EOSC 352 - Geophysical Continuum Dynamics
Introduction to tensor calculus and continuum mechanics. Stress, strain and strain-rate tensors. Mass, momentum and energy balance. Applications to problems of geophysical heat transport, elasticity and fluid dynamics illustrated using MATLAB.
For a full listing of course offerings please see the UBC
Required: Online notes (see below)
I highly recommend the text by Mase as it gives a very succinct description of the basic concepts and the mathematics involved. The text by Turcotte and Schubert also gives an abbreviated introduction, and applies continuum mechanics to real Earth Sciences problems. Some of the matieral in Turcotte and Schubert goes beyond the present course. Previous editions of the course have used the text by Middleton and Wilcox, which is less mathematical but gives a useful introduction to scaling.
- Continuum mechanics by G. E. Mase in the McGraw Hill Schaum Outline Series.
- Geodynamics by D. Turcotte and G. Schubert
- Mechanics in the Earth and Environmental Sciences, G. Middleton and P. Wilcox, Cambridge University Press, 1994.
Division of marks:
Assignments - 40%
Mid-term exam - 10%
Quizzes/Class participation - 10%
Final exam - 40%
Mid-Term Examination - tbd
I expect to set 5 assignments in this course. They will be set on Fridays and wil be due at the end of class on the following Friday. No marks for late assignments without a good reason.
Wednesday 3-4 pm, EOS-South 262. Contact me in advance if you can't make this but need to see me.
Course materials for EOS 352:
- EOS 352 Conservation laws notes
- EOS 352 Complex variables notes
- EOS 352 Temperature waves notes
- Temperature wave movie
- EOS 352 Scaling notes
- EOS 352 Similarity solution notes
- EOS 352 Subscript notation notes
- EOS 352 Momentum conservation notes
- EOS 352 Angular momentum conservation notes
- EOS 352 summary of conservation laws
- EOS 352 notes on scalars, vectors and tensors
- EOS 352 fluids notes
- EOS 352 expanded heat equation notes
- For supplementary reading on temperature waves, see Turcotte and Schubert, Geodynamics, chapter 4, especially section 4.14
- For supplemetary reading on similarity solutions, see Turcotte and Schubert, Geodynamics, chapter 4, especially section 4.15
- For supplementary reading on nondimensionalization, see Middleton and Wilcox, Mechanics in the Earth and Environmental Sciences, chapter 3
- For supplementary reading on vector conservation laws / momentum conservation, see Turcotte and Schubert, Geodynamics, chapter 2
- HIGHLY RECOMMENDED: For supplementary reading on subscript notation and vector conservation laws / momentum conservation, see Mase, Continuum Mechanics, chapters on Mathematical Foundations, Analysis of Stress, Motion and Flow and Fundamental Laws of Continuum Mechanics (chapters 1, 2, 4 and 5)
- Review of continuum physics
- Mathematical tools: volume and surface integrals, gradients and divergences
- Transport of conserved quantities: fluxes
- Conservation laws and the divergence theorem
- Partial differential equations as continuum physics models
- Methods: steady states, similarity and wave solutions for the heat equation
- Length scales, non-dimensionalization and dimensionless parameters
- Continuum mechanics: extending scalar continuum physics to vectors
- Fluxes for vectors: tensors
- Tensor calculus and subscript notation
- The stress tensor and conservation of linear and angular momentum
- Viscous flow
- Principal strsses
- Time permitting, elastic deformation
There are no labs for this course.