相关论文: Water waves over a strongly undulating bottom

Oceanic internal waves often have curvilinear fronts and propagate over various currents. We present the first study of long weakly-nonlinear internal ring waves in a three-layer fluid in the presence of a background linear shear current.…

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…

Surface and interfacial weakly-nonlinear ring waves in a two-layer fluid are modelled numerically, within the framework of the recently derived 2+1-dimensional cKdV-type equation. In a case study, we consider concentric waves from a…

A generalized version of the $abcd$-Boussinesq class of systems is derived to accommodate variable bottom topography in two-dimensional space. This extension allows for the conservation of suitable energy functionals in some cases and…

We study the behavior of shallow water waves over periodically-varying bathymetry, based on the first-order hyperbolic Saint-Venant equations. Although solutions of this system are known to generally exhibit wave breaking, numerical…

This paper provides a theoretical foundation for some common formulations of inverse problems in wave propagation, based on hyperbolic systems of linear integro-differential equations with bounded and measurable coefficients. The…

We show the existence of periodic traveling waves at the free surface of a two dimensional, infinitely deep, and constant vorticity flow, under gravity, whose profiles are overhanging, including one which intersects itself to enclose a…

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…

Special features of magnetohydrodynamic waves linear dynamics in smooth shear flows are studied. Quantitative asymptotic and numerical analysis are performed for wide range of system parameters when basic flow has constant shear of velocity…

This work studies the problem of predicting the loads and motions induced by wave systems on a ship in forward motion (seakeeping). Assuming that the hull is rigid, the motion of the ship is described by the equations of rigid body…

The Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymtotic expansion of the Euler's equations is taken (to a certain order of smallness of the scale parameters), relations to…

The formation and evolution of nonlinear and turbulent dynamical structures in two-dimensional complex plasmas and fluids is explored by means of generalised (drift) fluid simulations. Recent numerical results on turbulence in dusty…

We review here the derivation of many of the most important models that appear in the literature (mainly in coastal oceanography) for the description of waves in shallow water. We show that these models can be obtained using various…

Theoretical results on water waves almost always start by assuming irrotationality of the flow in order to simplify the formulation. In this work, we investigate the well-foundedness of this hypothesis via numerical simulations of the…

In this paper, we analyze the dynamics of two layers of immiscible, inviscid, incompressible, and irrotational fluids through a full nonlinear system. Our goal is to establish a virial theorem and prove the polynomial growth of slope and…

Shallow water waves are a striking example of nonlinear hydrodynamics, giving rise to phenomena such as tsunamis and undular waves. These dynamics are typically studied in hundreds-of-meter-long wave flumes. Here, we demonstrate a…

Numerical simulations of the recently derived fully nonlinear equations of motion for weakly three-dimensional water waves [V.P. Ruban, Phys. Rev. E {\bf 71}, 055303(R) (2005)] with quasi-random initial conditions are reported, which show…

Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics,…

A computational fluid model is developed to study waves and instabilities. A new technique involving initial perturbations in configuration space have been implemented to excite the plasma waves; i.e. the perturbations acting similar to a…

Direct phase-resolved simulations are performed to investigate the propagation and scattering of nonlinear ocean waves in fragmented sea ice. The numerical model solves the full time-dependent equations for nonlinear potential flow coupled…