12.800 | Fall 2004 | Graduate

Fluid Dynamics of the Atmosphere and Ocean




Class Aims 
Class Administration (Problem Sets, Exams, Grades, etc.) 
Scheduling Issues 
Introduction to Fluid Dynamics

Problem set 1 out

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)

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)

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)

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)

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)

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)


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

Course Info

As Taught In
Fall 2004