Readings

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.

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

LEC #

TOPICS

READINGS

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

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Fluid Dynamics of the Atmosphere and Ocean