Instructor: Andrew Belmonte

Contact info: 322 McAllister Building, telephone: 865-2491, email: belmonte.AT.math.psu.edu

Office hours: Tues 2:30-3:30, Wed 2:30-3:30, or by appointment.

Class location: 322 Sackett Bldg

Prerequisites:   Basic familiarity with the laws of physics; advanced undergraduate knowledge of ordinary and partial differential equations; rudiments of thermodynamics. For more information, please contact the instructor.

Course Texts (required):

• Introduction to Mathematical Fluid Dynamics, by Richard E. Meyer (Dover, 1971) ISBN: 0-486-61554-5.
• Fluid Mechanics, 2nd edition, by L. Landau and E. Lifshitz, (Pergamon, 1987) ISBN: 0-08-033932-8.
• An Album of Fluid Motion, by Milton Van Dyke (Parabolic Press, Stanford, 1982) ISBN: 0-915760-02-9.

Supplementary Texts (optional):

• Hydrodynamic Stability, by P. G. Drazin and W. H. Reid, (Cambridge, 1981).
• Viscous Flow, by H. Ockendon and J. R. Ockendon (Cambridge, 1995).
• Fluid Mechanics, by J. H. Spurk, 2nd ed. (Springer, 1997).

some of these books will be on reserve at the PAMS library in Davey Lab.

This one semester graduate course provides an overview and introduction to fluid dynamics -- a subject rich in both mathematical and experimental results and challenges. We will start from the foundations of the subject, introducing the governing partial differential equations for a flowing continuum and solving them in various limits: inviscid or irrotational (Euler's equation), viscous, the Navier-Stokes equation, acoustics, viscous flows, and non-Newtonian fluids. Following Prandtl and the development of asymptotic theory, we will discuss boundary layers and turbulence (including Kolmogorov's approach). Finally, we will examine the most important external forces applied to fluids from both a mathematical and experimental perspective. A common theme throughout the course will be the connections between the structure of the equations and experimental observations.

The basic syllabus for this course will be as follows:

I. Mathematical Approach to a Moving Continuum

II. Euler's Equation

III. Aspects of the Navier-Stokes Equation

IV. Overviews of Complex Fluids, Microfluidics, and Turbulence

V. Other forces applied to fluids: electrical, thermal, rotational