Related papers: Topological Derivative for Shallow Water Equations

The hillslope hydrological processes are very important in watershed hydrology research. In this paper we focus on the water flow over the soil surface with vegetation in a hydrographic basin. We introduce a PDE model based on general…

Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an…

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse…

Chemical erosion, one of the two major erosion processes along with mechanical erosion, occurs when a soluble rock like salt, gypsum or limestone is dissolved in contact with a water flow. The coupling between the geometry of the rocks, the…

Earth-mass planets are expected to have atmospheres and experience thermal tides raised by the host star. These tides transfer energy to the planet that can counter the dissipation from bodily tides. Indeed, even a relatively thin…

This work presents a new vortex dynamic equation for quasi-geostrophic flows over strongly variable sediment bottoms. The equation considers erosion/deposition exchanges near the bottom and the geometrical changes of the bed interface,…

From geometry and conservation we derive two nonlinear evolution equations for sand ripples. In the case of a strong wind leading to a net erosion of the sand bed, ripples obey the Benney equation. This leads either to order or disorder…

Oceanic tides are a major source of tidal dissipation. They are a key actor for the orbital and rotational evolution of planetary systems, and contribute to the heating of icy satellites hosting a subsurface ocean. Oceanic tides are…

Reliable estimates of sea level return levels are crucial for coastal flooding risk assessments and for coastal flood defence design. We describe a novel method for estimating extreme sea levels that is the first to capture seasonality,…

Geometric evolution represents a fundamental aspect of many physical phenomena. In this paper we consider the geometric evolution of structures that undergo topological changes. Topological changes occur when the shape of an object evolves…

Earth-like planets have viscoelastic mantles, whereas giant planets may have viscoelastic cores. The tidal dissipation of such solid regions, gravitationally perturbed by a companion body, highly depends on their rheology and on the tidal…

The Green-Naghdi equations are a nonlinear dispersive perturbation of the nonlinear shallow water equations, more precise by one order of approximation. These equations are commonly used for the simulation of coastal flows, and in…

Coastal upwelling, driven by alongshore winds and characterized by cold sea surface temperatures and high upper-ocean nutrient content, is an important physical process sustaining some of the oceans' most productive ecosystems. To fully…

Thermal tides are atmospheric tides caused by variations in day-night insolation, similar to gravitational tides but with key differences. While both result in delayed mass redistribution, energy dissipation, and angular momentum exchanges…

We propose a mathematical model which suggests that the two main geological observations about shingle beaches, i.e. the emergence of predominant pebble size ratios and strong segregation by size are interrelated. Our model is a based on a…

Thermal atmospheric tides can torque telluric planets away from spin-orbit synchronous rotation, as observed in the case of Venus. They thus participate to determine the possible climates and general circulations of the atmospheres of these…

Shallow free surface flows are often characterized by both subdomains that require high modeling complexity and subdomains that can be sufficiently accurately modeled with low modeling complexity. Moreover, these subdomains may change in…

Arctic coastal morphology is governed by multiple factors, many of which are affected by climatological changes. As the season length for shorefast ice decreases and temperatures warm permafrost soils, coastlines are more susceptible to…

The shoaling of surface gravity waves has been acknowledged as a mechanism of rogue wave formation. This problem is generally reduced to water waves passing over a step, but non-equilibrium physics allows finite slopes to be considered.…

Although deep learning models have demonstrated remarkable potential in weather prediction, most of them overlook either the \textbf{physics} of the underlying weather evolution or the \textbf{topology} of the Earth's surface. In light of…