相关论文: Recovering the Water-Wave Profile from Pressure Me…
The reconstruction of water wave elevation from bottom pressure measurements is an important issue for coastal applications, but corresponds to a difficult mathematical problem. In this paper we present the derivation of a method which…
Equations relating the pressure at a horizontal seabed, the free-surface profile and the surface-pressure are derived for two-dimensional irrotational steady water waves with arbitrary pressure at the free surface. Special cases include…
In this short note, we derive a system of two nonlocal equations for the water-wave problem following the work of [AFM06]. Specifically, we consider a fluid with a one-dimensional free surface for an irrotational fluid both with, and…
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…
We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure…
We propose higher-order approximation formulae recovering the surface elevation from the pressure at the bed and the background shear flow for small-amplitude Stokes and solitary water waves. They offer improvements over the pressure…
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.
We derived here in a systematic way, and for a large class of scaling regimes, asymptotic models for the propagation of internal waves at the interface between two layers of immiscible fluids of different densities, under the rigid lid…
The classical equations of irrotational water waves have recently been reformulated as a system of two equations, one of which is an explicit non-local equation for the wave height and for the velocity potential evaluated on the free…
In the general context of rotational water waves with a smooth vorticity it is shown that the wave profile can be recovered from the horizontal component of the velocity field on a line of symmetry. The method, which applies to waves of…
In this paper, we develop and numerically implement a novel approach for solving the inverse source problem of the acoustic wave equation in three dimensions. By injecting a small high-contrast droplet into the medium, we exploit the…
We extend the recent work of Oliveras arXiv:2008.00940 and Oliveras & Calatola-Young arXiv:2105.07580 to develop a new nonlocal formulation of the water-wave problem for a three-dimensional fluid with a two-dimensional free surface for an…
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…
A novel boundary integral approach for the recovery of overhanging (or not) rotational (or not) water waves from pressure measurements at the bottom is presented. The method is based on the Cauchy integral formula and on an…
We develop a rigorous asymptotic derivation for two mathematical models of water waves that capture the full nonlinearity of the Euler equations up to quadratic and cubic interactions, respectively. Specifically, letting epsilon denote an…
Effective spatio-temporal measurements of water surface elevation (water waves) in laboratory experiments are crucial for scientific and engineering research. Existing techniques are often cumbersome, computationally heavy and generally…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
We consider the 3D compressible isentropic Euler equations describing the motion of a liquid in an unbounded initial domain with a moving boundary and a fixed flat bottom at finite depth. The liquid is under the influence of gravity and…
The equations for waves on the surface of an irrotational incompressible fluid are derived in the coordinates of the velocity potential/stream function. The low frequency shallow water approximation for these waves is derived for a varying…
This paper is devoted to the stabilization of the water-wave equations with surface tension through of an external pressure acting on a small part of the free surface. It is proved that the energy decays to zero exponentially in time,…