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Mei, Chiang, and Guangda Li, 1.63 Advanced Fluid Dynamics of the Environment, Fall 2002. (Massachusetts Institute of Technology: MIT OpenCourseWare), (Accessed 08 Jul, 2010). License: Creative Commons BY-NC-SA

Advanced Fluid Dynamics of the Environment

Fall 2002

Rayleigh's Problem- velocity profile due to impulsive motion of x-plane.

Rayleigh's problem: velocity profile due to the impulsive motion of x-plane. (Simulation created by MATLAB®.)

Course Highlights

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.

Course Description

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.


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.


          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
          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  
  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

  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         Tell A Friend