Séminaire de Andrea Armaroli (Phlam, Univ. Lille)

Effect of wind on nonlinear water waves: analytical and experimental results
Andrea Armaroli, Laboratoire de Physique des Lasers, Atomes et Molécules, Lille

According to Feynman (Lectures on Physics, Vol I, Ch. 51), "[water waves] are usually used as an example of waves in elementary courses [...]. As we shall soon see, they are the worst possible example, because they are in no respects like sound and light; they have all the complications that waves can have." To these, the effect of wind adds further difficulties, albeit it is intuitive that wind is the main mechanism for wave generation in the ocean. The interface between the two fluids (air and water) plays also a crucial role in climate regulation, circulation of pollutants and marine ecosystems. A complete physical description of energy transfer from wind to water waves is still not achieved, though.
After recalling the basic properties of nonlinear surface water waves (Stokes wave, modulational instability...), I will present the approaches to modelling the effect of wind developed at the Department of Applied Physics at the University of Geneva (Switzerland). A propagation equation was derived that generalizes the celebrated nonlinear Schrödinger equation (NLSE) by including high- order nonlinear effects, forcing, and damping. We concentrate on wave patterns generated from deterministic initial conditions, that resemble (perturbed versions of) doubly periodic solutions of the NLSE. Analytical tools based on a low-dimensional truncation are introduced to classify the numerical results. These analyses led to the design of two experimental campaigns in collaboration with the University of Aix-Marseille that allowed us to better understand several interesting dynamical regimes. The agreement between theory and experiments is surprisingly good, despite the non- ideality of the experimental setup and the competition between different linear and nonlinear effects. Our results may allow oceanographers and marine engineers to understand the effect of wind in the appearance and evolution of extreme events in the ocean.

References and suggested readings
N. Pizzo, L. Deike, and A. Ayet, How Does the Wind Generate Waves?, Physics Today 74 (11) 38-43(2021)
M. J. Lighthill, Physical Interpretation of the Mathematical Theory of Wave Generation by Wind, J. Fluid Mech. 14, 385 (1962)
D. Eeltink, A. Lemoine, H. Branger, O. Kimmoun, C. Kharif, J. D. Carter, A. Chabchoub, M. Brunetti, and J. Kasparian, Spectral Up- and Downshifting of Akhmediev Breathers under Wind Forcing, Phys. Fluids 29, 107103 (2017)
A. Armaroli, D. Eeltink, M. Brunetti, and J. Kasparian, Nonlinear Stage of Benjamin-Feir Instability in Forced/Damped Deep-Water Waves, Phys. Fluids 30, 017102 (2018)
D. Eeltink, A. Armaroli, Y. M. Ducimetière, J. Kasparian, and M. Brunetti, Single-Spectrum Prediction of Kurtosis of Water Waves in a Nonconservative Model, Phys. Rev. E 100, 1 (2019)

Video recording of the seminar:  https://nextcloud.univ-lille.fr/index.php/s/YJzYtqdsGBKxEY5