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. [3-0-0] Prerequisite: One of EOSC 250, MATH 317.
Syllabus
Instructor: Christian Schoof
TA: Tyler Petillion
Textbook
Required: course lecture notes (see below)
Recommended:
- Continuum mechanics by G. E. Mase in the McGraw Hill Schaum Outline Series.
- Geodynamics by D. Turcotte and G. Schubert
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 material in Turcotte and Schubert goes beyond the present course.
Course Content
Division of marks:
Assignments - 40%
Mid-term 10 %
Quizzes/Class participation - 10%
Final - 40 %
Mid-Term Examination - tba
Assignments:
I expect to set 4 assignments in this course. They will be due at the end of the day indicated
Office hours
Wednesday 1230-130
Lecture Topics
- 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
- Time permitting, an introduction to convection
- Time permitting, principal strsses
Reference material from EOSC 250:
- vector calculus practice
- vector calculus practice answers
- Differential equations lecture notes
- Density and volume integrals lecture notes
- Flux and surface integrals lecture notes
- Divergence theorem notes
Course materials for EOSC 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 porous media notes
- EOS 352 Fourier series notes
- EOS 352 notes on convection in porous media
- Convection movie
- EOS 352 expanded heat equation notes
- Galerkin solver for porous medium convection problem
- For supplementary reading on temperature waves, see Turcotte and Schubert, Geodynamics, chapter 4, especially section 4.14
- For supplementary 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
- 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)
Sample exam materials: