ERTH 430:
Fluid Dynamics
in Earth Systems

Reading Questions #1
(for classes beginning Wednesday, 8/30/17)

Middleton and Wilcox, Mechanics in the Earth and Environmental Sciences,
Chapter 1, "Introduction", Sections 1.1 to 1.6, pp. 1-13.

Section 1.1: What this book is about

  1. The authors note that in the past (they don't say when), geologists spent most of their efforts trying to understand what, and how, geologic processes and events led to what we observe today, and there were good reasons for them to focus on the past as a way to understand the present. (Like what?) For many practical purposes (that is, for trying to solve environmental problems of some kinds), what shortcoming do they identify with this approach?

  2. If one course in fluid mechanics or dynamics can't be enough to learn how to apply physical principles to solve environmental problems (especially to predict how the environment will change in the future), what benefit is there, nonetheless, in taking at least one course, according to the authors?

  3. What basic assumption underlies the practical application of fluid mechanics (and dynamics)?

  4. What are governing equations? What are some of the governing equations, according to the authors? [Note: As an atmospheric dynamicist by training, I would have a slightly different, overlapping list. The general idea is the same, though.]

  5. What type(s) of mathematics are needed to describe motions in three-dimensional space, which is the kind of motion that fluids typically exhibit in Earth systems (with some exceptions)?

  6. To apply governing equations to solve a problem, what kinds of conditions about the problem do we need to know? What kind of mathematical equation are most of the governing equations?

  7. According to the authors, to apply physical principles to solve environmental problems (involving fluid flow), is it enough to know how to solve partial differential equations? If not, what else do they say is needed?

Section 1.2: Definition of a continuum

  1. In classical physics, what are three forms (or phases, or states) that matter is often assumed to take, as a way to simplify real problems enough to try to solve them?

  2. What is the continuum hypothesis?

  3. The continuum hypothesis is not correct at the molecular level. How does our assumption that it is correct limit our ability to solve problems?

  4. What is a gradient?

  5. What is meant by a length scale? We often apply physical principles to individual "particles" or "parcels" of fluid. (The authors also call these "volume elements".) There is a range of sizes of volume elements to which we can apply physical principles effectively to solve problems. What are the upper and lower limits of this range?

  6. The authors say that "mass is a property of points (or bodies considered as point masses)." [They really mean that mass is a property of bits of matter, which aren't points but can be treated as points when applying some physical principles.] When matter is treated as points, does it make sense to talk about the density of matter? Why not? Does it make sense to talk about density in a fluid continuum? Why or why not? What compromise to we make when talking about density of a fluid, to help us solve physical problems involving fluids?

  7. Why is differential calculus so important for describing, analyzing, and predicting the behavior of fluids?

  8. When are boundary conditions important?

Section 1.3: Governing equations

  1. What are the equations of motion? Why are there three of them?

  2. When a force acts on an object, in what direction does the object accelerate (that is, change its motion)?

  3. What sorts of distortion can "applied forces" (that is, forces acting on fluid particles) create in a fluid?

  4. How does consideration of how forces affect a small fluid volume differ from how forces affect a point mass?

  5. What are the dimensions of stress? [Note that the text doesn't fully define stress; there is more that needs to be added to the statement it makes about what stress is.]

  6. The text says that for fluids, the equations of motion are generally written in units [it actually means dimensions, not units] of force per unit volume, rather than force. Why? [Note: In my experience, the equations are generally written in terms of force per unit mass. Hence, there are multiple ways in which the equations of motion can be written, and the version that is useful depends on the problem of interest.]

  7. Why aren't the governing equations enough to tell us how a fluid will respond when forces are applied to it? What do constitutive equations say about materials (in a continuum)?

  8. How many types of constitutive equations seem to be enough to describe most types of (continuous) materials? What is each type of material called? What is an example of each?

  9. How do linearly elastic solids respond when a stress is applied to them? What is strain?

  10. How do plastic materials respond to stress?

  11. How do viscous materials respond to stress? [Note that the authors introduce the term "strain rate" without defining it here.]

Section 1.4: Vectors and tensors

  1. What is a vector? What are some examples? What is a tensor? What is an example? What are three examples of vector operators?

Section 1.5: Solving the equations

  1. To solve the governing equations applied to problems of fluid flow, we must specify initial conditions and boundary conditions. For the example of how the flow of water through a channel will evolve, what are the initial and boundary conditions that we must specify?

  2. Once initial conditions and boundary conditions are specified, what do we have to do to the governing equations to determine how the flow will evolve (that is, determine the future state of the fluid)?

  3. What technological tool has allowed us to take advantage of the governing equations to understand fluid flow?

Section 1.6: The art of modeling

  1. What three types of model do the authors mention, that we might use to study and understand fluid dynamics? In practice, what two compromises do we have to make to apply models of fluid flow to real world problems?

  2. Is it possible to predict exactly what the future state of our environment will be, by applying models (including the governing equations) to make predictions? Why or why not?

  3. What do we attempt to do with models, given that they can't ever be complete or detailed enough to predict the future state of the environment exactly?

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