**EOSC 514 Introduction to Geological Fluid Mechanics, Spring
2018**

**Instructor: **Mark
Jellinek, EOS South 257

**TA: **Anna Grau
(agraugal@gmail.com)

**Where: **ESB 5106

**When:** T (12:30-3:30) Th (2-3:30)

**Texts:** *Fluid
Mechanics* by Potter and Foss, some chapters from *Engineering
Fluid Mechanics* by Crowe, Elger and Roberson
and reading from other sources as needed.

**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. It is a reasonable prerequisite to courses
such as EOSC 512 (Advanced Geophysical Fluid Dynamics) and EOSC 554
(Theoretical Glaciology). The course will introduce generic problem solving
strategies in fluid mechanics and establish fundamental concepts including
the continuum mechanics and kinematics of fluids, integral and differential
forms of the equations of motion, boundary conditions and stability.
Understanding of core concepts is constructed by examining aspects of a
number of special limits and features of varied geological flows.

Geological flows are rich in their variety
and complexity and we will explore a lot of them. They are never boring and
they will constantly challenge the extent to which you understand fundamental
concepts. In many cases, to make the geological problem ÒtractableÓ we have to
make approximations or simplifications. Such exercises begin with learning to
observe, think physically and ask deliberate questions that inevitably
challenge whatever is our intuition. The process enables us to classify or
characterize behavior and build understanding of complex behavior in methodical
ways. This course consequently stresses physical insight: In addition to
developing strategies for solving the equations of motion in various limits
there is a strong emphasis on learning to observe characteristic features of
real flows such that physical understanding can be constructed with appropriate
scaling analysis or dimensional reasoning.

**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, ÒnotebookÓ and Journal
Review (20%)**

__Problem
sets.__* *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 and
most supplemental problems will be provided in class before your homework is
due. 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).

A format for each problem solved will
be provided in class. Please use
this framework for each homework problem.
If you do not use this format, you will get zero marks. The point is to
approach each problem in a systematic way every time. This process will help you ultimately
decide how you like to set up and solve problems.

__Notebook.__* *There is at least one
reading assignment per weekÑmost reading complements lecture material and is
related to your problem sets. Active reading is a key to learning new
materialÑand to developing your methods for how to learn methodically. This
takes some discipline. Who am I kiddingÑA LOT of discipline. To this end, with
each problem set you must also submit *electronically
*2-3 pages of hand-written notes that summarize what you have read about. 1
of these 3 pages must be a Òconcept mapÓ that identifies and links core
concepts. The concepts should involve self-serving cartoons that express
physical concepts and wordsÑno math. Page 2 could be a Òconcept mapÓ for
calculations that indicates how core concepts are identified and expressed
mathematically (more about this in class). A third page is up to you. It can
include concepts to which you need to return and additional information the importance
of which is unclearÑwhat goes on these 3 pages is up to you. You will return to
these concept maps regularly and change them as you learn. By the end of the
course your collection of concept maps and summary notes will reflect what you
have learned and also how you have learned. It will be your fluid mechanical
world according to you.

For an unimaginative picture of concept
mapping: https://en.wikipedia.org/wiki/Concept_map

A little more interesting about the
iterative process of ÒconstructingÓ understanding with a concept map: https://www.youtube.com/watch?v=sZJj6DwCqSU

For some theory about how and why they
work: https://cmap.ihmc.us/docs/theory-of-concept-maps

__Journal
Article Review.__* 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. Your review must be that is ² 4
double-spaced pages (1500 words or less). Here are a few guidelines for
constructing your succinct and precisely-written review:

- What is the
real problem? What question is
the paper addressing?
- What is the
analog problem?
- How is the
problem posed mathematically?
- What is the
strategy for solving the problem?
- What are
the meaning and significance of the results?
- What are
the strengths and limitations of the model (including the development of
the model and the solution approach)?
- How might
the model be realistically improved?

**2) Quizzes
(20%)**

There
will be 4 ~30 minute quizzes.
Quizzes will address basic concepts from lecture and the text. If you do
your homework you will do fine on these quizzes. All material covered and
assigned is open season. Students can bring 1 page (2 sides) of review notes *plus* one concept map to each quiz. Like your concept maps, these notes must
be handwritten.

**3)
Midterm Exam (15%). **

This will be a ~1.5
hour exam on an evening TBA in mid February. The exam is open book and you may use
your 3 one-page cheat sheets and 3 concept maps. One problem from this exam will be done also
as a group activity. This exam will be thorough but deliberately
straightforward. To complete the exam in 90 minutes will be challenging: You
must study.

If you do better individually on the
problem that you will also do as a group, you retain your individual mark.

**4)
Final Exam (15%).**

There will be a 2-hour take-home final
exam due in April followed by a 1 hour in-class group effort to attack one
problem. This exam will test not just whether you have completed your homework
carefully but also the extent to which you have constructed understanding of
this material. This exam will deliberately interrogate how you think.

**5)
Final Project (30%)**

The term project accounts for a
substantial part of your assessment and will include a ~2500-word paper and a
short (10-15 minute) presentation. You will do this project in an assigned
group of 2 people. 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 of your choice. For undergraduate
students, a *critical* literature
review of a problem is sufficient. Graduate students, however, must also carry
out a research project aimed at understanding some process or define a research
project aimed at addressing a well-posed and 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. More details
about the format of the paper and the talk will be provided later.

**Downloads
and links**

Supplemental Lecture Notes

Solutions
to problems in the text