**EOSC 514 Introduction to Geological Fluid Mechanics, Spring 2022**

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

**Where: **EOS Main 336a

**When:** T (10-12) Th (10-12)

**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.

**Other “equipment” required for the class: **A baking dish or pie plate, graph paper, a ruler and a smartphone

**Introduction**

Many problems in the Earth and planetary sciences involve fluid flow. Examples include the formation and subsequent thermal evolution of planets, the growth of mountains and volcanoes, the growth of sea ice, climatic effects on volcanism and volcanic effects on climate, ore genesis, 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. The course is designed to be approachable for students with diverse backgrounds and interests. It 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 in their sometimes forbidding complexity. 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 tractable 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 building physical insight: In addition to developing strategies for solving the equations of motion in various limits there is a strong emphasis on developing these equations from first principles by learning to identify and isolate characteristic features of real flows.

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**Student learning objectives in order of increasing levels of learning**

1) Solve simple problems in geological 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, notebook**

*Problem sets.** *Each problem set is designed to enhance your understanding of core material by looking at simple and sometimes classical 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 textbooks, which have 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 week. Most reading complements lecture material and is related to your problem sets. Active reading is a key to learning new materialѡnd to developing your methods for how to learn methodically. This takes some discipline. Who am I kidding: LOTS 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:

-Page 1 *must be* a mind map* that identifies and links core concepts. The concepts should involve self-serving cartoons and words/math that express physical concepts precisely.

-Page 2 *could be* a mind map for specific 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 unclear.

-Page 3 is up to you.

You will return to these mind maps regularly and change them as you learn. By the end of the course your collection of mind 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.

*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 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 three ~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 open-book, 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 (~15 minute) presentation. You will do this project in a group. 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. It does not have to work! But the question you ask, your strategy and what you learned must be clear. Equipment, facilities and/or computers may be available. More details about the format of the paper and the talk will be provided later.

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**Downloads and links**

Supplemental Lecture Notes

_ Continuum mechanics I

_ Continuum mechanics II

Textbooks and Solutions to problems

**For discussions of, examples and free apps to build concept maps and mind maps (they are not the same thing), see:*

https://en.wikipedia.org/wiki/Concept_map, https://en.wikipedia.org/wiki/Mind_map

and references at the end of each article.

See anything by Buzan (search on ‘mind map’ and not ‘concept map’). Here is a Ted talk with some inspiring moments (https://www.youtube.com/watch?v=nMZCghZ1hB4).

Examples of mind maps after a quick search (there are lots)

https://www.mindmeister.com/blog/students-guide-to-mind-mapping/

The best concept and mind maps are hand-drawn with pictures, precise language, physical and math concepts that reflect how *YOU* think. To get started, see:

https://mindmapsunleashed.com/how-to-mind-map-with-tony-buzan

https://learningfundamentals.com.au/resources/

https://www.open.edu/openlearn/ocw/mod/oucontent/view.php?id=19241§ion=2

https://www.lucidchart.com/pages/landing/concept_map_maker

https://www.visme.co/concept-map-maker/

Books on kindle if you prefer

Buzan: *Mind Map Mastery*

Knight: *Mind Maps: Quicker notes, better memory and improved learning 3.0*