Dr Anja Slim, Monash University
Dr Edward Hinton, The University of Melbourne
The geological world is full of interesting fluid flows that can be described remarkably accurately with a range of elegant mathematical techniques, giving insight into the key physical processes. This course will cover the basic concepts of fluid dynamics relevant to geological applications and then proceed to construct models and explore solutions for lava and mud flows, ice dynamics and subsurface flows.
- Derivation of the Cauchy stress equation. Constitutive relations. Stokes’ equations.
- Lava and mud flows. Viscous and viscoplastic gravity currents. Similarity solutions. Charpit’s method. Numerical solutions using method-of-lines. Asymptotic methods.
- Ice dynamics. Shear-thinning gravity currents. Characteristic solutions. Stefan problems and mushy layers.
- Guest lecture by applied-mathematician-turned-Antarctic-scientist Dr Felicity McCormack on the ice sheets of Antarctica
- Subsurface flows. Darcy’s law and multiphase flow in porous media. Laplace’s equation. Porous gravity currents. Hodograph solutions. Convection. Saffman-Taylor instability. Taylor dispersion.
- Basic methods for solving ordinary differential equations
- Vector calculus
- Div, grad, curl
- Gauss’ theorem
- Basic numerical methods
- Basic programming
- Some familiarity with coding is useful although not essential.
- No prior knowledge of fluid dynamics is expected.
- Lecture quizzes: 10%
- Weekly problem sheets (10% each): 40%
- Final assignment: 50%
(*Assessment components may be subject to change)
Resources/pre-reading (if available)
No specific pre-course reading required
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