Amath/Atm S 505/Ocean 511
MTuWF 11:30-12:20: JHN 175
ATG 704, email@example.com, x5-7414
Office Hours: Th 1-2 pm
NO CLASS OR OFFICE HOURS (Instructor travel absences):
We Sep. 27
Tu-Th Oct. 10-12
Tu-Th Oct. 24-26
Tu Oct. 3
Tu Oct. 17
Tu Dec. 5
Links to Pages
Eulerian equations for mass-motion; Navier-Stokes equation for viscous fluids, Cartesion tensors, stress-strain relations; Kelvin' s theorem, vortex dynamics; potential flows, flows with high-low Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory.
Prerequisites (not quite as in the course catalog)
Amath 401/501 (vector calculus; may be taken concurrently) and a working knowledge of Matlab or Python. A basic understanding of Fourier series will enrich your understanding of the course material.
Fluid motion is fascinating to watch and important in many areas of science and engineering. This graduate-level introduction will stress the interplay between mathematics and physical intuition, with a particular focus on two everyday fluids, air and water. You will become familiar with how Newton's laws and thermodynamics apply to fluids, fluid pressure, when you can use the approximation of incompressibility, Eulerian vs. Lagrangian perspectives on moving fluids, use of vorticity and circulation, the role of body forces such as gravity, the importance of viscosity, and the concepts of hydrodynamic instability and turbulence. The course will prepare you for discipline-specific advanced courses such as geophysical fluid dynamics (Atm S 509/Ocean 512), the study of rotating, density-stratified fluid motions.
There is no required textbook; scanned hand-written lecture notes will be posted on the course web site. I recommend the following comprehensive and well-written textbook as a supplement and useful further reference to the course material:
Kundu, P. K, I. M. Cohen, and D. R. Dowling, 2015: Fluid Mechanics (6th Ed.) Elsevier Academic Press, ISBN 978-0124059351 (Amazon link)
Older editions are also fine. Relevant sections are cross-referenced with a 'K' in the syllabus. They are for the 5th edition (which I have); it is possible they may have slightly changed for the 6th edition.
Homework (50%), posted to class web page and assigned on a quasi-weekly basis. Collaboration with your fellow students is encouraged, but everyone needs to write out the homework in their own words. You may submit homework in class (as a paper copy) or electronically through Canvas. Late homework (after 5pm on due date) accepted only by prior arrangement with instructor, and under no circumstances after 5 pm on the next class day following the due date. After your first late homework, there will be a 25% penalty on further late homeworks.
Midterm (20%), Wednesday Nov. 8, 50 min., in-class, closed book, 1 hand-written double-sided sheet of notes. No electronic devices. Bring your own paper. Here are some midterm-practice-problems.pdf which we can discuss next Tuesday; no written solutions will be provided.
Final (30%), take-home, open book/note, no consultation or collaboration with anyone. Posted Wednesday, Dec. 6; due Wed Dec 13 by 5:00 pm, either under the door of Prof. Bretherton's office, ATG 704 (note the building is locked at 6 pm) or electronically through Canvas. Please don't use my mailbox.
Overall course grades will be curved to a median of 3.6. Grades of 3.0 or above represent satisfactory performance. I may give a small amount of extra credit toward your overall grade for exceptional class participation that helps keep class lively and productive for all students.