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The handouts from Jim Price (Sr. Scientist, Woods Hole Oceanographic Institution) used in the lecture notes section of this course are now available as an online publication: Topics in Fluid Dynamics: Dimensional Analysis, the Coriolis Force, and Lagrangian and Eulerian Representations.
KC04 = Kundu, P. K., and I. M. Cohen. Fluid Mechanics. 3rd ed. New York: Elsevier Academic Press, 2004. ISBN: 9780121782535.
CR94 = Cushman-Roisin, B. Introduction to Geophysical Fluid Dynamics. New York: Prentice Hall, 1994. ISBN: 9780133533019.
| 1 |
Introduction
Class Aims
Class Administration (Problem Sets, Exams, Grades, etc.)
Scheduling Issues
Introduction to Fluid Dynamics |
|
| 2-5 |
Kinematics of Fluid Flow
Eulerian and Lagrangian Representations of Flow
The Material Derivative
Trajectories, Streaklines, and Streamlines
Cauchy-Stokes Theorem
The Velocity Gradient Tensor |
Session 2
KC04: 1.1-1.7, 3.1-3.5, 3.13 (optional Chap 2)
CR94: Chapter 1
KFF I, II, IV
Session 3
KC04: 3.6-3.10
Session 4
KC04: 3.6-3.10
Session 5
KFF V
KC04: 4.1-4.4 |
| 6-9 |
Conservation Equations
Reynolds Transport Theorem
Momentum Equations (Navier-Stokes, Boussinesq form of Navier-Stokes, Euler)
Total Energy Equation, Mechanical Energy Equation, Heat Equation
2nd Law of Thermodynamics |
Session 6
KC04: 4.5-4.11
Session 7
KC04: 4.13 - 4.15
Session 8
KC04: 4.13 - 4.17
Session 9
KC04: 4.16 - 4.18 |
| 10-13 |
Vortex Flows, Circulation, and Vorticity
Bernoulli Functions
Solid Body Rotation, Point Vortex, Rankine Vortex
Stokes' Theorem
Potential Flows: Interacting Point Vortices
Kelvin's Circulation Theorem
Helmholtz Vortex Theorems
Vorticity Equation |
Session 10
KC04: 4.16 - 4.18
Session 11
KC04: 5.1-5.3, 5.8-5.9, 3.11 (review)
Session 12
KC04: 5.4-5.5
Session 13
KC04: 5.4-5.5 |
| 14-15 |
Impact of The Earth’s Rotation
Momentum Eequations in a Rotating Frame
Centripetal Acceleration, Coriolis Acceleration
Vorticity Equation in a Rotating Frame
Kelvin's Circulation Theorem in a Rotating Frame |
Session 14
KC04: 4.12, CR: 2.1-2.5
Session 15
KC04: 5.7, 14.1-14.4 |
| 16-18 |
GFD Kinematics
Simplified Momentum Equations
Inertial Flow, Geostrophy, Gradient Wind, Cyclostrophic Flow, Isallobaric Flow
Impact of Viscosity
Taylor-Proudman Theorem
Thermal Wind |
Session 16
KC04: 14.5
Session 17
Holton 92: 3.2, 3.4 |
| 19-20 |
Ekman Layers
Brief Bboundary Layer Introduction
Mass Transport in Ekman Layer; Ekman Pumping and Suction
Ekman Spiral
Sverdrup Transport |
Session 20
14.6-14.7 |
| 21-24 |
Waves
Beta Effect
Wave Kinematics
Barotropic, Fixed Depth Rossby Waves
Shallow Water Equations, Shallow Water Gravity Waves, Inertia-Gravity Waves, Kelvin Waves
Potential Vorticity
Barotropic, Quasi-Geostrophic Rossby Waves
Kelvin-Helmholz Instability |
Session 21
KC04: 14.8
Session 22
KC04: 12.9, 14.16
Session 23
KC04: 14.13, 14.15
Session 24
KC04: 14.11-14.12 |