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. [3-0] Prerequisite: One of EOSC 250, MATH 317.

 Course Availability & Schedule

Instructor: Christian Schoof

TA: Luke Brown

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 - 30 %

Mid-Term Examination - tba

Assignments:

I expect to set 4-5 assignments in this course. They will be due at the end of class on the date indicated below (which I will generally try to make a Thursday). No marks for late assignments without a good reason

Office hours

Wednesday 2-3 pm, Canvas Collaboarte Ultra Course Room. Contact me if you can't make this but need to see me. I may make this a by-appointment office hour if there is little regular uptake.

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

Background material:

Course materials for EOS 352:

Sample exam materials:

Homework

Assignments