Related papers: Topological Derivative for Shallow Water Equations
We investigate the dynamical evolution of hierarchical three-body systems under the effect of tides, when the ratio of the orbital semi-major axes is small and the mutual inclination is relatively large (greater than 20 degrees). Using the…
Tidal disruption events involve numerous physical processes (fluid dynamics, magnetohydrodynamics, radiation transport, self-gravity, general relativistic dynamics) in highly nonlinear ways, and, because TDEs are transients by definition,…
In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed.…
The practically important problem of the wave run-up is studied in this article in the framework of Nonlinear Shallow Water Equations (NSWE). The main novelty consists in the usage of high order local asymptotic analytical solutions in the…
Past efforts to interrogate the mantle's contribution to Earth's topography suffer from inadequate in-situ measurements of true bathymetry and the involvement of an empirical plate model whose presumed lithospheric density profile…
When a star approaches a black hole closely, it may be pulled apart by gravitational forces in a tidal disruption event (TDE). The flares produced by TDEs are unique tracers of otherwise quiescent supermassive black holes (SMBHs) located at…
We have found that the expansion of the universe has immense consequences on our local systems. We present a model based on cosmic expansion that fits well with observation. The close approach problem inflicting tidal theory is averted in…
In this paper we consider a shape optimization problem for the minimization of the erosion, that is caused by the impact of inert particles onto the walls of a bended pipe. Using the continuous adjoint approach, we formally compute the…
We derive rigorously from the water waves equations new irrotational shallow water models for the propagation of surface waves in the case of uneven topography in horizontal dimensions one and two. The systems are made to capture the…
Tidal Downsizing (TD) is a recently developed planet formation theory that supplements the classical Gravitational disc Instability (GI) model with planet migration inward and tidal disruptions of GI fragments in the inner regions of the…
We build a conceptual coupled model of the climate and tidal evolution of the Earth-Moon system to find the influence of the former on the latter. An energy balance model is applied to calculate steady-state temperature field from the mean…
In this paper we study the problem of the optimal distribution of two materials on smooth submanifolds $M$ of dimension $d-1$ in $\mathbf R^d$ without boundary by means of the topological derivative. We consider a class of shape…
Distributions of wave characteristics of ocean waves, such as wave slope, waveheight or wavelength, are an important tool in a variety of oceanographic applications such as safety of ocean structures or in the study of ship stability, as…
Models for fluid deformable surfaces provide valid theories to describe the dynamics of thin fluidic sheets of soft materials. To use such models in morphogenesis and development requires to incorporate active forces. We consider active…
In this study the influence of stratification on surface tidal elevations in a two-layer analytical model is examined. The model assumes linearized, non-rotating, shallow-water dynamics in one dimension with astronomical forcing and allows…
High-resolution multispectral satellite imagery was utilized to quantify shoreline recession at eleven beaches around Lake Michigan during a record-setting water level increase between 2013 and 2020. Shoreline changes during this period…
In classical continuum physics, a wave is a mechanical disturbance. Whether the disturbance is stationary or traveling and whether it is caused by the motion of atoms and molecules or the vibration of a lattice structure, a wave can be…
We investigate the influence of the topography on the lake equations which describe the two-dimensional horizontal velocity of a three-dimensional incompressible flow. We show that the lake equations are structurally stable under Hausdorff…
An alternative way for the derivation of the new KdV-type equation is presented. The equation contains terms depending on the bottom topography (there are six new terms in all, three of which are caused by the unevenness of the bottom). It…
In this paper we present a new approach to tidal theory. Assuming a Maxwell viscoelastic rheology, we compute the instantaneous deformation of celestial bodies using a differential equation for the gravity field coefficients. This method…