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 BYNCSA
Rayleigh's problem: velocity profile due to the impulsive motion of xplane. (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 schoolwide 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 firstyear 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 hydrodynamic instability. Linearized analysis of KelvinHelmholtz instability. Effects of shear and stratifcation. OrrSommerfeld equation for boundary layer instability. Geophysical fluid dynamics of coastal waters. Effects of earth rotation on coastal flows. Windinduced flows in shallow seas. Coastal upwelling.
Calendar






LEC # 



TOPICS / READINGS 



ASSIGNMENTS 






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 Ttube 


4 



Forces in the Fluid, Stresses and Cauchy's Law 






5 



Momentum Conservation Law 






6 



Stress and Strain, NavierStokes 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 KelvinHelmholtz Instability; Linearized Analysis of KH Instability; KH 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 MicroMechanical Basis of Darcy's Law 






29 



SaffmanTaylor Instability and Viscous Lingering; Convection in a Porous Layer with a Geothermal Gradient (Rayleigh Number) 



Homework 6: (1) KH Instability with Gravity, (2) Dispersion in an Open Channel Flow Down an Incline, (3) HeleShaw Analogy 


30 



HortonRogersLapwood 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; ShallowSea Approximation 






33 



Steady WindInduced Flow in a Shallow Sea 






34 



Nonuniform Forcing on the Sea SurfaceEkman Pumping 



Take Home Final 


35 



WindForced Waves in a TwoLayered Sea 






36 



Coastal Upwelling 





