This course presents an introduction to the (broad) discipline of fluid mechanics and describes the relationship between fluid mechanics and geological processes. A lecture outline is given below.
The principles of conservation of mass, momentum and energy that are the basis of fluid mechanics are relatively straightforward, and can be easily derived. Finding solutions to these equations is in general not straightforward, and only in very special cases can exact solutions be obtained. Most often (justifiable) approximations must be made to the equations and boundary conditions in order to obtain solutions. In this class we will derive or present the very simple governing equations of fluid mechanics (they only appear simple -- these equations describe the rich complexity of flows we see in everyday life: flows in rivers, the atmosphere, waves in the ocean, flows in the bathtub and kitchen sink, flying airplanes, etc.); we will then look at the different simplifications that can be made for various classes of problems that allow us to understand the main features of common problems in geological and environmental fluid mechanics.
For more information about fluid mechanics people and courses at UC Berkeley visit Berkeley Fluids
Class meeting times:
Formal lectures are held Monday and Wednesday from 1:30-3:00 pm. There can be an optional discussion section (time to be arranged) to review basic math, and discuss progress with term projects.
We will be solving ordinary AND partial differential equations in this class. We will also be doing lots of vector calculus (sometimes involving second, third and even fourth rank tensors). The first problem set will cover some of the basic mathematical topics that will be commonly used (and are also commonly useful). Integral relations and equations are also very useful, but are unfortunately not usually covered in undergraduate classes.
Text and notes:
The most suitable book for this class is probably Fluid Physics in Geology by D.J. Furbish (Oxford University Press, 1997). You can compare its table of contents with the topics we cover in class in order to determine what pages you should read. In the outline below I provide references to books other that Furbish. I also include at the end of the outline a list of recommended references.
The term project clearly accounts for a substantial part of the evaluation. The topic of the project is chosen by each student. For undergraduate students, a critical literature review 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 problem, wither numerically, or experimentally; equipment, facilities and/or computers may be available. If appropriate students may also work in groups in order to work on more involved projects.
Students who register in the class can receive a more detailed list of suggested projects as a pdf file by email -- contact email@example.com once you register
Here are four examples of projects completed in previous years (of course only a small number of term projects lead to refereed research papers, but published papers are easier to find than unpublished term papers):
Hammer, J.E., M. Manga & K.V. Cashman (1998) Non-equilibrium and unsteady fluid degassing during slow decompression, Geophysical Research Letters, vol. 25: 4565-4568; Download pdf reprint
Weeraratne, D. & M. Manga (1998) Transitions in the style of mantle convection at high Rayleigh numbers, Earth and Planetary Science Letters, vol. 160: 563-568; Download pdf reprint
Dorsey, C. & M. Manga (1998) The spreading of drops and axisymmetric gravity currents along a free surface, Physics of Fluids, vol. 10: 3011-3013; Download pdf reprint
Gonnermann, H., M. Manga & A.M. Jellinek (2002) Dynamics and longevity of an initially stratified mantle, Geophysical Research Letters, vol. 29, paper number 10.1029/2002GL01485; Download pdf reprint
The purpose of the presentation is to provide students the experience of presenting scientific results in a format similar to those used a professional meetings.
Please point out any typographical errors and mistakes. Other comments are welcome.
Introduction and governing equations (August 27, 29)
A few other topics (November 26, 28)
Second midterm Dec 5, in class
Term project presentations (time and date TBD)
My favorite general fluid mechanics books:
Interesting and sometimes useful links
Last modified May 29, 2007