Advanced Fluid Dynamics of the Environment
Lecture Notes
This section contains the lecture notes which serve two purposes: to guide the lecture topics and to serve as the required course readings. Many of the lecture notes have 1.63J/2.21J listed as the course number. This is the new course number as of Spring 2004, when the course will be offered as a joint course with the Mechanical Engineering Department, as part of an iCampus school-wide modular program on fluid mechanics at MIT.
Chapter 1: Basics
1.1 Methods of Describing Fluid Motion (PDF)
1.2 Kinematics of Fluid Motion -- the Eulerian picture (PDF)
1.3 Kinematic transport theorem (PDF)
1.4 Forces in the Fluid (PDF)
1.5 Law of Momentum Conservation (PDF)
1.6 Relations between stress and rate-of-strain tensors (PDF)
1.7 Vorticity Theorem for a viscous fluid (PDF)
1.8 Rayleigh's Problem -- solid wall as a source of vorticity (PDF)
1.9 Scaling and similarity parameters (PDF)
Chapter 2: Low Viscous Flows
2.1 A thin fluid layer flowing down an incline (PDF)
2.2 Lubrication approximation for flow in a thin layer (PDF)
2.3 A gravity current (PDF)
2.4 Spreading of a shallow mass on an incline (PDF)
2.5 Stokes flow past a sphere (PDF)
2.6 Oseen's improvement for slow flow past a cylinder (PDF)
2.7 Aerosols and coagulation (PDF)
2.8 Selective withdrawal in an isothermal stratifed fluid (PDF)
Chapter 3: High-Speed Flows and Boundary Layers
3.1 Flow of invisid and homogeneous fluids (PDF)
3.2 Viscous Flow at High Reynolds Numbers (PDF)
3.3 Two dimensional laminar jet (PDF)
3.4 The effects of pressure gradient (PDF)
3.5 Karman's momentum integral approach (PDF)
3.6 Unsteady boundary layers (PDF)
3.7 Oscillatory Boundary Layers (PDF)
3.8 Impulsive motion of a blunt body and tendency for separation (PDF)
Chapter 4: Thermal Effects in Fluids
4.1 Heat and energy conservation (PDF)
4.2 Approximations for small temperature variation (PDF)
4.3 Buoyancy-driven convection -- The Valley Wind (PDF)
4.4 Buoyant plume from a steady heat source (PDF)
4.5 Selective withdrawl of thermally stratified fluid (PDF)
4.6 Dispersion of supension in a steady shear flow (PDF)
4.7 Dispersion in an oscillatory shear flow (PDF)
Chapter 5: Rudiments of Hydrodynamic Instability
5.1 Rudiments of Hydrodynamic Instability (PDF)
5.2 Kelvin-Helmholtz Instability for continuous shear and stratification (PDF)
5.3 Inviscid Instability mechanism of parallel flows (PDF)
5.4 Viscous Effects on the Instability of parallel flows (PDF)
Chapter 6: Seepage and Thermal Effects in Porous Media
6.1 Empirical basis of Darcy's law for seepage flow (PDF)
6.2 Micro-scale basis of seepage flow; Theory of homogenization (PDF)
6.3 Saffman-Taylor instability in porous layer -- Viscous fingering (PDF)
6.4 Geothermal convection in porous media (PDF)
6.5 Geothermal Plume (PDF)
6.6 Rayleigh-Darcy (or Horton-Rogers-Lapwood) instability in a porous layer (PDF)
6.7 Thermohaline instability in a porous layer-doubly-diffusive instability (PDF)
Chapter 7: Geophysical Fluid Dynamics of Coastal Region
7.1 Equations of Motion in Rotating Coordinates (PDF)
7.2 Vorticity in inviscid rotating fluids -- Taylor-Proudman theorem (PDF)
7.3 The Shallow-Water Approximation (PDF)
7.4 Steady onshore wind in a shallow Sea (PDF)
7.5 Cyclonic current forced by a swirling wind (PDF)
7.6 Transient longshore wind (PDF)
7.7 Transient motion in a two-layered sea (PDF)
7.8 Coastal upwelling in a two-layered sea (PDF)
Assignments
This section contains the homework assignments for the course, which are assigned and organized by topics covered in the lecture notes. Many of the assignments have 1.63J/2.21J listed as the course number. This is the new course number as of Spring 2004, when the course will be offered as a joint course with the Mechanical Engineering Department, as part of an iCampus school-wide modular program on fluid mechanics at MIT.
CHAPTER 1: BASICS
Vorticity evolution in an inhomogeneous fluid (PDF)
Mechanical energy (PDF)
Cavity collapse (PDF)
Draining of a T tube (PDF)
CHAPTER 2: LOW VISCOUS FLOWS
Radome in the rain (PDF)
Spreading of lava on a horizontal plane (PDF)
Slow mud flow (PDF)
Separating a flat object from a smooth surface (PDF)
CHAPTER 3: HIGH-SPEED FLOWS AND BOUNDARY LAYERS
Motion of water beneath a spreading oil film (PDF)
Jet from a point source of momentum (PDF)
Jet from a broken pipe (PDF)
Oil slick on the sea surface (PDF)
CHAPTER 4: THERMAL EFFECTS IN FLUIDS
Differential heating of the water surface (PDF)
Channel flow through a geothermal gradient (PDF)
Dispersion in an artery (PDF)
Dispersion in an open channel (PDF)
Dispersion in an oscillating flow in a pipe (PDF)
Hot spring at Yellowstone (PDF)
CHAPTER 6: SEEPAGE AND THERMAL EFFECTS IN POROUS MEDIA
Hele-Shaw analogy between lubrication and seepage flows (PDF)
CHAPTER 7: GEOPHYSICAL FLUID DYNAMICS OF COASTAL REGION
Ekman layer under oscillatory flow (PDF)