((MSc (École Centrale de Nantes), PhD (Otago))
Director of Studies for 400-level and Honours Mathematics
I am an applied mathematician with broad interests across the physical and environmental sciences. I graduated with a Master of Science in Engineering (Diplôme d'Ingénieur) from the École Centrale de Nantes (France), specialising in the discipline of ocean engineering. I came to New Zealand in 2008 for a 6-month internship (as part of my MSc degree) at the University of Auckland in the Department of Mathematics. After graduating, I came back in 2009 to start my PhD at the University of Otago in the Department of Mathematics and Statistics to carry out the project Numerical and Experimental Analysis of Water Wave Scattering by Floating Elastic Plates. After my graduation in 2012, I carried on as a postdoc in the department for four years and was appointed lecturer in 2017. I was promoted to senior lecturer in 2020.
My teaching responsibilities include:
- MATH 120 Mathematics for Scientists (coordinator)
- COMO 204 Differential Equations (coordinator)
- MATH 4PD Numerical methods for PDEs (coordinator)
My research focusses on modelling and understanding wave propagation phenomena in complex media and spans a range of disciplines in applied mathematics, physical oceanography, acoustics and sea ice physics.
Approximation methods for differential equations
I devise novel approaches to represent solutions of partial differential equations with non-homogeneous, high-order boundary conditions, using methods derived from spectral analysis, complex analysis and integral equations to obtain their numerical approximation.
Wave scattering in complex media
I develop efficient semi-analytical methods to obtain numerical solutions of multiple wave scattering problems characterised by large arrays of scattering sources, to model the evolution of a wave field in inhomogeneous media with regular or disordered structure.
The main application of my research is to combine process-informed models and data analysis to investigate the physical processes governing the interaction between ocean waves and sea ice in the Arctic and Southern Oceans.
I'm also interested in modelling the transport of buoyant particles (e.g. ice floes, kelp) in the Southern Ocean and evaluating the potential for wave energy harvesting in coastal New Zealand.
Sea ice physics
I study the emergence of the statistical properties of sea ice floe sizes from underlying physical processes, e.g. the breakup caused by ocean waves.
Another application of my research is the design and characterisation of the scattering properties of locally resonant structures using spectral methods for testing efficiently the sound control abilities of sonic crystal barriers composed of large arrays of such structures.
- Nicolas Mokus, PhD, “Large scale modelling of wave-induced sea ice breakup in the marginal ice zone.”
- Ben Wilks, PhD, “Rainbow trapping in water waves.” (co-supervised with A/P. Sarah Wakes, Otago)
- Lilac Fendrake, MSc, “Simulating ocean waves in the Ross Sea marginal ice zone using WaveWatch III.”
- Yiming Ma (2022), PhD, “Mathematical and Statistical Modelling of Slow Slip Events.” (co-supervised with A/P. Ting Wang, Otago)
- Johannes Mosig (2018), PhD, “Contemporary wave–ice interaction models.” (co-supervised with Prof. Vernon Squire, Otago)
- Ben Wilks (2018), Honours, “An exploration of the scattering modes of cylindrical Helmholtz resonators.”
Funded research projects
- How vulnerable are Antarctica's coasts to colonisation? (2021-2024), Marsden Fund project administered by Royal Society Te Apārangi.
- Seasonal and Interdecadal variability of sea ice in the Ross Sea (2019-2025), NZ Government funded project as part of the Antarctic Science Platform (project 4).
- Breaking the ice: process-informed modelling of sea ice erosion due to ocean wave interactions (2019-2022), Marsden Fast Start project administered by Royal Society Te Apārangi.
- Targeted observation and process-informed modelling of Antarctic sea ice (2015-2020) funded by the Deep South National Science Challenge.
- Sea State and Boundary Layer Physics of the Emerging Arctic Ocean (2013-2017) funded by the Office of Naval Research.
Wilks, B., Montiel, F., & Wakes, S. (2023). A mechanistic evaluation of the local Bloch wave approximation in graded arrays of vertical barriers. Journal of Fluid Mechanics, 967, A20. doi: 10.1017/jfm.2023.466
Montiel, F., & Mokus, N. (2022). Theoretical framework for the emergent floe size distribution in the marginal ice zone: The case for log-normality. Philosophical Transactions of the Royal Society A, 380, 20210257. doi: 10.1098/rsta.2021.0257
Wilks, B., Montiel, F., & Wakes, S. (2022). Rainbow reflection and broadband energy absorption of water waves by graded arrays of vertical barriers. Journal of Fluid Mechanics, 941, A26. doi: 10.1017/jfm.2022.302
Montiel, F., Kohout, A. L., & Roach, L. A. (2022). Physical Drivers of Ocean Wave Attenuation in the Marginal Ice Zone. Journal of Physical Oceanography, 52, 889-906. doi: 10.1175/JPO-D-21-0240.1
Willmott, G., Sellier, M., Wilgar, C., & Montiel, F. (2021). Ka rere ngā mea katoa: Everything flows. Journal of the Royal Society of New Zealand, 51(2), 187-193. doi: 10.1080/03036758.2021.1912120