ATM S 505 - Autumn 2008

Overview: The purpose of the course is to obtain a thorough understanding of the basic mathematical relations that describe atmospheric and oceanic motions. We will consider both the fundamental governing equations applicable to almost all geophysical motions and simplifed models describing elementary stable and unstable circulations.

Reading Assignments

Chapter 1 by lab on Thursday, Oct 2nd
Read Chapter 2 to gain sufficient familiarity with the material to be able to refer back to it as needed when performing mathematical manipulations.
Chapter 3, Sections 1-13 by lab on Thursday Oct 9th
- Animated comparison of streamlines and trajectories
Chapter 4, Sections 1-7,10-11, 13-16 by lab on Thursday Oct 16th
Chapter 4, Section 17; Chapter 5, Sections 1-3 by lab on Thursday Oct 23th
Chapter 5, Sections 4-6, 8-9 by lab on Thursday Oct 30th.
Chapter 7, Sections 1-6, and the notes on plane waves (download pdf), by lab on Thursday November 6th.
Chapter 7, Sections 8-11 by lab on Thursday November 12th
- Velocities under water waves
Chapter 7, Sections 18-21 by Wednesday November 19th
Skim Chapter 7, Sections 13-14. Read Chapter 12, Sections 1,2,6 by Lab on Thursday November 26th
- Aaron Donohoe makes KH billows in Cambridge
- Animation of KH instability
  Kelvin-Helmholtz billows in the atmosphere

Homework

Policy for late homework for homeworks due on Wednesday: papers submitted after class, but before the end of Wednesday -10%; papers submitted Thursday -25%, papers submitted Friday -35%. No late homework will be accepted after Friday.

Exercise 1 (pdf): Due Wednesday October 8th

Exercise 2 (pdf): (Notational clarification added to problem 2) Due Wednesday October 22nd

Midterm/Exercise 3 (pdf): (Prob 4 is now reworded.) Work independently. Due Wednesday, November 5th. (Weight in final grade is the same as other homeworks.)

Exercise 4 (pdf): Due Wednesday, November 19th

Exercise 5 (pdf): (Minor editing added to Prob 4.) Due Wednesday, December 3rd

Lab Notes

Lab 1: Weather Ball: example of variations in atmospheric pressure (green curve) and temperature (red curve) at Seatax Airport betweeen 15 UTC (8 AM PDT) on September 27 to 15 UTC on September 29, 2006. Note that the water in the outflow tube of the weather ball will rise roughly one cm due to a 1.2 K increase in the temperature of the air inside the sphere or a 1 hPA (1 mb) drop in the atmospheric pressure. Writeup.

Lab 2: Cartesian Diver: Writeup

Lab 3: U-tubes: Writep. Notes on Pressure.

Lab 4: Vorticity Kinematics: Writeup.

Lab 5: Bernoulli's Principle: Writeup.

Lab 6: Open Channel Flow: Writeup. For another interpretation of open channel flow see Section 3 of This.

Lab 7: Vorticity Dynamics: Writeup.

Lab 8: Surface Waves: Writeup.

Lab 9: Stirring and Mixing: Writeup .

Lab 10: Multi-layer fluids Writeup.

Web Links

Time lapse by Dale Ireland

Website with all National Committe for Fluid Mechanics films

Introduction

· Statics

· Classical thermodynamics

· Static stability

Physical conservation laws applied to a continuum

· Conservation of momentum (Newton’s 2^ndLaw)

· Conservation of mass

· Conservation of energy (First Law of thermodynamics)

· Equations of state

· Lagrangian and Eulerian coordinates

Useful approximations

· Hydrostatic balance

· Irrotational and nondivergent flow

· Heuristic discussion of the Boussinesq approximation; buoyancy

Vorticity dynamics

· Circulation, Kelvin’s and Bjerknes’ theorems

· Vorticity equation

· Vortex lines, Helmholtz theorem

· Ertel Potential Vorticity

Plane-wave kinematics

· Wave phase, wave vector, wavenumber, and wavelength

· Frequency, period, and phase speed

· Imaginary phase (growth in space and/or time)

· Group velocity

Linearizing nonlinear equations; neutral-wave solutions

· Surface gravity waves (water waves)

· Internal gravity waves

Instabilities; unstable-wave solutions

· Kelvin-Helmholtz instability

Grading: 75% of the grade will be based on five homework assignments; the remaining 25% on the final. One homework assignment will be a take-home midterm (worth 15% of the total grade, just like all the other homeworks). The take-home midterm must be done independently. You may work with other students on the other four homeworks.