I am a mathematical scientist working on problems in the geosciences and industrial processes. My research involves developing mathematical models to describe physical phenomena, using analytical and computational methods to investigate underlying processes, and communicating practical understanding that is gained from the models. Principal areas of research are in glaciology, volcanology, and fluid-structure interactions.

I currently hold a postdoctoral research fellowship from the Killam Trust at the University of British Columbia. Previously I studied for both my undergraduate degree and my doctorate at the University of Oxford, where I wrote a thesis entitled 'Mathematical modelling of geophysical melt drainage' [pdf].

Please email me if you'd like to know more about any of my research.

Glacial ice deforms by dislocation creep and can typically be described as a non-Newtonian fluid on timescales longer than a few hours. In some places glaciers are frozen to the underlying rock, but in others they are melting at their base and a thin layer of water allows the ice to slide. Changes in speed provide the potential for rapid loss of land-ice and for consequent sea level rise, but the speed at which the ice slides, and the factors that control it, are not well understood - this represents a major uncertainty in models that forecast the future climate. Observations certainly seem to show that water at the bed plays a crucial role, and my interest is in understanding how such water moves and how it affects the speed of the ice.

The subglacial drainage system has to evacuate water produced both at the base of the ice, due to geothermal and frictional heating, and on the surface, from where it descends via crevasses to the base. The drainage system may consist of a widespread patchy sheet of water comprising linked cavities adjacent to bumps in the bed. Alternatively it may organize itself into a network of subglacial channels, like a river system draining rainwater over land. In all likelihood it does both, and I am currently working to develop models that incorporate these different modes of water flow.

• I. J. Hewitt, C. Schoof & M. A. Werder (2011) Flotation and open water flow in a model for subglacial drainage. Part II: Channel flow. submitted to Journal of Fluid Mechanics [AGU poster] [pdf]
  

  This paper serves two purposes: first, it presents a model to combine porous sheet flow in cavities with a random network of potential channels, combining aspects of the earlier models of Schoof (2010) and Hewitt (2011); secondly it extends the methods used in Part I to allow for partially filled channels as well as uplift of the ice during periods of overpressure. Numerical solutions are shown for a one-dimensional flow-line configuration, exhibiting partially filled channels, rapid pressure variations during diurnal melt cycles, and growth and decay of channels over an annual cycle.

• C. Schoof, I. J. Hewitt & M. A. Werder (2011) Flotation and open water flow in a model for subglacial drainage. Part I: Linked Cavities. submitted to Journal of Fluid Mechanics
  

  We use a porous sheet model to describe linked cavity flow and try to address what happens when subglacial water pressure reaches the ice overburden pressure or atmospheric pressure (most previous models have implicitly assumed the pressure does not reach these bounds). When overburden is reached we suppose that little excess pressure is required to lift the ice from its bed and modify the model to allow for this uplift; when atmospheric pressure is reached we allow the cavities to be only partially filled with water. The free boundaries of these 'overpressure' and 'underpressure' regions must be located as part of the solution to his model, and we develop a variational method to facilitate the numerical solution in one-dimension.

• I. J. Hewitt (2011) Modelling distributed and channelized subglacial drainage: the spacing of channels. Journal of Glaciology 57, 302-314 [pdf]
  

  This paper presents a two-dimensional model of the drainage system consisting of an averaged 'porous sheet' description of linked-cavities and a localized linear description of channels. Cavities are assumed to open due to sliding of the ice over bed roughness while channels open due to dissipation-induced melting of the ice. Aside from the development of the model, the focus of this study was to understand how efficiently water can be drawn into a channel from surrounding cavities, and thus how widely spaced one might expect channels to form.

• I. J. Hewitt & A. C. Fowler (2008) Seasonal waves on glaciers. Hydrological Processes 22, 3919-3930 [pdf]

  In this paper we tried to explain some observations of seasonal speed-up in which the peak velocity occurs progressively later further downglacier - the speed-up can be described as a downglacier propagating 'seasonal wave'. The explanation proposed here is that this wave is the surface expression of the passage of water through a slow subglacial drainage system. The paper uses a simple flow-line model of drainage in linked-cavity / channel systems to calculate the seasonal evolution of subglacial water pressure.

The Earth's mantle is predominantly solid, but deforms viscously on a geological timescale, and is caused to convect by internal heating from the core. In some upwelling regions, especially beneath mid-ocean ridges where tectonic plates are moving apart, decompression causes the rock to partially melt, and the buoyant magma that is produced migrates upwards through the residual solid. Understanding the nature of the magma flow has important implications for the formation of volcanoes and for the chemical composition of the rocks which eventually make up the Earth's crust. A number of field constraints suggest that rapid ascent of the magma must occur, and I have been using models to try to understand if efficient channels for the magma flow provide a viable mechanism for this.

Melting is driven by heat transport and by the varying composition of the rock as it ascends. Heat transport by the rising melt (the magma) has the potential to cause enhanced melting in regions where there is disproportionately more melt. This can lead to an erosive instability that results in the formation of thin channels of magma.

• I. J. Hewitt (2010) Modelling melting rates in upwelling mantle. Earth and Planetary Science Research Letters 300, 264-274 [EGU poster] [pdf]

  This paper re-examines models for partial melting beneath mid-ocean ridges; my intention was to emphasize the importance of considering the melting process when modelling the fluid dynamics of magma extraction. I use a simple idealized model of a two-component rock in an upwelling column, and calculate the melting rate of the rock determined from standard conservation principles; the rate is proportional to the average upwelling velocity of matrix and melt. Using this, I find that a reactive channelization instability is unlikely to occur for a purely uniform upwelling column. Nevertheless, focussing of melt from a wider area, or preexisting heterogeneities of the upwelling rock, might enable a strongly reactive instability that leads to extremely localized channels.

• I. J. Hewitt & A. C. Fowler (2009) Melt channelization in ascending mantle. Journal of Geophysical Research 114 B06210 [pdf]
  

  We considered the possibility for open channels in the upper mantle providing a mechanism for rapid magma extraction. The two dimensional version of the model presented in Hewitt & Fowler (2008) has the potential to produce such channels through the feedback of melt transport on melting rate. We find that if such channels were to form, the rapid ascent of warm melt would cause considerable melting of the channel walls that would be counteracted by inward creep of the mantle matrix. The pressure in the channels would be essentially 'magmastatic', causing melt to be drawn in from a surrounding region comparable to the so-called 'compaction length'.

• I. J. Hewitt & A. C. Fowler (2008) Partial melting in an upwelling mantle column Proceedings of the Royal Society A 464, 2467-2491 [pdf]
  

  This paper presents a framework for consistent thermodynamical modelling of upwelling regions of the mantle that partially melt. The model equations based on mass, momentum and energy conservation are essentially the same as the widely used equations proposed by McKenzie (1984). We studied one-dimensional solutions for a single-component upwelling column, the most important new contribution being to use the equation of energy conservation to determine the region that undergoes melting and the extent of melting.

Skipping stones is a familiar way to idle away time at the beach - throwing the stone into the water in such a way that it bounces several times before sinking. The force that enables the stone to bounce is an inertial response from the water - the acceleration of the displaced water providing an equal and opposite thrust that is enough to send the stone back up again. Might this type of skipping continue indefinitely if the stone's horizontal velocity were somehow maintained? We conducted experiments to investigate this question using a paddle suspended over a flowing stream. The experimental findings were compared to a shallow-water model for a similar situation.

• I. J. Hewitt, N. J. Balmforth & J. N. McElwaine (2011) Granular and Fluid washboards. Journal of Fluid Mechanics [pdf]
• I. J. Hewitt, H. Scolan & N. J. Balmforth (2011) Flow-destabilized seiche modes in a reservoir with a movable dam. Journal of Fluid Mechanics 678, 294--316 [pdf]
• I. J. Hewitt, N. J. Balmforth & J. N. McElwaine (2011) Continual skipping on water. Journal of Fluid Mechanics 669, 328--353 [pdf]
• I. J. Hewitt (2009) Continual skipping - getting a kick from water. Proceedings of the 50th GFD Summer School, Woods Hole Oceanographic Institute [pdf]

• N. J. Balmforth & I. J. Hewitt (2012) Viscoplastic beams and threads submitted to Journal of Non-Newtonian Fluid Mechanics [pdf]
• I. J. Hewitt & N. J. Balmforth (2012) Viscoplastic lubrication theory with application to mud washboards. Journal of Non-Newtonian Fluid Mechanics 169-170, 74--90 [pdf]

I regularly attend these week-long workshops to work on various (loosely) industrial problems.

• Geoscience Study Group, Lake District, UK, 2007 (Salt weathering of building materials)
• European Study Group with Industry, Limerick, Ireland, 2008 (Laser welding)
• European Study Group with Industry, Edinburgh, UK, 2008 (Freeze-protection of gas holders)
• Medical Study Group, Loughborough, UK, 2008 (Design of cell growing scaffolds)
• European Study Group with Industry, Southampton, UK, 2009 (Diffusive decontamination)
• European Study Group with Industry, Limerick, Ireland, 2009 (Sewage treatment)
• European Study Group with Industry, Limerick, Ireland, 2010 (Medical stent manufacturing, Granular mixing)