Autumn 2003: ATMS 505 / AMATH 505 / OCEAN 511

Introduction to Geophysical Fluid Dynamics

Lectures: MWF 11:30-12:20, Room MEB 246
Lab: Thursday 10:30-11:20, Room EE1 045

Final Exam: In-class Wednesday, December  10th
Take-home component due 2 PM December 17th

Special Office Hours for Durran: Tues December 9th: 2-4 PM

Instructor: Professor Dale Durran
606 ATG, 543-7440, durrand@atmos.washington.edu
Office hours: Monday 2:30-3:30,  Thursday 1:00-2:00

TA: Eleanor Williams
503 APL, 616-7143, eleanor@ocean.washington.edu
Office hours held in 420 ATG : Tues 10:30-11:30, Wed 10:30-11:30

Textbook: Kundu-Cohen, 2002: Fluid Mechanics,  2nd Ed.  Academic Press.

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
  • Skim 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 1-5, 8, 11-13 by lab on Thursday Oct 9th
  • Chapter 4, Sections 1-3, 5-7,10-11, 13-16 by lab on Thursday Oct 16th
  • Chapter 4, Section 17; Chapter 5, Sections 1,2,4,5,7,8 by lab on Thursday Oct 30th
  • Chapter  7, Sections 1-5, 9 through "For surface gravity waves having the dispersion ...", and the notes on plane waves (download pdf), by lab on Thursday November 13th., 
  • Web animations (quicktime) on water waves
  • Chapter  7, Sections 6,8-11 by lab on Thursday November 20th
  • Chapter  7, Sections  18-21 by  Wednesday December  3rd 
  • Chapter 12, Sections 1,2,6 by Monday December 8th

Homework

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

Exercise 1 (pdf): Due Friday October 10th

Exercise 2 (pdf): Due Friday October 24th

Exercise 3 (pdf): Due Friday November 7th

Take-home midterm (pdf):  Work independently on this!   Due Friday November 21st

Exercise 5 (pdf): Due Friday December 5th

Web Links
  • Trajectories produced by a vortex translating a uniform speed: how would the streamlines compare to the animated trajectory shown at  http://archives.math.utk.edu/visual.calculus/0/parametric.5/    Imagine  the circular motion is produced by a Rankine Vortex of radius equal to that of the blue disk and that this vortex is imbedded in a uniform left to right flow.

Course Outline


Physical conservation laws applied to a continuum

·        Conservation of momentum (Newton’s 2nd Law)

·        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.