# AMATH 505 A: Introduction to Fluid Dynamics

Autumn 2024
Meeting:
MWThF 11:30am - 12:20pm / ATG 610
SLN:
10227
Section Type:
Lecture
Joint Sections:
OCEAN 511 A , ATM S 505 A
Instructor:
Georgy Manucharyan
APPLIED MATH STUDENTS HAVE PRIORITY REGISTRATION; ALL OTHERS MUST WAIT UNTIL REGISTRATION PERIOD II.
Syllabus Description (from Canvas):

Professor Dale Durran
502 ATG Building
Email Me

Our goal: To gain a thorough understanding the basic mathematical relations that describe atmospheric and oceanic motions.  Our introduction to the broader field of fluid mechanics will be in a geophysical context. We will consider both the fundamental governing equations applicable to almost all geophysical motions and simplifed models describing elementary stable and unstable circulations.  In both lecture and lab, we will try to connect the theory with real-world examples.

Textbook:  Pijush Kundu, Ira Cohen and David Dowling: Fluid Mechanics, 6th Edition.

Meeting Time:  Lecture: MWF 11:30-12:20.  ATG 610
Lab Th 11:30-12:20.  Location varies between ATG 610 and OCN 107

Course Notes:  Hand written notes from the lecture, interspersed with figures, will be posted as pdfs after each lecture. PDFs of the lecture notes are here

Contact Info/Office hours: Th 1:30-2:30 PM ATG 502
W 1:30-2:30 PM ATG 311  or by appointment.

Grading: 75% homework, 20% final, 5% lab participation. 100%  of the 5% overall grade is awarded if you participate in all but one lab (i.e., you can miss one).  Credit is rounded to nearest percent for those with a fraction of labs attended: (# labs attended)*5% / (total # labs -1)

Final Exam:  Wednesday December 11, 2:30-4:30 PM

Course Outline (detail will be added)

Introduction (Chapter 1: 1.1 -1.10)

• Solids, liquids, gases  1.1-1.3
• Fluid statics  1.7
• Classical thermodynamics  1.8
• Static stability of stratified fluids  1.9-1.10

Kinematics (Chapter 3)

• Lagrangian and Eulerian coordinates 3.1-3.2
• Streamlines and trajectories 3.3
• Streamfunction 4.3 (p. 114-115, emphasis on 2D case)
• Relative motion near a point in the fluid 3.4-3.5
• Strain
• Vorticity and circulation

Conservation Laws (Chapter 4)

• Conservation of mass (4.2)
• Conservation of momentum (4.4)
• Navier-Stokes momentum eqn (4.5-4.6)
• Conservation of energy (4.8)
• Bernoulli eqn p. 144

Vorticity (Chapter 5)

• Kelvin and Helmholtz theorems (5.1-5.2)
• Velocity induced by a vortex filament (5.4)
• Interaction of vortices (5.6)
• Vorticity equation (5.3)

Gravity waves (Chapter 8)

Kelvin-Helmholtz instability (Chapter 11: 11.1-11.3)

-------------------------------------

Mathematical Reference Material (Chapter 2)

Catalog Description:
Eulerian equations for mass-motion; Navier-Stokes equation for viscous fluids, stress-strain relations; Kelvin's theorem, vortex dynamics; potential flows, flows with high-low Reynolds numbers; boundary layers, surface gravity waves; sound waves, and linear instability theory. Prerequisite: either a course in partial differential equations or permission of instructor. Offered: jointly with ATM S 505/OCEAN 511; A.
Credits:
4.0
Status:
Active
Last updated:
September 5, 2024 - 6:49 am