Week

Topic

HW Problems and Reading:

DUE ON THE DAY

1 (January 11)

Physical Principles: What are fluids? The continuum hypothesis and the complexity of geological materials. Observing “physically”. Control volumes and problem-solving strategies.

TUESDAY

Heuberger et al., Density Fluctuations Under Confinement: When Is a fluid not a fluid? Science, 292, 905-908, 2001.

CER Ch. 1 - 3 (review material as needed for day 1 and return to this through the course as you need)

THURSDAY

Home experiment: CV choice. Turbulent jets and plumes in the kitchen

Reading:

CER Ch. 4.1-4.3, 5

2

Physical Principles: Systems, control volumes and integral forms of the conservation laws.

Practice with various geological fluid flow problems.

Building physical insight: Dimensional analysis and scaling analysis basics

TUESDAY

Reading:

PF 2.1-2.4.2

Probs:  CER 5.3, 5.4, 5.5, 5.10, 5.12, 5.16;

Supplemental problems: Review 1

THURSDAY

Reading:

CER Ch. 6.1-6.4; PF 2.4.3-2.4.4

Probs: PF 2.3, 2.4, 2.8

3-5

Euler and Bernoulli equations. Momentum conservation.  Surface and body forces; Dimensional analysis and physical thinking.

Links between variations in momentum flux, dynamic pressure variations, boundary conditions and drag. 

Forces on river bends; Volcanic ballistics; Periodic variations in the length of day

TUESDAY

Re-read as needed:

CER Ch. 6.1-6.4; PF 2.4.3-2.4.4

QUIZ 1

THURSDAY (1/26)

Home experiments on momentum fluxes and drag; Find one image involving a flow disturbed around anything—rocks, plants, biology, islands, planets, whatever

TUESDAY (2/1)

Probs: PF 2.12, 2.14, 2.18 , 2.19

5

Mass and momentum conservation with the Bernoulli equation. Boundary conditions, closure problems

Pressure (form) drag and the flight of volcanic bombs;  Inner core-Outer core- mantle coupling and Earth’s length of day: Effects of gravitational and magnetic “drag”

THURSDAY (2/3)

Supplemental problem (if we get there): Integral momentum conservation, rigid boundaries and drag. Volcanic bombs and reconstructing vent conditions from a field map

THURSDAY (2/10)

QUIZ 2.

6

Continuum mechanics review; Div, Grad, Curl; Links between vorticity, circulation and dynamic pressure variations

TUESDAY (2/15)

Supplemental problems: Review 2

Read and outline supplemental notes on continuum mechanics as needed;

Reading: PF 1.3

THURSDAY

7

Finish Continuum Mechanics; Kinematics of fluids; Lagrangian and Eulerian reference frames; Velocity gradients and acceleration

TUESDAY (after break)

Reading:

CER Ch. 4; PF Ch. 3 (this is long)

Home experiment: Pure and simple shear; boundary conditions

THURSDAY

8

PDEs of fluid flow; Navier Stokes Equations; Boundary Conditions

Working with the equations of motion; Non-dimensionalization and scaling; simplifying the PDEs of fluid flow

TUESDAY

Probs: PF 1.7,1.16,1.18, 3.3, 3.5

Supplemental problems: Kinematics

THURSDAY

Probs: PF   3.5 ; 3.20 ; 3.22 (ignore heat transfer!)

Journal Article Review Due

9

Velocity boundary layers, diffusion of momentum and vorticity

TUESDAY

Reading (week 9):

PF Ch. 4; 6.1-6.4

Supplemental problem:

-Scaling, self-similarity and the growth of velocity boundary layers

THURSDAY (3/17)

IN CLASS MIDTERM

10

Very slow gravity currents and mantle plumes

Flows driven by lateral gradients in hydrostatic pressure and retarded by viscous stresses arising through the growth of velocity gradients

Problems potentially drawn from plate tectonics; the rise and spread of mantle plumes beneath the lithosphere; the flow of very viscous lavas; post-glacial rebound; the growth of mountain ranges

Tools: Scaling and control volume analysis; similarity solutions

TUESDAY

Paper: Kerr and Lister

THURSDAY

Home Experiment: Spread of very viscous gravity currents

11,12

Turbulent gravity currents and plumes

Flows driven by small buoyancy sources and lateral gradients in dynamic and hydrostatic pressure and retarded through the production of turbulent accelerations, entrainment and mixing across density interfaces

Examples potentially drawn from the intrusion and spread of volcanic and hydrothermal clouds; the melting of icebergs and sea ice; turbidity currents; avalanches;

Tools: Scaling and control volume analysis (integral models); possibly some linear stability analysis

TUESDAY

Supplemental problem on lubrication: Plume-lithosphere interaction

Reading:

PF: 5.2, 9.1-9.2 (9.8 is neat but optional)

Papers: Turner, 1986; Linden, 1979

FINAL TALKS

THURSDAY APRIL 7, 10 am (in class)

13

(time-permitting) Natural convection from plane layers

Problems potentially drawn from ore genesis, solidifying magma reservoirs, growing/ melting sea ice, black smoker clouds in the deep ocean, salt domes and mantle convection; hydrothermal circulation

Tools: Scaling and control volume analysis; stability analysis/considerations (depending on time)

TUESDAY

Reading: TBA

Home experiment: Ice melting in scotch vs. soda

THURSDAY

TUESDAY

Home experiment

FINAL EXAM

TBA