Advanced Fluid Dynamics of the Environment

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 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
	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 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
	Chapter 7: Earth Rotation and Coastal Flows
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