Mei, Chiang, and Guangda Li, 1.63 Advanced Fluid Dynamics of the Environment, Fall 2002. (Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed 08 Jul, 2010). License: Creative Commons BY-NC-SA
Rayleigh's problem: velocity profile due to the impulsive motion of x-plane. (Simulation created by MATLAB®.)
This course has virtually all of its course materials online, including a full set of lecture notes and assignments. The materials for this course are also used in an iCampus school-wide modular program on fluid mechanics at MIT.
Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.
1.63 FLUID DYNAMICS
Lecturer: Chiang C. Mei
Graduate credit.
Prerequisites: 2.25 or an equivalent intermediate level course in Fluid Mechanics or permission of instructor, plus one advanced level engineering mathematics course at the level of 18.085 or 1.131J(2.090J/13.475J) or equivalent.
Advanced treatment of fluid dynamics intrinsic to natural physical phenomena and/or engineering processes. A wide range of topics and mathematical techniques are discussed and may vary from year to year. Modules may be taken by students with different interests.
Sample topics include: Brief review of basic laws of fluid motion. Cartesian tensor convention.Scaling and approximations. Slow flows: Stokes' flow past a particle. Oseen's improvement for a cylinder. Spreading and gravity current on a slope. Selective withdrawal from a stratfied fluid. Boundary layers in high speed flows: Jets. Thermal plumes in pure fluids and in porous media. Similarity method of solution. Transient boundary layers. Buoyancy driven convection in porous media. Dispersion in steady or oscillatory flows. Introduction to hydro-dynamic instability. Linearized analysis of Kelvin-Helmholtz instability. Effects of shear and stratifcation. Orr-Sommerfeld equation for boundary layer instability. Geophysical fluid dynamics of coastal waters. Effects of earth rotation on coastal flows. Wind-induced flows in shallow seas. Coastal upwelling.
Calendar
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LEC # |
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TOPICS / READINGS |
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ASSIGNMENTS |
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Chapter 1: Basics |
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1 |
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Eulerian and Lagrangian Descriptions of Fluid Motion |
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2 |
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Kinematics, Strain and Vorticity |
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3 |
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Kinematic Transport Theorem and Consequences |
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Homework 1: (1) Flow in a T-tube |
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4 |
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Forces in the Fluid, Stresses and Cauchy's Law |
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5 |
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Momentum Conservation Law |
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6 |
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Stress and Strain, Navier-Stokes Equations |
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Recitation and Supplementary Reading: Cartesian Tensors |
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Chapter 2: Simple Deductions |
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7 |
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Vorticity Theorems for Homogeneous and Stratified Fluids |
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Homework 2: (1) Voriticity and Mountain Waves, (2) Bubble Dynamics |
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8 |
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Rayleigh Problem -- Where Does Vorticity Come From? |
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9 |
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Scaling and Approximations |
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Chapter 3: Slow Flows |
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10 |
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Slow Spreading of a Mud Layer on an Incline |
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Homework 3: Mechanical Energy; Radome in the Rain; Lubrication Approximation |
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11 |
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Selective Withdrawal into a Line Sink, Boundary Layer Approximation and Similarity Solution |
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12 |
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Stokes Flow Past a Sphere |
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13 |
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Mechanics of Aerosols |
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Homework 4: Spreading of Lava on a Plane
Take Home Midterm |
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Chapter 3: High Reynolds Number Flows |
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14 |
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Inviscid Irrotational Flows of a Homogeneous Fluid |
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15 |
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Bernoulli's Theorems for Inviscid Homogeneous Fluids |
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16 |
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Example of Steady Boundary Layer; The Laminar Jet |
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17 |
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Effects of Variable Pressure Gradient |
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18 |
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Kármán's Momentum Integral Approximation |
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19 |
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An Application to Transient Boundary Layer Along a Flat Plate |
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20 |
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Unsteady Boundary Layers |
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21 |
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Gust and Separation |
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Homework 5: Jet from a Point Source |
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22 |
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Thermal Energy; Mountain Wind |
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23 |
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Buoyant Plume from a Steady Source of Heat |
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24 |
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Homogenization and Dispersion in Oscillatory Flows in a Pipe |
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Chapter 5: Introduction to Instability |
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25 |
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Heruristic Argument of Kelvin-Helmholtz Instability; Linearized Analysis of K-H Instability; K-H Instabilty of a Continuously Stratified Fluid |
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26 |
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Rayleigh's Inviscid Theory of Instability of Parallel Flows; Fjortoft's Theorem |
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27 |
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Viscous Effects on Parallel Flow Instability |
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Chapter 6: Flow and Transport in Porous Media |
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28 |
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Porous Media and Darcy's Law; Homogenization and Micro-Mechanical Basis of Darcy's Law |
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29 |
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Saffman-Taylor Instability and Viscous Lingering; Convection in a Porous Layer with a Geothermal Gradient (Rayleigh Number) |
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Homework 6: (1) K-H Instability with Gravity, (2) Dispersion in an Open Channel Flow Down an Incline, (3) Hele-Shaw Analogy |
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30 |
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Horton-Rogers-Lapwood Instability |
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Recitation and Supplemental Reading: Double Diffusion and Thermohaline Instability
Supplemental Reading: Geothermal Plume as a Boundary Layer
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31 |
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Rotating Coordinates and Coriolis Force |
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32 |
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Vorticity Theorem in Rotating Fluid; Shallow-Sea Approximation |
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33 |
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Steady Wind-Induced Flow in a Shallow Sea |
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34 |
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Nonuniform Forcing on the Sea Surface-Ekman Pumping |
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Take Home Final |
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35 |
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Wind-Forced Waves in a Two-Layered Sea |
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36 |
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Coastal Upwelling |
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