|
|
|
|
|
|
|
|
|
|
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 |
|
|
|
|
|
|
|
|
|
|