Date

Applied Mathematics

Physics

Reading*

1/20
1/22

Small Reynolds no.
Long-wave approx.

Narrowly confined flows
Thin liquid films

B: 4.8; T: 8.1-2; L: 4.A-C, 7.B
L: 7.C-D

1/27
1/29

Linearize about no flow
Lin. about uniform flow

Stokes flow
Oseen flow

B: 4.9; T: 9.4-5, 12.3; L: 4.E
B: 4.10; L: 8.F

2/3
2/5

Suspended microstructure
Non-Newtonian flows

B: 4.11; L: 4.E
L: 2.I; BAH: 2

2/10
2/12

Linear viscoelasticity
No lecture

Oscillatory shear
No lecture

BAH: 5.1-3

2/17
2/19

Nonlinear viscoelasticity
Method of characteristics

Fiber spinning
Acoustics

BAH: 7.1-4
LR: 1.1-12, 2.1-11

2/24
2/26

Acoustics; Isentropic flow
Isentropic flow; shocks

LR: 3.3-7
LR: 2.12-3.2

3/2
3/4

Wave-front expansions

Unsteady waves
Shock formation

LR: 3.9-12

3/9
3/11

Viscous acoustics
Irrotational flows

B: 6.1-4; T: 10

3/16
3/18

Complex potential
Conformal mapping

2D inviscid flows
2D inviscid flows

B: 6.5
B: 6.6-7; T: 13

3/23
3/25

No lecture
No lecture

No lecture
No lecture

3/30
4/1

Water waves
Cavitation; bubbles

Li: 3.1-4, 3.6
B: 6.11-12

4/6
4/8

Introduction to stability
Linear analysis

Two fluid streams
Two fluid streams

T: 17; DR: 1-5

4/13
4/15

Boussinesq approximation
Calculus of variations

Onset of convection
Onset of convection

T: 14, 22; DR: 6-10.1, 12-13

4/20
4/22

Calculus of variations
Energy analysis

General flows
Onset of convection

J: 1-5
J: 54-62

4/27
4/29

Linear analysis

Parallel flows
Nature of turbulence

DR: 20-24
T: 18-19

5/4
5/6

Turbulent diffusion
Scaling laws

T: 20
T: 21

5/11

Project presentations

Project presentations

Date

Applied Mathematics

Physics

Reading*

8/25
8/27
8/29

Introduction
Cartesian tensors
Change basis; eigenprobs

9/1
9/3
9/5

Holiday (no lecture)
Polar decomposition
Eulerian vs. Lagrangian

Holiday (no lecture)
Kinematics
Kinematics

 
B: 2.1, 2.3; T: 5.3, 5.5

9/8
9/10
9/12

Objectivity
Transport theorem

Balance laws

B: 3.1-4; T: 5.4, 5.6; L: 2.A-D

9/15
9/17
9/19

Constitutive theory
Constitutive theory

B: 3.1-4; T: 5.4, 5.6; L: 2.E-J

9/22
9/24
9/26

Curvilinear tensors
 

Equations of motion
Elementary flows

B: 3.6, 4.1-2; T: 2.1-5, 5.8, 9.1-3; L: 3.A-B

9/29
10/1
10/3

Boundary conditions

Elementary flows
Clean free surfaces

B: 4.3, 4.5; L: 3.C-E
B: 1.9, 3.3; L: 2.K

10/6
10/8
10/10

Green's identities
 

Vorticity & velocity
Discrete vorticity

B: 2.4-5, 2.9; T: 6.4-6
B: 2.6, 7.1-3; T: 6.6

10/13
10/15
10/17

Diffusion of vorticity
Vortex stretching

Decaying viscous vortex
Necklace vortex

B: 4.5
B: 5.2; T: 10.2

10/20
10/22
10/24

Vorticity confinement

Vorticity generation
Flow to a solid boundary

B: 5.4: T: 11.1
B: 5.5

10/27
10/29
10/31

Vorticity confinement
Regular perturbations

Converging channel
Oscillating pressure grad

B: 5.6
B: 5.7; L: 3.F, 6.A-B

11/3
11/5
11/7

Singular perturbations
Boundary layer equations

Oscillating pressure grad
Flat plate boundary layer

B: 5.7; L: 6.A-B
B: 5.8; T: 11.2-4; L: 10.A-C

11/10
11/12
11/14

No lecture

Effects of pressure grad
Separation & attachment
No lecture

B: 5.9; T: 12.2; L: 10.D
B: 5.10-11; T: 12, 3; L: 10.E

11/17
11/19
11/21

B: 5.12; T: 11.5-6

Low Peclet number limit

Holiday (no lecture)

Heat & mass transfer

12/1
12/3
12/5

High Peclet number limit

Heat & mass transfer

L: 9.A-B