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)

- Sound waves: simple example of wave propagation
- Linear water waves (8.1-8.2)
- Animation, deep water case.
- Fluid parcel motion in DEEP WATER waves
- Group velocity - phase speed comparison
- Time lapse of compact deep-water wave packet in Hong Kong channel.
- Simulation of the 2004 Boxing Day tsunami using nonlinear shallow-water equations.

- Standing waves (8.4)
- Group velocity, energy flux, dispersion (8.5)

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

- Rachel Gordon's KH BillowsBBC: "The billowy phenomenon was visible on Tuesday [12/6/2022] above the crest of the Bighorn Mountains from the city of Sheridan."
- Aaron Donohoe makes KH billows in Cambridge
- Setup for Cambridge Billows
- Lab demo and explanation of KH instability

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

**Mathematical Reference Material **(Chapter 2)