Filamentation; climate; Femtosecond laser; tipping point; Non-linear optics; rogue wave; Modelling
Eeltink D., Armaroli A., Brunetti M., Kasparian J. (2020), Reconciling different formulations of viscous water waves and their mass conservation, in Wave Motion
, 97, 102610-102610.
Armaroli Andrea, Gomel Alexis, Chabchoub Amin, Brunetti Maura, Kasparian Jérôme (2020), Stabilization of uni-directional water wave trains over an uneven bottom, in Nonlinear Dynamics
, 101(2), 1131-1145.
Béguin Chloé, Brunetti Maura, Kasparian Jérôme (2019), Quantitative analysis of self-organized patterns in ombrotrophic peatlands, in Scientific Reports
, 9(1), 1499-1499.
Eeltink D., Armaroli A., Ducimetière Y. M., Kasparian J., Brunetti M. (2019), Single-spectrum prediction of kurtosis of water waves in a nonconservative model, in Physical Review E
, 100(1), 013102-013102.
Armaroli Andrea, Eeltink Debbie, Brunetti Maura, Kasparian Jérôme (2018), Viscous damping of gravity-capillary waves: Dispersion relations and nonlinear corrections, in Physical Review Fluids
, 3(12), 124803-124803.
Béjot P., Kasparian J. (2018), Energy conservation in self-phase modulation, in Physical Review A
, 97(6), 063835-063835.
Due to intrinsic non-linearity of the equations at play (e.g., fluid dynamics), as well as numerous cross-interactions between sub-systems, many natural systems including the climate are highly nonlinear. This nonlinearity implies the occurrence of extreme events like oceanic rogue waves, as well as tipping points in which the system dramatically changes its state (e.g., the ice cover over sea or Greenland). While such events and changes can have severe human consequences, their prediction is still a challenge.I propose to investigate these extreme events and changes in natural non-linear systems by buinding on analogies between natural and physical systems sharing the same driving equations. I will especially focus on non-linear optics, in particular laser filamentation. In that purpose, we propose to work in three directions simultaneously.First, we will investigate, both experimentally at the laboratory scale and numerically, the ability of non-linear optics guided in one dimension by a sandwich structure to provide a realistic analogue of a two-dimensional sea surface. A particular attention will be dedicated to isolate the effect of the guiding reducing the system dimensionality, from the effect of beam geometry, by comparing the two-dimensional propagation with that of highly elliptical beams.In parallel, we will evaluate the relevance of the statistics of extreme events, summarized in a « rogueness index », as an early warning for dramatic changes or tipping points in a physical system. We will use turbulence-perturbed filamentation as a first benchmark, by progressively increasing the laser incident power considered as the system forcing parameter. Similar « rogueness indices » will be sought for simple systems like the Ising model, where numerical investigation is easier. This will allow us to tune the optimal definition of the « rogueness index » before applying it to the sea ice cover, based on both column and general-circulation models.Finally, considering the influence of wind on the wave growth and their spectrum, we will refine its modelling in the hydrodynamics propagation equation. A particular care will be dedicated to the balance between wind and losses due to viscosity, as we showed that they cannot exactly balance due to the contribution of different orders in steepness. The critical regime where wind and viscosity balance each other at one order but an unbalance persists at higher orders will be particularly investigated, both numerically and experimentally, first at a reduced scale, and then in a large-scale wavetank.By both creating new descriptions of highly non-linear natural phenomena and transferring existing knowledge from non-linear optics, we expect to contribute to a better understanding of dramtic system changes and tipping points, in the aim or reducing the associated dammage and fatalities.