Related papers: Topological Derivative for Shallow Water Equations
Numerical simulations have historically played a major role in understanding the hydrodynamics of the tidal disruption process. Given the complexity of the geometry of the system, the challenges posed by the problem have indeed stimulated…
Tsunamis are often generated by a moving sea bottom. This paper deals with the case where the tsunami source is an earthquake. The linearized water-wave equations are solved analytically for various sea bottom motions. Numerical results…
Tides represent the daily alternations of high and low waters along coastlines and in oceans, and the current theory (termed the gravitational forcing mechanism) explains them as a manifestation of the response of ocean water to the Moon's…
A hydrodynamic formulation of the evolution of large-scale structure in the Universe is presented. It relies on the spatially coarse-grained description of the dynamical evolution of a many-body gravitating system. Because of the assumed…
In recent literature several derivations of incompressible Navier-Stokes type equations that model the dynamics of an evolving fluidic surface have been presented. These derivations differ in the physical principles used in the modeling…
Damage cost curves -- relating the typical damage of a natural hazard to its physical magnitude -- represent an indispensable ingredient necessary for climate change impact assessments. Combining such curves with the occurrence probability…
In recent years it has been shown that the tidal coupling between extrasolar planets and their stars could be an important mechanism leading to orbital evolution. Both the tides the planet raises on the star and vice versa are important and…
The evolution of surface gravity waves is driven by nonlinear interactions that trigger an energy cascade similarly to the one observed in hydrodynamic turbulence. This process, known as wave turbulence, has been found to display anomalous…
A continuum theory is used to predict scaling laws for the morphological relaxation of crystal surfaces in two independent space dimensions. The goal is to unify previously disconnected experimental observations of decaying surface…
Erosion shapes our landscape and occurs when a sufficient shear stress is exerted by a fluid on a sedimented layer. What controls erosion at a microscopic level remains debated, especially near the threshold forcing where it stops. Here we…
We investigate the Riemann Problem for a shallow water model with porosity and terrain data. Based on recent results on the local existence, we build the solution in the large settings (the magnitude of the jump in the initial data is not…
Saltwater intrusion is a critical challenge to coastal ecosystems, impacting freshwater resources, biogeochemical cycles, and habitat stability. While relevant studies often focus on the long-term trends of salinity, its episodic…
Seismic and geodynamic studies indicate that the boundary between the Earth's liquid outer core and solid mantle is not spherical, but is likely characterized by topography in the form of inverted mountains and valleys that have typical…
This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can…
Complex systems have motivated continuing interest from the scientific community, leading to new concepts and methods. Growing systems represent a case of particular interest, as their topological, geometrical, and also dynamical properties…
Storm surges cause coastal inundations due to the setup of the water surface resulting from atmospheric pressure, surface winds and breaking waves. The latter is particularly difficult to be accounted for. For instance, it was observed that…
The problem of submarine sediment slide which generates the surface water waves is considered. To simulate numerically the landslide motion it is used the method which permits to take into account detailed rheological properties of slide…
The physics of swash i.e. a layer of water that washes up on the beach after an incoming wave has broken is complicated and intriguing. It includes perplexed hydrodynamic and sediment transport events. In our paper we address to the…
This paper presents specific features of solitary wave dynamics within the framework of the Ostrovsky equation with variable coefficients in relation to surface and internal waves in a rotating ocean with a variable bottom topography. For…
The Taylor expansion of wave fields with respect to shape parameters has a wide range of applications in wave scattering problems, including inverse scattering, optimal design, and uncertainty quantification. However, deriving the high…