Syllabus for Continuum Mechanics in Geophysics

Learning outcomes

On completion of the course, the student should be able to:

• Write down and apply the conservation equations of momentum, energy, and mass in continuum form.
• Describe conceptually and in equations the fundamentally different types of material behaviour (rheologies).
• Formulate and solve a complete set of dynamical equations.
• Find the principal orientations and values of the tensor fields of stress and strain.
• Derive the Navier-Stokes equation from the conservation equations and a viscous rheology and apply it to fluid mechanics problems.
• Derive the seismic wave equations and solve the equations for simple systems.

Content

Continuum hypothesis. Stress tensor, pressure and deviatoric stresses. Eigenvectors and eigenvalues. Conservation of linear momentum. Conservation of angular momentum and symmetry of the stress tensor. Strain tensor and displacement gradient tensor. Stress and strain invariants. Isotropic elasticity. Airy stress function. Heat transfer and conservation of energy. Compressibility and the mantle adiabat. Newtonian fluids, Navier-Stokes equation. Eulerian vs. Lagrangian description and concept of advection. Conservation of mass. Scaling, dynamic similarity, Reynolds- and Rayleigh number. The stream function. Non-Newtonian viscosity, plasticity, and visco-elasticity.

Instruction

Lectures, homework, exercise sessions.

Assessment

Written examination (4 credits) and homework assignments (1 credit).

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.