相关论文: Extreme water wave profile recovery from pressure …

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…

We provide a new method to recover the profile of Stokes waves, and more generally of waves with smooth vorticity, from measurements of the horizontal velocity component on a vertical axis of symmetry of the wave surface. Although we…

A new method is proposed to recover the water-wave surface elevation from pressure data obtained at the bottom of the fluid. The new method requires the numerical solution of a nonlocal nonlinear equation relating the pressure and the…

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…

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 paper we investigate the qualitative behaviour of the pressure function beneath an extreme Stokes wave over infinite depth. The presence of a stagnation point at the wave-crest of an extreme Stokes wave introduces a number of…

In this paper we consider the dynamic pressure in a deep-water extreme Stokes wave. While the presence of stagnation points introduces a number of mathematical complications, maximum principles are applied to analyse the dynamic pressure in…

We consider Stokes' conjecture concerning the shape of the extremal two-dimensional water wave. By new geometric methods including a nonlinear frequency formula, we prove Stokes' conjecture in the original variables. Our results do not rely…

Babenko's equation describes traveling water waves in holomorphic coordinates. It has been used in the past to obtain properties of Stokes waves with smooth profiles analytically and numerically. We show in the deep-water limit that…

We put forward a simple but effective explicit method of recovering initial data for the nonlinear shallow water system from the reading at the shoreline. We then apply our method to the tsunami waves inverse problem.

Consider a two-dimensional stratified solitary wave propagating through a body of water that is bounded below by an impermeable ocean bed. In this work, we study how such a wave can be reconstructed from data consisting of the wave speed,…

Periodic water waves of permanent form traveling at constant speed, the so-called Stokes waves, are studied in water of fixed finite depth using methods previously used in water of infinite depth. We apply our methods to waves of varying…

In this paper we prove that the pressure beneath an extreme Stokes wave over finite depth is strictly increasing with depth. Additionally it is shown that the pressure decreases in moving between a crest-line and trough-line, while it is…

This is a study of singular solutions of the problem of traveling gravity water waves on flows with vorticity. We show that, for a certain class of vorticity functions, a sequence of regular waves converges to an extreme wave with…

Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the…

As mentioned by Schwartz (1974) and Cokelet (1977), it was failed to gain convergent results of limiting Stokes' waves in extremely shallow water by means of perturbation methods even with the aid of extrapolation techniques such as…

A new highly efficient method is developed for computation of traveling periodic waves (Stokes waves) on the free surface of deep water. A convergence of numerical approximation is determined by the complex singularites above the free…

Extreme sea level estimates are fundamental for mitigating against coastal flooding as they provide insight for defence engineering. As the global climate changes, rising sea levels combined with increases in storm intensity and frequency…