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Geological Fluid Dynamics

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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.

Course Overview

  • 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
    • Euler’s method
  • Basic programming
    • Some familiarity with coding is useful although not essential.
  • No prior knowledge of fluid dynamics is expected.


  • Quizzes (Flux questions in class 5%, group quiz 10%, Perusall commenting on lecture notes 5%) 20% total
  • Weekly problem sheets (10% each): 40%
  • Final take home exam (24-hours): 40%

(may be subject to change)

Attendance requirements

  • For those completing the subject for their own knowledge/interest, flux questions must be completed as an attendance requirement

Resources/pre-reading (if available)

  • No specific pre-course reading required
  • MATLAB will be required for this course. Please contact coordinator_rhed@amsi.org.au if you do not have access to this program through your home university.

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Dr Anja Slim, Monash University

Anja Slim is a Senior Lecturer at Monash University, with a joint appointment between the School of Mathematics and the School of Earth, Atmosphere and Environment. She works at the intersection of applied mathematics and geosciences, looking at problems such as the the surprising ways in which very dense sulfide droplets in magmas may be transported into mineable ore deposits, the dynamics of volcanic ash clouds and the practicality of carbon capture and storage as a means of reducing carbon dioxide emissions.

Dr Edward Hinton, The University of Melbourne

Edward Hinton is a Harcourt-Doig research fellow at The University of Melbourne (https://blogs.unimelb.edu.au/edward-hinton/). He previously held a London Mathematical Society research fellowship at The University of Bristol, UK and prior to that completed his PhD at the University of Cambridge, UK. His PhD thesis investigated various low Reynolds number environmental flows with applications to carbon dioxide storage and civil defences to lava flows . Edward’s research aims to deploy low order models to capture the dominant aspects of a particular problem and then use numerical methods, laboratory experiments and mathematical techniques to provide physical insights.

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