Mathematical Fluid Mechanics, Math 272B Spring 2006

  • Instructor: Andrea Bertozzi
  • Offices: 7619D Math Sciences, 1100B IPAM
  • email: bertozzi(at)math.ucla.edu (preferred method of communication)

  • Class meets MWF 3pm MS5117

    Books: We will follow the first two chapters of `Vorticity and Incompressible Flow' by Majda and Bertozzi, as well as some of the less analytical material from later chapters of that book (for example basic vortex patches and vortex sheet). We will also use some material from Acheson's book on Elementary Fluid Dynamics. Both books are available for purchase in paperback form and are highly recommended reading for the course and for a reference.

    Where can I buy the books? Here are some links:

  • Majda and Bertozzi in paperback through Amazon .
  • Majda and Bertozzi in ebook (electronic) format.
  • Acheson Elementary Fluid Dynamics through Amazon .
  • These links are provided as information only and do not constitute any personal endorsement of the vendor. Students are encouraged to find their own vendors for the reading material.

    Syllabus

  • The Euler and Navier-Stokes Equations: Symmetry groups, exact solutions, conserved quantities and Hodge decomposition (ref ch1 MB)
  • The Vorticity-Stream Formulation of the Euler and Navier-Stokes Equations (ref ch2 MB)
  • Energy methods - elementary concepts and viscous splitting (ref secs 3.1, 3.4 MB), some discussion of the Clay Math Prize problem
  • Computational Vortex methods (ch 6 MB)
  • Vortex patches (ch 8 MB)
  • Vortex sheets (ch 9 MB)
  • Additional topics on low Reynolds number flows, boundary layers, and surface tension effects, from Acheson (depending on time)

    Course Format and Grading

    Attendance is very important for the course. Student attendance will be counted towards the grade. In lieu of homework students will make in class presentations related to the material in class. Typically this will involve reading a section of one of the books, or perhaps a research paper related to the topic, and giving a presentation in class.

    Lectures will be broad and general and students will be encouraged and advised to read more details and work out some problems outside of class.

    We will organize the schedule on the first day of class.