相关论文: A Direct Approach for Detection of Bottom Topograp…

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,…

Accurate prediction of shallow water flows relies on precise bottom topography data, yet direct bathymetric surveys are expensive and time-consuming. In contrast, remote sensing platforms such as radar or satellite altimetry provide…

In this paper, we consider a problem inspired by the real-world need to identify the topographical features of ocean basins. Specifically we consider the problem of estimating the bottom impermeable boundary to an inviscid, incompressible,…

We consider the Boussinesq-Peregrine (BP) system as described by Lannes [Lannes, D. (2013). The water waves problem: mathematical analysis and asymptotics (Vol. 188). American Mathematical Soc.], within the shallow water regime, and study…

In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…

We analyze the scattering of linear internal waves in a two dimensional channel with subcritical bottom topography. We construct the scattering matrix for the internal wave problem in a channel with straight ends, mapping incoming data to…

We develop an adjoint approach for recovering the topographical function included in the source term of one-dimensional hyperbolic balance laws. We focus on a specific system, namely the shallow water equations, in an effort to recover the…

In this work, we develop a computational method that to provide realtime detection for water bottom topography based on observations on surface measurements, and we design an inverse problem to achieve this task. The forward model that we…

We consider the propagation of surface water waves in a straight planar channel perturbed at the bottom by several thin curved tunnels and wells. We propose a method to construct non reflecting underwater topographies of this type at an…

In this paper, we investigate steady states of shallow water moment equations including bottom topographies. We derive a new hyperbolic shallow water moment model based on linearized moment equations that allows for a simple assessment of…

We present a new high-resolution, non-oscillatory semi-discrete central-upwind scheme for one-dimensional two-layer shallow-water flows with friction and entrainment along channels with arbitrary cross sections and bottom topography. These…

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…

In this paper, we consider the inverse problem of determining the permeability of the subsurface from hydraulic head measurements, within the framework of a steady Darcy model of groundwater flow. We study geometrically defined prior…

Analysing two-dimensional shallow water equations with idealised bottom topographies have many applications in the atmospheric and oceanic sciences; however, restrictive flow pattern assumptions have been made to achieve explicit solutions.…

Here we propose a technique that successfully reconstructs ocean bathymetry from the free surface velocity and elevation data. This technique is based on the principles of open-channel hydraulics, according to which a sub-critical flow over…

We focus here on the water waves problem for uneven bottoms in the long-wave regime, on an unbounded two or three-dimensional domain. In order to derive asymptotic models for this problem, we consider two different regimes of bottom…

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…

The magnetohydrodynamic equations system for heavy fluid over an arbitrary surface in shallow water approximation is studied in the present paper. It is shown that simple wave solutions exist only for underlying surfaces that are slopes of…

This paper establishes Lipschitz stability for the simultaneous recovery of a variable density coefficient and the initial displacement in a damped biharmonic wave equation. The data consist of the boundary Cauchy data for the Laplacian of…

The classic Stoker dam-break problem is revisited in cases of different channel widths upstream and downstream of the dam. The channel is supposed to have a rectangular cross section and a horizontal and frictionless bottom. The system of…