This course rigorously develops the Navier-Stokes equations from first principles, reinforcing a range of skills from applied mathematics (e.g., Cartesian index notation, vector calculus, integral theorems). We then study exact solutions, and use scaling theory to extend the equations to approximate solutions. The course focuses on application of these equations to fluid flows in natural systems.
This course examines transport, mixing, and reaction of scalar contaminants (e.g. toxins, nutrients, heat) in laminar and turbulent flows. The course is split between analytical formulations and solutions in the first half, and numerical formulations and simulations in the second half.
This course provides a basic introduction to the mechanics of fluids relevant to a variety of engineering applications. The focus will be on providing a strong foundation and understanding of fundamental concepts, including fluid statics, kinematics, the Bernoulli equation, and concepts of momentum and energy.