Related papers: Extreme water wave profile recovery from pressure …
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
Periodic traveling waves are numerically computed in a constant vorticity flow subject to the force of gravity. The Stokes wave problem is formulated via a conformal mapping as a nonlinear pseudo-differential equation, involving a periodic…
The processes that generate rogue waves on the sea surface remain a mystery. Despite their different natures, the nonlinear bending waves generated in a thin elastic plate share some similarities with waves on the surface of the sea. For…
We consider the problem of reconstructing the seabed topography from observations of surface gravity waves. We formulate the problem as a classical inverse scattering problem using the mild-slope equation, and analyze the topographic…
We revisit the problem of recovering wave speeds and density across a curved interface from reflected wave amplitudes. Such amplitudes have been exploited for decades in (exploration) seismology in this context. However, the analysis in…
Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when…
This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
Reliable estimates of sea level return levels are crucial for coastal flooding risk assessments and for coastal flood defence design. We describe a novel method for estimating extreme sea levels that is the first to capture seasonality,…
This paper introduces an infinite-dimensional Bayesian framework for acoustic seabed tomography, leveraging wave scattering to simultaneously estimate the seabed and its roughness. Tomography is considered an ill-posed problem where…
Waves traveling through random media exhibit random focusing that leads to extremely high wave intensities even in the absence of nonlinearities. Although such extreme events are present in a wide variety of physical systems and the…
We revisit experimental studies performed by Ekman on dead-water using modern techniques in order to present new insights on this peculiar phenomenon. We extend its description to more general situations such as a three-layer fluid or a…
Two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth can be described by a conformal map of the fluid domain into the complex lower half-plane. Stokes wave is the fully nonlinear gravity wave…
Knowledge of the bottom topography, also called bathymetry, of rivers, seas or the ocean is important for many areas of maritime science and civil engineering. While direct measurements are possible, they are time consuming and expensive.…
Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The…
This paper investigates the geometric inverse problem of recovering the bottom shape from surface measurements of water waves. Using the general water-waves system on a bounded subdomain of the fluid domain, we address this inverse problem,…
Stokes wave is a finite amplitude periodic gravity wave propagating with constant velocity in inviscid fluid. Complex analytical structure of Stokes wave is analyzed using a conformal mapping of a free fluid surface of Stokes wave into the…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
A Stokes wave is a traveling free-surface periodic water wave that is constant in the direction transverse to the direction of propagation. In 1981 McLean discovered via numerical methods that Stokes waves are unstable with respect to…
The estimation of extreme loads from waves is an essential part of the design of an offshore wind turbine. Standard design codes suggest to either use simplified methods based on regular waves, or to perform fully nonlinear computations.…