Syllabus

Download a full course syllabus here.

Course Description

Heat most any material enough and it begins to flow. Whether it becomes a gas, a fluid, or a plasma, the resulting flows are all governed by the same underlying physical principles and mathematics. And yet, despite this underlying theoretical coherence, microscopic details of the motions and observations of fluids are marvelously diverse. This course will explore the conceptual coherence of fluid dynamics and touch on a few of the many applications to oceanography, meteorology, astrophysics, geophysics, biophysics, chemistry, and engineering. One additional hour of class recitation time will be scheduled in consultation with enrolled students.

We will briefly study the origin of the governing (Navier-Stokes) equations and the idea of dimensionless parameters, in particular, the Reynolds number. Next we will turn to the limits of low Reynolds number (viscous) flow and high Reynolds number (inviscid) flow. Further topics include boundary layers, drag and lift, convection, stratified flow, and rotating fluids. Finally, we will study instabilities, and transition to turbulence. Our emphasis will be on the physical phenomena, though the course will use mathematics freely.