Selected Publications
Determination of the bottom deformation from space- and time-resolved water wave measurements
In this paper we study both theoretically and experimentally the inverse problem of indirectly measuring the shape of a localized bottom deformation with a non-instantaneous time evolution, from either an instantaneous global state (space-based inversion) or a local time-history record (time-based inversion) of the free-surface evolution. We conduct a series of laboratory experiments in which an axisymmetric three-dimensional bottom deformation of controlled shape and time evolution is imposed on a layer of water of constant depth, initially at rest. The detailed evolution of the air–liquid interface is measured by means of a free-surface profilometry technique providing space- and time-resolved data. Based on these experimental data and employing our regularization scheme, we are able to show that it is indeed possible to reconstruct the seabed profile responsible for the linear free-surface dynamics either by space- or time-based inversions.
In Journal of Fluid Mechanics,
2017
Revisiting the anisotropy of metamaterials for water waves
We establish, both theoretically and experimentally, that metamaterials for water waves reach a much higher degree of anisotropy than the one predicted using the analogy between water waves and their electromagnetic or acoustic counterparts. This is due to the fact that this analogy, based on the two-dimensional shallow water approximation, is unable to account for the three-dimensional near field effects in the water depth. To properly capture these effects, we homogenize the fully three-dimensional problem and show that a subwavelength layered structuration of the bathymetry produces significant anisotropic parameters in the shallow water regime. Furthermore, we extend the validity of the homogenized prediction by proposing an empirical anisotropic version of the dispersion relation.
In Physical Review B,
2017