Seminar "Homogenized Boussinesq and Korteweg-De Vries models for anisotropic propagation of water waves over a structured ridge In collaboration with Amin Chabchoub"

Speaker 1)　Kim Pham, ENSTA, Palaiseau, France

Title: Homogenized Boussinesq and Korteweg-De Vries models for anisotropic propagation of water waves over a structured ridge in collaboration with Amin Chabchoub

Abstract: The propagation of gravity waves over variable bathymetry has been extensively studied over the past 40 years. In the linear regime, several theoretical, numerical, and experimental studies have demonstrated the anisotropic nature of effective wave propagation over rapidly varying periodic bathymetries in the long-wavelength/shallow-water regime. More recently, this topic has gained attention in the context of metamaterials for coastal protection. However, solitons -which can cause significant damage to offshore structures and coasts (e.g., rogue waves) - are inherently nonlinear, and their interaction with variable bathymetry remains poorly understood. This study revisits the problem of nonlinear wave motion on the free surface of a liquid column with a periodically varying bottom. We first derive the corresponding anisotropic homogenized Boussinesq and KdV equations and then analyze how soliton properties, such as celerity and spatial extent, are modified by the presence of rapidly varying bathymetry.

Kim Pham, ENSTA, Palaiseau, France
PhD inSolid Mechanics (2011), Professor, author of over 50 scientific publications.
I work on wave phenomena across various physical contexts, including electromagnetism, acoustics, elastodynamics, and water waves.
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Speaker 2) Agnès Maurel, Langevin Institute, ESPCI Paris – France

Title: Theoretical and experimental evidence of negative refraction of water waves in elliptic and hyperbolic regimes in collaboration with  L.P. Euvé, P. Petitjeans and V. Pagneux

Abstract: Metamaterials push the boundaries of wave control by enabling the exploitation of unusual physical properties such as negative refraction and extreme anisotropy. In the context of surface water waves, these advances pave the way for innovative applications, transforming propagation characteristics through specially designed resonant systems. This work investigates unconventional wave propagation phenomena on water surfaces using metamaterials designed to alter their dispersion. On one hand, elliptical dispersion with double negativity is achieved through a system of underwater resonant cavities, demonstrating both positive and negative refractive indices depending on the regime. On the other hand, hyperbolic dispersion is realized in devices combining open channels with subwavelength resonators, resulting in an effective negative water depth and negative refraction. Together, these studies highlight innovative mechanisms for wave manipulation, bridging concepts of double negativity and hyperbolic dispersion with the properties of water-wave metamaterials.

Agnès Maurel, Langevin Institute, ESPCI Paris – France
PhD in Fluid Mechanics (1994), CNRS Senior Researcher, author of over 130 scientific publications.
I work on wave phenomena across various physical contexts, including electromagnetism, acoustics, elastodynamics, and water waves.