Chapter 1: Basics
1 Eulerian and Lagrangian Descriptions of Fluid Motion
2 Kinematics, Strain and Vorticity
3 Kinematic Transport Theorem and Consequences Homework 1: (1) Flow in a T-tube
4 Forces in the Fluid, Stresses and Cauchy's Law
5 Momentum Conservation Law
6 Stress and Strain, Navier-Stokes Equations
Recitation and Supplementary Reading: Cartesian Tensors
Chapter 2: Simple Deductions
7 Vorticity Theorems for Homogeneous and Stratified Fluids Homework 2: (1) Voriticity and Mountain Waves, (2) Bubble Dynamics
8 Rayleigh Problem -- Where Does Vorticity Come From?
9 Scaling and Approximations
Chapter 3: Slow Flows
10 Slow Spreading of a Mud Layer on an Incline Homework 3: Mechanical Energy; Radome in the Rain; Lubrication Approximation
11 Selective Withdrawal into a Line Sink, Boundary Layer Approximation and Similarity Solution
12 Stokes Flow Past a Sphere
13 Mechanics of Aerosols Homework 4: Spreading of Lava on a Plane
Take Home Midterm
Supplementary Reading: Transient Slow Spreading of a Mud Layer on an Incline
Supplementary Reading: Oseen's Theory of Slow Flow Past a Cylinder
Chapter 3: High Reynolds Number Flows
14 Inviscid Irrotational Flows of a Homogeneous Fluid
15 Bernoulli's Theorems for Inviscid Homogeneous Fluids
16 Example of Steady Boundary Layer; The Laminar Jet
17 Effects of Variable Pressure Gradient
18 Kármán's Momentum Integral Approximation
19 An Application to Transient Boundary Layer Along a Flat Plate
20 Unsteady Boundary Layers
21 Gust and Separation Homework 5: Jet from a Point Source
Supplementary Reading: Wave Boundary Layers; Stokes Theory
Supplementary Reading: Induced Streaming - Eulerian and Lagrangian
Chapter 4: Transport of Heat or Mass
22 Thermal Energy; Mountain Wind
23 Buoyant Plume from a Steady Source of Heat
24 Homogenization and Dispersion in Oscillatory Flows in a Pipe
Chapter 5: Introduction to Instability
25 Heruristic Argument of Kelvin-Helmholtz Instability; Linearized Analysis of K-H Instability; K-H Instabilty of a Continuously Stratified Fluid
26 Rayleigh's Inviscid Theory of Instability of Parallel Flows; Fjortoft's Theorem
27 Viscous Effects on Parallel Flow Instability
Chapter 6: Flow and Transport in Porous Media
28 Porous Media and Darcy's Law; Homogenization and Micro-Mechanical Basis of Darcy's Law
29 Saffman-Taylor Instability and Viscous Lingering; Convection in a Porous Layer with a Geothermal Gradient (Rayleigh Number) Homework 6: (1) K-H Instability with Gravity, (2) Dispersion in an Open Channel Flow Down an Incline, (3) Hele-Shaw Analogy
30 Horton-Rogers-Lapwood Instability

Recitation and Supplemental Reading: Double Diffusion and Thermohaline Instability
Supplemental Reading: Geothermal Plume as a Boundary Layer

Chapter 7: Earth Rotation and Coastal Flows
31 Rotating Coordinates and Coriolis Force
32 Vorticity Theorem in Rotating Fluid; Shallow-Sea Approximation
33 Steady Wind-Induced Flow in a Shallow Sea
34 Nonuniform Forcing on the Sea Surface-Ekman Pumping Take Home Final
35 Wind-Forced Waves in a Two-Layered Sea
36 Coastal Upwelling