Fabien Montiel, Our people, Department of Mathematics and Statistics, University of Otago, New Zealand

((MSc (École Centrale de Nantes), PhD (Otago)) Fabien Montiel (2022)

Senior Lecturer
Director of Studies for 400-level and Honours Mathematics

Office: Science III, room 514
Tel +64 3 479 7760
Email fabien.montiel@otago.ac.nz

About

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.

Teaching responsibilities

My teaching responsibilities include:

MATH 120 Mathematics for Scientists (coordinator)
COMO 204 Differential Equations (coordinator)
MATH 4PD Numerical methods for PDEs (coordinator)

Research Interests

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.

Physical oceanography

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.

Acoustics

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.

Postgraduate supervision

Current

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.”

Completed

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

Current 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.

Past projects

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.

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Publications

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

Kohout, A. L., Smith, M., Roach, L. A., Williams, G., Montiel, F., & Williams, M. J. M. (2020). Observations of exponential wave attenuation in Antarctic sea ice during the PIPERS campaign. Annals of Glaciology, 61(82), 196-209. doi: 10.1017/aog.2020.36

Journal - Research Article

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

Journal - Research Article

Journal - Research Other

Journal - Research Article

Montiel, F., & Chung, H. (2020). Planar acoustic scattering by a multi-layered split ring resonator. Journal of the Acoustical Society of America, 148(6), 3698-3708. doi: 10.1121/10.0002883

Journal - Research Article

Montiel, F., Bennetts, L., Chung, H., Kessissoglou, N., & McPhedran, R. (2020). Theoretical and numerical advances in wave sciences. Wave Motion, 92, 102392. doi: 10.1016/j.wavemoti.2019.102392

Journal - Research Other

Mosig, J. E. M., Montiel, F., & Squire, V. A. (2019). A transport equation for flexural-gravity wave propagation under a sea ice cover of variable thickness. Wave Motion, 88, 153-166. doi: 10.1016/j.wavemoti.2019.03.010

Journal - Research Article

Eggler, D., Chung, H., Montiel, F., Pan, J., & Kessissoglou, N. (2019). Active noise cloaking of 2D cylindrical shells. Wave Motion, 87, 106-122. doi: 10.1016/j.wavemoti.2018.08.006

Journal - Research Article

Montiel, F., Squire, V. A., Doble, M., Thomson, J., & Wadhams, P. (2018). Attenuation and directional spreading of ocean waves during a storm event in the autumn Beaufort Sea marginal ice zone. Journal of Geophysical Research: Oceans, 123(8), 5912-5932. doi: 10.1029/2018jc013763

Journal - Research Article

Thomson, J., Ackley, S., Girard-Ardhuin, F., Babanin, A., Boutin, G., Brozena, J., … Montiel, F., … Squire, V., … Wadhams, P. (2018). Overview of the Arctic sea state and boundary layer physics program. Journal of Geophysical Research: Oceans, 123, 8674-8687. doi: 10.1002/2018JC013766

Journal - Research Article

Montiel, F., Chung, H., Karimi, M., & Kessissoglou, N. (2017). An analytical and numerical investigation of acoustic attenuation by a finite sonic crystal. Wave Motion, 70, 135-151. doi: 10.1016/j.wavemoti.2016.12.002

Journal - Research Article

Cheng, S., Rogers, W. E., Thomson, J., Smith, M., Doble, M. J., Wadhams, P., … Montiel, F., & Shen, H. H. (2017). Calibrating a viscoelastic sea ice model for wave propagation in the Arctic fall marginal ice zone. Journal of Geophysical Research: Oceans, 122(11), 8770-8793. doi: 10.1002/2017JC013275

Journal - Research Article

Bennetts, L. G., Peter, M. A., & Montiel, F. (2017). Localisation of Rayleigh–Bloch waves and damping of resonant loads on arrays of vertical cylinders. Journal of Fluid Mechanics, 813, 508-527. doi: 10.1017/jfm.2016.855

Journal - Research Article

Montiel, F., & Squire, V. A. (2017). Modelling wave-induced sea ice break-up in the marginal ice zone. Proceedings of the Royal Society A, 473(2206), 20170258. doi: 10.1098/rspa.2017.0258

Journal - Research Article

Mosig, J. E. M., Montiel, F., & Squire, V. A. (2017). Water wave scattering from a mass loading ice floe of random length using generalised polynomial chaos. Wave Motion, 70, 222-239. doi: 10.1016/j.wavemoti.2016.09.005

Journal - Research Article

Montiel, F., Squire, V. A., & Bennetts, L. (2016). Attenuation and directional spreading of ocean wave spectra in the marginal ice zone. Journal of Fluid Mechanics, 790, 492-522. doi: 10.1017/jfm.2016.21

Journal - Research Article

Squire, V. A., & Montiel, F. (2016). Evolution of directional wave spectra in the marginal ice zone: A new model tested with legacy data. Journal of Physical Oceanography, 46, 3121-3137. doi: 10.1175/JPO-D-16-0118.1

Journal - Research Article

Mosig, J. E. M., Montiel, F., & Squire, V. A. (2015). Comparison of viscoelastic-type models for ocean wave attenuation in ice-covered seas. Journal of Geophysical Research: Oceans, 120(9), 6072-6090. doi: 10.1002/2015JC010881

Journal - Research Article

Montiel, F., Squire, V. A., & Bennetts, L. G. (2015). Evolution of directional wave spectra through finite regular and randomly perturbed arrays of scatterers. SIAM Journal on Applied Mathematics, 75(2), 630-651. doi: 10.1137/140973906

Journal - Research Article

Montiel, F., Squire, V. A., & Bennetts, L. G. (2015). Reflection and transmission of ocean wave spectra by a band of randomly distributed ice floes. Annals of Glaciology, 56(69), 315-322. doi: 10.3189/2015AoG69A556

Journal - Research Article

Montiel, F., Bennetts, L. G., Squire, V. A., Bonnefoy, F., & Ferrant, P. (2013). Hydroelastic response of floating elastic discs to regular waves: Part 2: Modal analysis. Journal of Fluid Mechanics, 723, 629-652. doi: 10.1017/jfm.2013.124

Journal - Research Article

Montiel, F., Bonnefoy, F., Ferrant, P., Bennetts, L. G., Squire, V. A., & Marsault, P. (2013). Hydroelastic response of floating elastic discs to regular waves: Part 1: Wave basin experiments. Journal of Fluid Mechanics, 723, 604-628. doi: 10.1017/jfm.2013.123

Journal - Research Article

Montiel, F., Bennetts, L. G., & Squire, V. A. (2012). The transient response of floating elastic plates to wavemaker forcing in two dimensions. Journal of Fluids & Structures, 28, 416-433. doi: 10.1016/j.jfluidstructs.2011.10.007

Journal - Research Article

More publications...

Dr Fabien Montiel

About

Teaching responsibilities

Research Interests

Approximation methods for differential equations

Wave scattering in complex media

Physical oceanography

Sea ice physics

Acoustics

Postgraduate supervision

Current

Completed

Funded research projects

Current projects

Past projects

Publications