1 Introduction

Class Aims
Class Administration (Problem Sets, Exams, Grades, etc.)
Scheduling Issues
Introduction to Fluid Dynamics
Problem set 1 out
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
Problem set 1 due (Ses 2)
Problem set out (Ses 2)
Quiz 1 out (Ses 2)
Quiz 1 due (Ses 3)
Quiz 2 out (Ses 3)
Quiz 2 due (Ses 4)
Problem set 2 due (Ses 4)
Problem set 3 out (Ses 4)
Quiz 3 out (Ses 5)
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
Quiz 3 due (Ses 6)
Problem set 3 due (Ses 7)
Problem set 4 out (Ses 7)
Problem set 4 due (Ses 9)
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
Problem set 5 out (Ses 10)
Quiz 4 out (Ses 10)
Quiz 4 due (Ses 11)
Problem set 5 due (Ses 12)
Problem set 6 out (Ses 12)
Quiz 5 out (Ses 12)
Quiz 5 due (Ses 13)
14-15 Impact of The Earth’s Rotation

Momentum Equations in a Rotating Frame
Centripetal Acceleration, Coriolis Acceleration
Vorticity Equation in a Rotating Frame
Kelvin's Circulation Theorem in a Rotating Frame
Quiz 6 out (Ses 14)
Problem set 6 due (Ses 15)
Problem set 7 out (Ses 15)
Quiz 6 due (Ses 15)
16-18 GFD Kinematics

Simplified Momentum Equations
Inertial Flow, Geostrophy, Gradient Wind, Cyclostrophic Flow, Isallobaric Flow
Impact of Viscosity
Taylor-Proudman Theorem
Thermal Wind
Quiz 7 out (Ses 16)
Quiz 7 due (Ses 17)
Problem set 7 due (Ses 17)
Problem set 8 out (Ses 17)
19-20 Ekman Layers

Brief Boundary Layer Introduction
Mass Transport in Ekman Layer; Ekman Pumping and Suction
Ekman Spiral
Sverdrup Transport
Problem set 8 due (Ses 19)
Problem set 9 out (Ses 20)
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
Problem set 9 due (Ses 21)
25 Final exam due