Courses:

Advanced Fluid Dynamics of the Environment >> Content Detail

Calendar / Schedule

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

Course Home

Courses:

Advanced Fluid Dynamics of the Environment >> Content Detail

Table of Contents

Calendar / Schedule