EOSC 514 Introduction to Geological Fluid Mechanics, Spring
2012
Instructor: Mark Jellinek, EOS South 257
Text: Fluid Mechanics
by Potter and Foss and some chapters from Engineering
Fluid Mechanics by Crowe, Elger and Roberson
DVD: Multimedia
Fluid Mechanics (MFM) by Homsy et al.
Introduction
Many problems in the Earth
and planetary sciences involve fluid flow. Examples include the formation and
subsequent thermal evolution of planets, the generation of planetary magnetic
fields, the generation, rise, chemical differentiation, flow and eruption of
magmas, sedimentation and mechanical erosion at riverbeds, the flow of
groundwater, and circulation and mixing in the atmosphere and oceans.
This course presents a
general introduction to the broad discipline of geological fluid mechanics.
First and foremost, the course will introduce concepts and problem solving
strategies in fluid mechanics. We will explore fundamental concepts including
the continuum hypothesis, systems and control volumes, kinematics of fluids, integral and differential forms of the equations of motion,
boundary conditions, dimensional analysis, scaling and stability. We will build
understanding of core concepts in part by examining aspects of a number of
special limits and features of flows occurring in geological situations such as
boundary layers, potential flow, vorticity,
lubrication theory, turbulence and waves. Geological flows are rich in their
variety and complexity. They are never boring and they will constantly
challenge the extent to which you understand the fundamentals. Why, for
example, can you treat a snow avalanche composed of widely-spaced
ice crystals and entrained air as Òa fluidÓ? In many cases,
to make the geological problem ÒtractableÓ we have to make what you will probably
regard as grotesque simplifications.
Such exercises enable us to classify or characterize behavior and build
understanding in methodical ways.
Student learning objectives in order of increasing levels of
learning
1)
Solve simple problems in fluid mechanics. The student will acquire and apply
necessary analytical skills
(mathematical and physical) to classify and solve simple given problems
involving fluids.
2)
Pose simple problems in geological fluid mechanics as models. The student will
develop a personalized approach for constructing a conceptual and technical
understanding of the mechanics involved in straightforward fluids problems.
3)
Understand analog models of complex problems. The student will be able to
reconstruct and understand existing mathematical representations of complicated
problems involving fluids. The student will be able to discern and articulate
verbally the strengths and weaknesses of such models.
4)
Reduce complex (intractable) problems in geological fluid mechanics into some
number of simpler (tractable) component problems. The student will be able to
construct a model of a complex system and understand the strengths and
limitations of such a model system. The student will be able to articulate
verbally the value and limitations of such a model.
Assessment (5 parts)
1)
Problem sets and Journal Review (20%)
Each
problem set is designed to enhance your understanding of core material by
looking at simple and sometimes ÒclassicalÓ problems. Viewed collectively, one
of the aims of the problem sets is also to illustrate how fluids problems are
classified and thus simplified such that they may be solved. Most assigned
problems are drawn from the textbook, which has an engineering emphasis. These
problems establish some basic principles. Complementary geological problems
will be assigned, in part, to indicate the generality of the concepts being
addressed.
Solutions
to all textbook problems are posted on the web. Solutions to supplemental problems will
be provided in class. To receive
full credit all problem sets must be self-graded with your own
comments related to where you went wrong and why, what you did and why you did
it. No comments
means no grade (i.e., 0 marks).
No late work is accepted. Please read that twice.
A
format for each problem solved will be provided in class. Please use this framework for each
homework problem. The point is to
approach each problem in a systematic way.
This process will help you ultimately decide how you like to set up and
solve problems.
All
graduate students are required to review a journal article of their choice
after consultation with me.
Undergraduate students are encouraged to do this as well but are not
required. We will discuss how to do
this in greater detail as the due date approaches but here are a few guidelines
for constructing your review:
2) Quizzes
(20%)
There will be 4 30
minute quizzes. Quizzes will
address basic concepts from lecture and the text. All material covered and
assigned is open season. Students can bring 1 page (2 sides) of review notes to
each quiz. These notes must be
handwritten.
3)
Midterm Exam (15%).
This
will be a 1.5 hour exam on the evening of Feb.
20. The exam is open book and you
may use your 3 one-page cheat sheets.
4)
Final Exam (15%).
There
will be a 3 hour take-home final exam due around December
11.
5)
Final Project (30%)
The
term project accounts for a substantial part of your assessment and will
include a paper and a short presentation. Whereas exams, quizzes and problem
sets are aimed at helping you build some familiarity and understanding of the
vocabulary and core concepts of fluid mechanics the project will allow you to
explore in detail an actual problem in geological fluid mechanics. For
undergraduate students, a critical
literature review of a problem is sufficient. Graduate students, however, must
also describe a research project aimed at understanding some process or
addressing an unsolved problem. All students are encouraged to attempt to
actually solve a theoretical/numerical or experimental problem. Equipment,
facilities and/or computers may be available. If appropriate students may also work in groups in order to work on
more involved projects. More
details about the format of the paper and the talk will be provided later.
Downloads and
links
Supplemental Lecture Notes
Numerical
Computing with MATLAB (an online textbook)
Notes
on the numerical solution of differential equations [PDF (76 KB)]
MATLAB
script odeexamplemain.m
MATLAB
function oneode.m
MATLAB function twoodes.m
Solutions to problems in the text
Tentative
Lecture Outline
|
Week |
Lecture |
Topic |
HW
Problems and Reading: DUE
ON THE DAY |
|
1/4 |
0 |
Introduction: Geological flows and a
few concepts |
|
|
1/11 |
1 |
Physical Principles: What are fluids?
The continuum hypothesis and geological materials. |
Heuberger
et al., Density Fluctuations Under Confinement: When Is a fluid not a fluid? Science, 292, 905-908,
2001. |
|
|
|
Physical Principles: Systems, control
volumes (CVs), conservation of mass and momentum; Practice solving problems |
Read: PF 1.1-1.2,1.5,1.6, 2.1-2.3 Read:
CER 4 (as needed) and ch. 5 Note:
We will not work with the energy equation here. |
|
1/18 |
2 |
Physical Principles: More about CV
formulation of conservation laws. More practiceÉ. Some geological
problems. |
Read PF 2.4 ; Read CER ch. 6 MFM: CVs=>Balance of momentum; art.
898-923; 936-948 Supplemental
problems: Review 1 Probs:
2.3, 2.4, 2.8, 2.19 |
|
1/25 |
3 |
QUIZ
1. Continuum Mechanics Review |
Read and outline supplemental notes
on continuum mechanics; PF 1.3 Supplemental problems: Review 2 |
|
2/1 |
4 |
Lab: In-class
group project: Measuring the slow spread of an oil layer, the shape of
volcanic jets and the spread of volcanic clouds |
|
|
2/8 |
|
Kinematics of fluids |
Read: PF Ch. 3 |
|
2/15 |
5 |
QUIZ
2. PDEs of fluid flow Navier
Stokes Equations and Boundary Conditions |
Probs:
1.7,1.16,1.18, 3.3 Supplemental problems: Kinematics (pdf) R:
PF Ch. 6 MFM:
160-167; 173-176 Probs:
3.5, 3.7, 3.19, 3.22 (ignore heat transfer!), 6.1, 6.2 |
|
2/29 |
6 |
Steady
unidirectional flows. A Òclassical problem or twoÓ; Plate tectonics and a
plume-fed asthenosphere |
|
|
3/6 **TUESDAY** |
7 |
Review
for midterm: Problem-solving session |
|
|
3/7 |
MIDTERM |
MIDTERM EXAM
AT 3 PM (mj away) |
|
|
3/14 |
8 |
Unsteady
unidirectional flows: Lava lake tectonics and other examples Dimensional
analysis and scaling: Working with what nature provides and making sense of
the Navier Stokes equations. |
R: PF Ch. 4; Middleton and Wilcock Ch. 3 Probs:
PF 4.1, 4.2, 4.10 MFM: 520-562; DO LABS: 560&562! |
|
3/21 |
9 |
Creeping gravity currents: Mantle
plumes and very sticky lava flows. |
R: 6.1-6.4 Project Proposal Due |
|
3/28 |
10 |
QUIZ
3. Laminar and turbulent gravity currents on the ground.
Scaling, stability, entrainment, mixing and drag. |
R:
Ch. 5.1-5.4, 9 ; 7.1-7.3 R: Simpson Chs
1, 11, 12 15 Supplemental problems: Analyzing your
experimental gravity currents MFM:
676-686, MFM: 710-719; 728-743 Journal Article Review Due |
|
4/4 |
11 |
More about laminar and turbulent
gravity currents on the ground. Turbulent jets and gravity currents
in the atmosphere and ocean: Explosive volcanic eruptions Time-permitting (unlikely this year):
Simply a cool problem-- the gravitational collapse of molecular clouds to
form solar systems |
MFM:
376-450; 676-686; 728-736; 832,856 |
|
4/11 |
12 |
Evening of
Project Talks (Food Provided) |
|
|
4/16 |
13 |
Take
Home Final Exam Due |
|