Fluids (AMATH-ATM S 505/OCEAN 511)

AMATH - ATM S 505/OCEAN 511 Fluid Dynamics Autumn 2011
http://www.atmos.washington.edu/academics/classes/2011Q4/505/

MTuWThF 11:30-12:20: ATG 310c

Note: I have changed the Tuesday class to 11:30-12:20 and we will use it for a quiz (problem-solving) section. Thursdays at 11:30-12:20 will be used for making up lectures missed due to my travel schedule.

Instructor:
Prof. Chris Bretherton
breth@washington.edu
ATG 704, x5-7414
Office hours: MW 12:30-1:20, (after class) or by appointment.

Course description

Prerequisites

Textbook

Schedule/Syllabus

Grading

Homework and Exams

Matlab scripts

Course Description (from UW course catalog)

Eulerian equations for mass, motion; Navier-Stokes equation for viscous fluids, Cartesian tensors, stress, strain relations; Kelvin's theorem, vortex dynamics; potential flows, flows with high, low Reynolds numbers; boundary layers, introduction to singular perturbation techniques; water waves; linear instability theory.

Note: We won't discuss Cartesian tensors or singular perturbation theory in any depth, but we will do sound waves. We will emphasize air and water as example fluids.

Prerequisites

Amath 401/501 (vector calculus; may be taken concurrently). AMATH 403/503 (partial differential equations) recommended but not required.

Textbook

Kundu, P. K, and I. M. Cohen, 2004: Fluid Mechanics. Elsevier Academic Press [K in syllabus]
...this book is more comprehensive and formalistic than the course will be, and makes a great reference.

Course organization and schedule

The lecture schedule is organized around the instructor's travel schedule. Scanned lecture notes will be linked in the table below.

Day	Date	Type	Topic	Kundu Reading
We	28 Sep	Lecture+videos	What is a fluid? Continuum approx., viscosity,	1.1-1.5
Th Fr	29 Sep 30 Sep	Lecture	Surface tension. Statics & thermodynamics: Pressure, hydrostatic balance, thermodynamics, compressibility, potl density, scale height	1.6-1.10
Mo Tu We	3 Oct 4 Oct 5 Oct	NO CLASS	Instructor at NRC meeting in Washington DC
Th Fr	6 Oct 7 Oct	Lecture	Essentials of vector analysis, indicial notation, div, grad and curl. Vorticity and circulation.	2.1-2.3 2.7-2.10
Mo	10 Oct	Lecture	Lagrangian vs. Eulerian views, material derivative, mass conservation	3.1-3.4, 4.3
Tu	11 Oct	Quiz section
We Th Fr	12 Oct 13 Oct 14 Oct	Lecture	Forces and stresses. Momentum conservation equation.	4.5-4.8
Mo	17 Oct	Lecture	Energy conservation equations I	4.13-4.15
Tu	18 Oct	Quiz section
We	19 Oct	Lecture	Energy conservation equations II	4.13-4.15
Th	20 Oct	Lecture	Bernoulli's equation for steady inviscid barotropic flow.	4.16-4.17
Fr	21 Oct	Lecture	Boundary Conditions	4.19
Mo Tu We	24 Oct 25 Oct 26 Oct	NO CLASS	Instructor at WCRP meeting in Denver
Th Fr	27 Oct 28 Oct	Lecture	Linear sound waves and Mach number	16.1-16.2
Mo Tu	31 Oct 1 Nov	NO CLASS	Instructor at CPT meeting in Boulder CO
We	2 Nov	Lecture	Kelvin's circulation theorem	5.4
Th	3 Nov	Lecture	Vortex tubes and vortex lines.	5.1-2, 5.4
Fr	4 Nov	Lecture	Vorticity equation, vortex stretching and tilting	5.5-5.7
Mo Tu We	7 Nov 8 Nov 9 Nov	NO CLASS	Instructor at NRC meeting in Irvine CA
Th	10 Nov	MIDTERM	Closed book, 1 double-sided page of notes. Covers thru 28 Oct.
Fr	11 Nov	NO CLASS	Veterans Day Holiday
Mo	14 Nov	Lecture	Some vortical flows	3.11, 5.8-5.9
Tu	15 Nov	Quiz section	Includes discussion of midterm
We	16 Nov	Lecture	Potential (irrotational incompressible) flow - general properties and mathematical description	6.1-6.2
Th Fr	17 Nov 18 Nov	Lecture	Potential flow around a cylinder and airfoil. Circulation, lift and drag	6.9-6.10
Mo	21 Nov	Lecture	Swirling flow in a narrowing pipe	10.1-10.10
Tu	22 Nov	Quiz section
We	23 Nov	Lecture	Surface gravity waves - mathematical formulation	7.4
Th Fr	24 Nov 25 Nov	NO CLASS	Thanksgiving Holiday
Mo	28 Nov	Lecture	Surface gravity waves - dispersion reln.	7.4
Tu	29 Nov	Quiz section
We	30 Nov	Lecture	Surface gravity wave physics	7.5
Th	1 Dec	Lecture	Viscous stress vs.strain for Newtonian fluids. Navier-Stokes equation.	4.10-11
Fr	2 Dec	Lecture	Scaling analysis, dynamical similarity, Reynolds number, low Re flow.	8.7
Mo	5 Dec	Lecture	Laminar shear and pipe flow.	9.4-5
Tu	6 Dec	Quiz section
We Th	7 Dec 8 Dec	Lectures	Shear instability at a stratified interface	12.6
Fr	9 Dec	Lecture	Catchup and/or Final Review
We	14 Dec	Final Exam	2:30-4:20pm, open book

Please email or call me to arrange another meeting time if you need to talk to me outside office hours.

I will be out of town on:

Mo-We 3-5 Oct (DC)
Mo-We 24-26 Oct (Denver)
Mo-Tu 31 Oct-1 Nov (Boulder)
Mo-We 7-9 Nov (DC)

NCFMF Videos

In the 1960's, the National Committee on Fluid Mechanics Films produced an excellent series of movies describing various basic fluid dynamics topics, usually illustrated using simple experiments. Because there is nothing like seeing fluids actually move to visualize theoretical concepts, I expect you to view all the movies linked below by the dates indicated. The fashions and methods are dated, and some of the digitization is grainy, but the science hasn't changed.

View before	Topic
Fr 30 Sep	Introduction to the Study of Fluid Motion (24 min)
We 10 Oct	Eulerian and Lagrangian Descriptions in Fluid Mechanics (27 min)
Fr 21 Oct	Pressure fields and fluid acceleration (31 min)
Th 4 Nov	Vorticity Part 1 and Part 2 (45 min combined)
Th 1 Dec	Waves in Fluids (33 min)
Th 8 Dec	Fundamentals of Boundary Layers (24 min) Flow Instabilities (25 min)
TBD	Turbulence (29 min)

HW #2 Solutions

Grading

Homework (50%), posted to class web page and assigned on most Fridays. Collaboration with your fellow students is encouraged, but everyone needs to write out the homework in their own words. PDFs emailed using DropBox are fine. There will be a 25% penalty on late homeworks (after 5pm on due date) except for your first one, unless there are extenuating circumstance and a mutually acceptable arrangement has been made prior to the due date. Late homework will not be accepted after 11 am on the Tuesday following the due date.
Midterm (20%), Thursday 10 Nov, 50 min., in-class, closed book, 1 double -sided sheet of notes.
Final (30%), Wednesday 14 Dec 2:30-4:20, in-class, open book and note.

Homework and Exams

Item	Due Date	Download Solutions
HW1	Fri 7 Oct	HW #1 Solutions
HW2	Fri 14 Oct	HW #2 Solutions
HW3	Fri 21 Oct	HW #3 Solutions
HW4	Fri 28 Oct	HW #4 Solutions
HW5	Fri 4 Nov

Matlab scripts

HW2, problem 2: Script to make this plot of velocity vectors, sample streamlines, and the evolution of a square of dye in a deformation flow u=D*x, v=-D*y, D = 1, y > 0.