Related papers: Topological Derivative for Shallow Water Equations
Revealing the ongoing changes in ocean dynamics and their impact on marine ecosystems requires the joint analysis of multiple variables. Yet, global observational records only cover a few decades, posing a challenge in the separation of…
Studies agree on a significant global mean sea level rise in the 20th century and its recent 21st century acceleration in the satellite record. At regional scale, the evolution of sea level probability distributions is often assumed to be…
Three phenomena are involved in sand movement: erosion, wind transport, and sedimentation. This paper presents a comprehensive easy-to-use multiphase model that include all three aspects with a particular attention to situations in which…
While topological derivatives have proven useful in applications of topology optimisation and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial…
Scattering of random surface gravity waves by small amplitude topography in the presence of a uniform current is investigated theoretically. This problem is relevant to ocean waves propagation on shallow continental shelves where tidal…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
A poleward-thinning ice shell can drive circulation in the subsurface oceans of icy moons by imposing a meridional temperature gradient--colder at the equator than the pole--through the freezing point suppression due to pressure. This…
We calculate the rate of ocean waves energy dissipation due to whitecapping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
Oceanic geostrophic turbulence is mostly forced at the surface, yet strong bottom-trapped flows are commonly observed along topographic anomalies. Here we consider the case of a freely evolving, initially surface-intensified velocity field…
Semidiurnal atmospheric thermal tides are important for terrestrial exoplanets in the habitable zone of their host stars. With solid tides, they torque these planets, thus contributing to determine their rotation states as well as their…
The propagation of long waves onto a continental shelf is of great interest in tsunami modeling and other applications where understanding the amplification of waves during shoaling is important. When the linearized shallow water equations…
We study partial tidal disruption and present a quantitative analysis of the orbital dynamics of the remnant self-bound core. We perform smoothed particle hydrodynamical simulations to show that partial disruption of a star due to the tidal…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a…
We address surface gradient flows which allow for energy dissipation by evolving the surface and a scalar quantity on it, simultaneously. A proper choice of the time derivative and the gauge of surface independence guarantees energy…
We investigate through computational simulations with a pore network model the formation of patterns caused by erosion-deposition mechanisms. In this model, the geometry of the pore space changes dynamically as a consequence of the coupling…
The most used form of the Shallow Water Equations doesn't take into account the variation of the curvature of the base flow surface. In this paper, we compare the theoretical and numerical solutions of the standard model and with the…
Surfaces eroded by ion-sputtering are sometimes observed to develop morphologies which are either ripple (periodic), or rough (non-periodic). We introduce a discrete stochastic model that allows us to interpret these experimental…
We consider propagating, spatially localised waves in a class of equations that contain variational and non-variational terms. The dynamics of the waves is analysed through a collective coordinate approach. Motivated by the variational…