AMS 227 SYLLABUS, Winter 2016
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). You should decide for yourself whether you wish to purchase them or not. If you do wish to purchase some, I strongly recommend the first three in the list below. The next two are the textbooks from AMS217 and AMS212A, that are pre-requisites to this class. The remaining ones are classical texts on the topics, excellent references to consult now and then as we go along.
- 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):
- Jan 4: General introduction to fluid dynamics
- Jan 6: Continued
- Jan 8: Pressure waves, part 1. Derivation of the wave equation, D'Alembert's solution.
- Week 2:
- Jan 11: Pressure waves, part 2. Monochromatic wave solutions, sound waves in an acoustic cavity.
- Jan 13: Pressure waves, part 3. Waves in a 3D isothermal sphere.
- Jan 15: Pressure waves, part 4. Wave packet solutions.
- Week 3:
- Jan 18: Holiday.
- Jan 20: Waves in an inhomogeneous medium.
- Jan 22: Waves in stars, energy conservation
- Week 4:
- Jan 25: (Time permitting) The Boussinesq equations.
- Jan 27: Internal gravity waves, derivation of the equations, monochromatic solutions.
- Jan 29: Internal gravity waves: the wave packet formalism
- Week 5 (February):
- Feb 1: Internal gravity waves: waves over topography
- Feb 3: Surface waves, part 1: derivation of the equations.
- Feb 5: Surface waves, part 2: dispersion relation and particle paths.
- Time permitting : introduction to wave-mean-flow interaction.
- Week 6:
- Feb 8: Convection, part 1. Local stability analysis
- Feb 10: Convection, part 2. Rayleigh-Benard convection
- Feb 12: Convection, part 3. Energy stability
- Week 7:
- Feb 15: HOLIDAY
- Feb 17: Convection, part 4. Weakly nonlinear theory (1)
- Feb 17: Convection, part 5. Weakly nonlinear theory (2)
- Time permitting: the effect of rotation on convection
- Week 8:
- Feb 20: Shear instabilities, part 1. Energetics, the Richardson criterion
- Feb 22: Shear instabilities, part 2. Local linear stability analysis.
- Feb 23: Shear instabilities, part 3. Global linear stability analysis for unstratified nonviscous flows
- Week 9:
- Feb 26: Shear instabilities, part 4. Global linear stability analysis for viscous flows
- Feb 28: Shear instabilities, part 5. Stratified shear instabilities.
- Feb 30: Shear instabilities, part 6. Interfacial instabilities.
- Week 10:
- Project presentations.