We consider the problem of recovering the surface wave profile from noisy bottom pressure measurements with (\textit{a priori} unknown) arbitrary pressure at the surface. Without noise, the direct approach developed in \cite{clamond2023steady} provides an effective way to recover the sea surface. However, the assumption of analyticity for the measurement renders this method inefficient in the presence of noise. Therefore, we introduce an optimisation procedure based on the minimisation of a distance between a recovered bottom pressure and its measurement. Such method proves to be well-designed to handle perturbed signals. We illustrate the effectiveness of this approach in the recovery of gravity-capillary waves from unfiltered noisy data.
The aim of this note is to examine the efficacy of a recently developed approach to the recovery of nonlinear water waves from pressure measurements at the seabed, by applying it to the celebrated extreme Stokes wave.
The study examines the influence of a sloping porous bed on the efficiency of an oscillating water column (OWC) device facing oblique water waves. A vertical, surface piercing, thin plate near a rigid wall approximates the OWC. The system is simulated using a multi-domain boundary element method assuming the linear potential theory. The impact of varying sloping bed structural parameters and influence of the incident wave angle on the performance of the OWC is evaluated and discussed. The significance of this model to act as a breakwater protecting near-shore marine facilities is also highligh…
We present a broadband waveguide for water waves obtained through mere manipulation of seabed properties and without any need for sidewalls. Specifically, we show that a viscoelastic seabed results in a modified effective gravity term in the governing equations of water waves, which provides a generic broadband mechanism to control oceanic wave energy and enables confining surface waves inside a long narrow path without sidewalls. Our findings have promising applications in guiding and steering waves for oceanic wave energy farms or protecting shorelines.
Generation of an acoustic wave by two pump sound waves is studied in a three-phase marine sediment that consists of a solid frame and the pore water with air bubbles in it. To avoid shock-wave formation the interaction is considered in the frequency range where there is a significant amount of sound velocity dispersion. Nonlinear equations are obtained to describe the interaction of acoustic waves in the presence of air bubbles. An expression for the amplitude of the generated wave is obtained and numerical analysis of its dependence on distance and on the resonance frequency of bubbles is per…
Here we show that the distribution of internal gravity waves energy over a patch of seabed corrugations strongly depends on the "distance" of the patch to adjacent seafloor features. Specifically, we consider the energy distribution over a patch of seabed ripples neighbored to i. another patch of ripples, and ii. a vertical wall. Seabed undulations with dominant wavenumber twice as large as overpassing internal waves reflect back part of the energy of the internal waves (Bragg reflection), let the rest of the energy to transmit or to be transferred to higher and lower modes. In the presence of…
Trajectory of surface gravity waves in potential flow regime is affected by the gravitational acceleration, water density, and seabed depth. While the gravitational acceleration and water density are approximately constant, the effect of water depth on surface gravity waves exponentially decreases as the water depth increases. In shallow water, cloaking an object from surface waves by varying the seabed topography is possible, however, as the water depth increases, cloaking becomes a challenge since there is no physical parameter to be engineered and subsequently affects the wave propagation. …
Two-dimensional free-surface potential flows of an ideal fluid over a strongly inhomogeneous bottom are investigated with the help of conformal mappings. Weakly-nonlinear and exact nonlinear equations of motion are derived by the variational method for arbitrary seabed shape parameterized by an analytical function. As applications of this theory, band structure of linear waves over periodic bottoms is calculated and evolution of a strong solitary wave running from a deep region to a shallow region is numerically simulated.
UFPR/Federal University of Paraná（巴拉那联邦大学）；School of Sciences and Engineering, Universidad del Rosario（罗萨里奥大学理学院）；Sección Matemáticas, Departamento Académico Ciencias, Pontificia Universidad Católica del Perú（秘鲁天主教大学科学学术部数学组）
We show that significant water wave amplification is obtained in a water resonator consisting of two spatially separated patches of small-amplitude sinusoidal corrugations on an otherwise flat seabed. The corrugations reflect the incident waves according to the so-called Bragg reflection mechanism, and the distance between the two sets controls whether the trapped reflected waves experience constructive or destructive interference within the resonator. The resulting amplification or suppression is enhanced with increasing number of ripples, and is most effective for specific resonator lengths …
A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The obtained Euler-Lagrange equations contain infinite series and can rederive various existing model equations upon truncation. In this paper, the infinite series are summed up, resulting in two exact Hamiltonian equations for the free-surface elevation and the free-surface potential, coupled with a time-independent horizontal system of equations. The Dirichlet to Neu…
The emergence of quantum consciousness stems from dynamic flows of hydrogen ions in brain liquid. This liquid contains vast areas of the fourth phase of water with hexagonal packing of its molecules, the so-called exclusion zone (EZ) of water. The hydrogen ion motion on such hexagonal lattices shows as the hopping of the ions forward and the holes (vacant places) backward, caused by the Grotthuss mechanism. By supporting this motion using external infrasound sources, one may achieve the appearance of the superfluid state of the EZ water. Flows of the hydrogen ions are described by the modified…
How Sparse and How Noisy? Systematic Benchmarking of Inverse Physics-Informed Neural Networks for Manning Friction Estimation in Shallow Water Equations
This paper deals with the implementation of a new, efficient, non-perturbative, Hamiltonian coupled-mode theory (HCMT) for the fully nonlinear, potential flow (NLPF) model of water waves over arbitrary bathymetry, Papoutsellis and Athanassoulis (2017) (arXiv:1704.03276). Applications considered herein concern the interaction of solitary waves with bottom topographies and vertical walls both in two- and three-dimensional environments. The essential novelty is a new representation of the Dirichlet-to-Neumann operator, needed to close the Hamiltonian evolution equations. This representation emerg…
