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. Pics of flow around a cylinder from Van Dyke's Album of Fluid Motion (1982, Parabolic Press) scanned by physics.bu.edu/~redner/542/refs/flow-pix.pdf. 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

    Video

    Turbulence (29 min, NCFMF)

    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:

    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)

    Grading

    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 HW #5 Solutions
    HW6 Wed 23 Nov HW #6 Solutions
    HW7 Fri 2 Dec HW #7 Solutions
    HW8 Fri 9 Dec HW #8 Solutions

    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.

    Evolution of steady inviscid constant-density swirling flow in a pipe with an upstream nondimensional radius 1, uniform along-pipe flow U=1 and a swirling velocity component V = S*r after the flow moves into a part of the pipe where the pipe radius narrows by 50%. The script swirl_demo_commands.m calls functions to make the plot and animations we saw in class. To use it, open a Matlab command window and hit any key when it pauses. Plots (see links for examples) include

    To run the script swirl_demo_commands, you will need to download the following functions to the same directory as the script:

    Homework 6 solution scripts for problems 1, 2 and 3. All use ComplexPotlCirc.m and ComplexPotlCircDeriv.m.