This page contains selections from a recent course syllabus, with annotations, additional description, and commentary. Please drop me an email if you have any questions.
This course will provide a general introduction to basic concepts of fluid dynamics including: viscosity, diffusion, vorticity, turbulence, convection, and instabilities (e.g. Kelvin-Helmholtz, Rayleigh-Taylor, Richtmyer-Meshkov). Advanced topics of chemically reactive flows, boundary layers, relativistic flows, particle-fluid interactions, and shocks will be discussed. Fluid concepts will be applied to astrophysical settings including: stellar oscillations and pulsations, and galactic dynamics with smoothed particle hydrodynamics. Numerical methods and computational frameworks will be introduced for approaching each application, and advantages and weaknesses discussed.
Prerequisites: none.
There are no classes in our current curriculum that are required as prerequisites. Here are some things to consider if you are thinking of taking this class. This class will ask you to plot functions, plot data that is provided, log in to a departmental server, and follow directions to solve fluid equations. It is assumed that students are familiar with using computers for these basic functions. It is also assumed that students are familiar with derivatives, integrals, and matrices at the level of undergrduate physics majors. The course will not provide any guidance in these areas.
Credit Hours: 3
There will be regular homework assignments of 1-3 problems each week. Although there are a small number of problems, expect that you will need to spend something like 9-10 hours solving them.
Suggested Textbook: Regev, Umurhan, and Yecko. Modern fluid dynamics for physics and astrophysics. Springer, 2016.
Note that this textbook is not required for completing assignments, but it is recommended that students purchase and read the textbook to better understand the topics discussed in class.
At the completion of this course, students will be able to:
define a fluid.
understand the physical settings where a fluid model can be applied.
describe what fluid instabilities are.
distinguish between laminar and turbulent flows.
solve evolution equations for fluids computationally.
These objectives should give you the idea that this class will cover the theory of fluid dynamics, as well as how fluid equations are solved for practical problems (such as engineering flows) and extreme problems (such as astrophysical flows). The solution of fluid equations involves numerical methods. This class does not cover any aspect of programming. Take note that basic familiarity with computers is a necessary prereq for this class.
Kato, S., and Fukue, J. Fundamentals of Astrophysical Fluid Dynamics: Hydrodynamics, Magnetohydrodynamics, and Radiation Hydrodynamics. Springer Nature. 2020.
Steve Shore. Astrophysical Hydrodynamics: An Introduction (2nd Edition) 2007.
Christensen-Dalsgaard, Jørgen. Lecture Notes on Stellar Oscillations. (5th Edition) 2014.
Pringle, James E., and Andrew King. Astrophysical Flows. Cambridge University Press, 2007.
Clarke, Cathie, and Bob Carswell. Principles of Astrophysical Fluid Dynamics. Cambridge University Press, 2007.
Springel, Volker. Smoothed particle hydrodynamics in astrophysics. Annual Review of Astronomy and Astrophysics 48:391-430, 2010.
These texts are great references and can help you to formulate your class project (discussed below).
The course syllabus provides a general plan for the course; deviations may be necessary.
Lecture | Date | Topic |
---|---|---|
1 | 8/28 | Introduction: Fluids vs. Particles and kinetic models |
2 | 9/4 | Fluid Equations |
3 | 9/11 | Viscosity and Diffusion |
4 | 9/18 | Vorticity, Helicity, and Rotation |
5 | 9/25 | Laminar Flows and Turbulence |
6 | 10/2 | Numerical Solution of Fluid Equations |
7 | 10/9 | Convection and Stellar Pulsation |
8 | 10/16 | Boundary Layers and Chemically Reactive Flows |
9 | 10/23 | Interaction of Particles and Fluids |
10 | 10/30 | Relativistic flows |
11 | 11/6 | Waves: stellar oscillations, Kelvin–Helmholtz instability, Rayleigh–Taylor instability |
12 | 11/13 | Shocks, Sedov Blast Waves, Richtmyer–Meshkov Instabilities |
13 | 11/20 | Magnetohydrodynamics |
14 | 11/27 | ————- Thanksgiving Break, no class ————– |
15 | 12/4 | Project Presentations |
A final project will be assigned for this class instead of a final exam.
Reading assignments and problems will be given regularly. A project and presentation will be assigned for the semester, which will make up the course grade. Assignments will be announced on the iCollege page for this course.
Components of the coursework will be weighted:
Project Report | 65% |
Presentation of Project | 25% |
Class Assignments | 10% |
Final grades will be assigned on a curve. The official grading scale is given below, and percentages will be curved before final grades are assigned.
Notice that your discussion and write-up of a project makes up the largest part of this course grade. That project is losely available for you to design, but requires that you use an approved code, and think about how fluid equations can be solved. No student can pass the class without completing such a project.
General
This class will be run as an advanced (graduate level) course.
Assignments
Reading assignments and problems will be given out each week.
It is the student’s responsibility to understand the reading, engage with the material on iCollege, and to solve the problems.
Attendance and Absences
In accordance with GSU policies, attendance is not required.
Course Feedback
Your constructive assessment of this course plays an indispensable role in shaping education at Georgia State. Upon completing the course, please take time to fill out the online course evaluation.
GSU holds students to appropriate ethical and professional standards of conduct. The Policy on Academic Honesty (Section 409) exists to inform students and faculty of their obligations in upholding the highest standards of professional and ethical integrity. All student work is subject to this policy. Properly cite, reference, and attribute all intellectual property used in your coursework.
Online submission of, or placing one's name on an exam, assignment, or any course document is a statement of academic honor that the student has not received or given inappropriate assistance in completing it and that the student has complied with the Policy on Academic Honesty in that work. In the event of an offense against the Policy on Academic Honesty, the instructor may impose a sanction on the student that varies depending upon the instructor's evaluation of the nature and gravity of the offense.