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Advanced Fluid Dynamics of the Environment >> Content Detail



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LEC #TOPICS / READINGS    ASSIGNMENTS
Chapter 1: Basics
1Eulerian and Lagrangian Descriptions of Fluid Motion
2Kinematics, Strain and Vorticity
3Kinematic Transport Theorem and ConsequencesHomework 1: (1) Flow in a T-tube
4Forces in the Fluid, Stresses and Cauchy's Law
5Momentum Conservation Law
6Stress and Strain, Navier-Stokes Equations
Recitation and Supplementary Reading: Cartesian Tensors
Chapter 2: Simple Deductions
7Vorticity Theorems for Homogeneous and Stratified FluidsHomework 2: (1) Voriticity and Mountain Waves, (2) Bubble Dynamics
8Rayleigh Problem -- Where Does Vorticity Come From?
9Scaling and Approximations
Chapter 3: Slow Flows
10Slow Spreading of a Mud Layer on an InclineHomework 3: Mechanical Energy; Radome in the Rain; Lubrication Approximation
11Selective Withdrawal into a Line Sink, Boundary Layer Approximation and Similarity Solution
12Stokes Flow Past a Sphere
13Mechanics of AerosolsHomework 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
14Inviscid Irrotational Flows of a Homogeneous Fluid
15Bernoulli's Theorems for Inviscid Homogeneous Fluids
16Example of Steady Boundary Layer; The Laminar Jet
17Effects of Variable Pressure Gradient
18Kármán's Momentum Integral Approximation
19An Application to Transient Boundary Layer Along a Flat Plate
20Unsteady Boundary Layers
21Gust and SeparationHomework 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
22Thermal Energy; Mountain Wind
23Buoyant Plume from a Steady Source of Heat
24Homogenization and Dispersion in Oscillatory Flows in a Pipe
Chapter 5: Introduction to Instability
25Heruristic Argument of Kelvin-Helmholtz Instability; Linearized Analysis of K-H Instability; K-H Instabilty of a Continuously Stratified Fluid
26Rayleigh's Inviscid Theory of Instability of Parallel Flows; Fjortoft's Theorem
27Viscous Effects on Parallel Flow Instability
Chapter 6: Flow and Transport in Porous Media
28Porous Media and Darcy's Law; Homogenization and Micro-Mechanical Basis of Darcy's Law
29Saffman-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
30Horton-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
31Rotating Coordinates and Coriolis Force
32Vorticity Theorem in Rotating Fluid; Shallow-Sea Approximation
33Steady Wind-Induced Flow in a Shallow Sea
34Nonuniform Forcing on the Sea Surface-Ekman PumpingTake Home Final
35Wind-Forced Waves in a Two-Layered Sea
36Coastal Upwelling
 


 



 








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