3:
- Pressure waves in inhomogeneous media
- Week 4:
- Internal gravity waves
- Week 5 (February):
- Surface waves
- Week 6:
- Convection (the basics)
- Week 7:
- Feb 19: Holiday
- Convection (weakly nonlinear theory)
- Week 8:
- Shear instabilities
- Week 9:
- Interfacial instabilities
- Week 10:
- Project presentations.