Related papers: An inverse technique for reconstructing ocean's de…
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,…
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 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…
Oceanic tides are a major source of tidal dissipation. They drive the evolution of planetary systems and the rotational dynamics of planets. However, 2D models commonly used for the Earth cannot be applied to extrasolar telluric planets…
Understanding subsurface ocean dynamics is essential for quantifying oceanic heat and mass transport, but direct observations at depth remain sparse due to logistical and technological constraints. In contrast, satellite missions provide…
Turbulent water motions are important for the exchange of momentum, heat, nutrients, and suspended matter including sediments in the deep-sea that is generally stably stratified in density. To maintain ocean-density stratification, an…
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 present experimental and computational studies of the propagation of internal waves in a stratified fluid with an exponential density profile that models the deep ocean. The buoyancy frequency profile $N(z)$ (proportional to the square…
Geophysical fluids such as the ocean and atmosphere can be stratified: their density depends on the depth. As a consequence, they can host internal gravity waves that propagate in the bulk of the fluid, far from the surface. These waves can…
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating…
We investigate the inverse source problem for the wave equation, arising in photo- and thermoacoustic tomography. There exist quite a few theoretically exact inversion formulas explicitly expressing solution of this problem in terms of 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…
This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean…
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…
In this letter a new method based on modified self-organizing maps is presented for the reconstruction of deep ocean current velocities from surface information provided by satellites. This method takes advantage of local correlations in…
To investigate the formation mechanism of energy spectra of internal waves in the oceans, direct numerical simulations are performed. The simulations are based on the reduced dynamical equations of rotating stratified turbulence. In the…
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…
This paper is concerned with inverse scattering of plane waves by a locally perturbed infinite plane (which is called a locally rough surface) with the modulus of the total-field data (also called the phaseless near-field data) at a fixed…
Lee waves generated by stratified flow over rough bottom topography in the ocean extract momentum and energy from the geostrophic flow, causing drag and enhancing turbulence and mixing in the interior ocean when they break. Inviscid linear…
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,…