My research interests consist of numerical and theoretical modeling of physical processes applicable to the solid Earth. My PhD research consisted of numerical modeling of convection in Earth's mantle. Convection in Earth's mantle is the driving force for the motion of Earth's tectonic plates which, in turn, cause earthquakes, mountain and basin formation and volcanism. Convection in Earth's mantle also controls the rate at which Earth cools, controls the formation of continents and controls the amount of heat removed from the core which affects the geodynamo (the process that creates Earth's magnetic field). A lot of my early research looked at the effects of the solid-solid phase transition that occurs in the mantle at 660-km depth and its tendency to cause convection in the mantle to be layered or split vertically into two separate convection cells. It has become reasonably clear that the 660-km depth mantle phase transition causes incomplete layering and I have been quite interested in how incomplete layering affects the transfer of heat by convection in the mantle and hence how efficiently the Earth can cool. This work lead me to become interested in the issue of the Earth's energy budget and how the temperature inside the Earth has changed over time. This is known as the Earth thermal history problem and one important issue concerns the fact that most models for the current amount of radioactive internal heating in the mantle indicate that there is far less current heat production in the mantle than is currently flowing out the top. Prof. Peltier, my PhD supervisor, and I proposed a mechanism where the degree of layering decreased over time, which gradually released heat to the upper mantle W.R. Peltier , my PhD supervisor, and I proposed a mechanism where the degree of layering decreased over time, which gradually released heat to the upper mantle. Incomplete mantle layering can lead to the phenomenon of mantle avalanches, where a lot of material from the upper mantle breaks through the phase boundary all at once.

Below you can see two temperature contour snapshots from the numerical model, one in which the effects of the phase transition have not been included and circulation mixes from the core-mantle boundary all the way to the surface and one in which partial layering is occurring due to the presence of the phase transition. The blue arrows indicate the fluid velocity.

You can also watch a movie of mantle convection without phase transitions or one in which weak phase transitions are acting or one with earth-like phase transitions (only available as a windows movie file currently). There is also a movie with a very strong phase transition effect. Note the mantle "avalanches" that are taking place in the last two movies, particularly the last one. Most recently, I have made a simulation of convection when there is a very large viscosity increase between the lower and upper mantle (see the movie) . Note how little the plumes in the lower mantle move and how the down-going cold plumes from the surface are slowed when they hit the top of the lower mantle (there are no phase transitions in this simulation).

I have continued to be interested in the Earth thermal history problem and my graduate student, Simona Costin and I, have investigated issues related to the growth rate of the inner core, potassium in the core, and the effects of a layer of enhanced internal heating, and a nonconvecting layer, at the base of the mantle on the generation of Earth's magnetic field. Most of our estimates for the temperature in the deep mantle come from assuming an adiabatic variation in temperature through the mantle. Adiabatic temperature variations are typical of the interiors of convecting systems. However, recently, a number of analyses have shown that when there is internal heating, the temperature may increase with depth more slowly than an adiabatic variation (the temperature gradient is said to be subadiabatic). It is conventionally assumed that this variation from adiabaticity is caused by the direct effects of internal heating. My graduate student, Gunjan Sinha , and I showed that much of the subadiabatic gradient is actually caused by the change in convective planform that occurs when internal heating is present. Gunjan and I are currently looking at the combined effects of the 660-km depth mantle phase transition and continents on Earth's surface.

In 2001 I did a post-doc with Prof. Garry Jarvis at York University where we looked at the magnitude of stresses imparted on continents caused by mantle flow. We showed that these are reduced in spherical as opposed to Cartesian geometery.

In 2002, I spent eight months at Cambridge University working at the Institute for Theoretical Geophysics with Herbert Huppert and Grae Worster on modeling mushy layers. Mushy layers are porous media where solidification and melting can take place. A great deal of interesting dynamical behaviour can occur because of the change density that can occur because of solidification and melting and because of the effects on permeability. Click here to see a movie of a porous layer melting due to heating from above. The colours show the porosity and the top layer becomes completely molten.

An interesting issue in porous media is that a dissolved solute and heat both advect and diffuse at very different rates. This can lead to interesting behaviour if a liquid with a different solute concentration and temperature is injected into a porous layer. Julia Milne, a summer student, and I carried out a number of simulations to better understand this problem. Take a look at some simulations that Julia made in the summer of 2003.

In 2007, I itook a sabbatical leave to Brown University in Providence Rhode Island where I became interested in issues related to compaction in porous layers. Theory and experiments have shown that if the viscosity of the solid matrix decreases with porosity, that if the matrix is strained, the matrix will spontaneously separate into regions of high and low porosity. When buoyancy is also present, porosity waves can also occur. I created a numerical model to investigate the combined effects of these two phenomenon and showed that porosity localization still occurs in bands, but there may be more than one set of porosity bands. Click here to see a movie of a compacting porous layer undergoing pure shear with horizontal compression and buoyancy where the viscosity depends only on porosity. Here is a movie of the same thing with vertical compression. Note the change in the oscillations because of the different orientation of the bands relative to gravity. You can see a model with vertical compression and gravity where the viscosity of the matrix depends on the strain-rate of the matrix as well here . Notice how there are now two sets of bands at roughly 20 degrees to vertical.

Hydrothermal circulation occurs in porous media with open tops near mid-ocean ridges. This process carries much of the heat near the ridge axis and is also thought to control the oxygen isotopic composition of the oceans due to isotopic exchange between the circulating water and the newly formed oceanic crust. I have been working with undergraduate student, John Kuttai, and Prof. Chris Holmden on this problem.

I have recently been working with Prof. Mel Stauffer on tektites. Splash-form tektites are found in many intriguing shapes including oblate ellipsoids, bi-concave forms and dumbbells. I have collaborated with Prof. Ray Spiteri in creating a numerical model of a rotating fluid drop with surface tension and many aspects of these shapes, and the distribution in which they are found can be explained by the model. You can see a movie of a drop first becoming oblate and then becoming a dumbbell and oscillating here .

Since I have been at the University of Saskatchewan, I have been teaching a course in gravity, magnetic and electromagnetic methods. I have developed a number of numerical models of these methods using the commercial software, COMSOL . Undergradute student, Chris Fowlie, worked with me and Prof. Jim Merriam on models of electromagnetic methods this past summer.