









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 
















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 
















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 
















Supplementary Reading: Wave Boundary Layers; Stokes Theory
Supplementary Reading: Induced Streaming  Eulerian and Lagrangian 




















Chapter 4: Transport of Heat or Mass 
















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





















Chapter 7: Earth Rotation and Coastal Flows 
















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 









