Related papers: Topological Derivative for Shallow Water Equations
Numerical models have long been used to understand geoscientific phenomena, including tidal currents, crucial for renewable energy production and coastal engineering. However, their computational cost hinders generating data of varying…
Topography on a wet rocky exoplanet could raise land above its sea level. Although land elevation is the product of many complex processes, the large-scale topographic features on any geodynamically-active planet are the expression of the…
This is a brief review of the recent progress in understanding the evolution of the accretion disks in tidal disruption events (TDEs). Special attention is paid to (1) thermal-viscous instability that causes the disk to transition from a…
We analyze the long-term tidal evolution of a single-planet system through the use of numerical simulations and averaged equations giving the variations of semi-major axis and eccentricity of the relative orbit. For different types of…
The classical problem of irrotational long waves on the surface of a shallow layer of an ideal fluid moving under the influence of gravity as well as surface tension is considered. A systematic procedure for deriving an equation for surface…
The burgeoning need to sequester anthropogenic CO$_2$ for climate mitigation and the need for energy sustenance leading upto enhanced geothermal energy production has made it incredibly critical to study potential earthquakes due to fluid…
The description of complex wave processes, in addition to the shoaling problem, is often cumbersome even for the evolution of regular waves. For reflection under the regime of wave breaking, the surf similarity is generally accepted as the…
The mechanism that causes an interdecadal oscillation in a coarse resolution sector ocean model forced by mixed boundary conditions is studied. The oscillation is characterized by large fluctuations in convective activity and air/sea heat…
This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for…
Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…
Venus may have had both an Earth-like climate as well as extensive water oceans and active (or incipient) plate tectonics for an extended interval of its history. The topographical power spectrum of Venus provides important clues to the…
We propose a modification of a maximum likelihood procedure for tuning parameter values in models, based upon the comparison of their output to field data. Our methodology, which uses polynomial approximations of the sample space to…
Salinity and submergence have shaped coastal wetlands into one of the most productive and yet fragile ecotones worldwide. Sea-level rise alters both salinity and submersion regimes, threatening the future existence of these habitats. Still,…
Rogue wave formation and enhancement over coastal areas have been documented over the last decade. However, this recent knowledge is in apparent contradiction with the established observation of sub-Gaussian wave statistics near shallow…
By solving Laplace's tidal equations with friction terms we study the surface tide on a rapidly rotating body. When $\epsilon=\Omega^2 R/g$, the square of the ratio of dynamical timescale to rotational timescale, is very small for the Earth…
Theoretical studies on the modulation of unidimensional regular waves over a flat bottom due to a current typically assign an asymmetry between the effects of opposing/following streams on the evolution of major sea variables, such as…
This study proposes the topology optimization method for moving rigid bodies subjected to forces from fluid flow, such as sails and turbines, with an unsteady time-dependent formulation. Unlike existing topology optimization frameworks in…
We propose a gradient descent method for solving optimization problems arising in settings of tropical geometry - a variant of algebraic geometry that has attracted growing interest in applications such as computational biology, economics,…
Our aim in this note is to introduce and study a mathematical model for the description of traveling sand dunes. We use surface flow process of sand under the effect of wind and gravity. We model this phenomena by a non linear…
The competition between the torques induced by solid and thermal tides drives the rotational dynamics of Venus-like planets and super-Earths orbiting in the habitable zone of low-mass stars. The tidal responses of the atmosphere and…