Table of Contents
Study Materials
Readings
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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.| LEC # | TOPICS | READINGS |
|---|---|---|
| 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 |