相关论文: Theory of small aspect ratio waves in deep water

So far most studies on mathematical models for microelectromechanical systems (MEMS) are focused on the so-called small aspect ratio model which is a wave or beam equation with a singular source term. It is formally derived by setting the…

We introduce a new model equation for Stokes gravity waves based on conformal transformations of Euler's equations. The local version of the model equation is relevant for dynamics of shallow water waves. It allows us to characterize the…

A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…

We consider steady surface waves in an infinitely deep two--dimensional ideal fluid with potential flow, focusing on high-amplitude waves near the steepest wave with a 120 degree corner at the crest. The stability of these solutions with…

We derive scaling laws for the steady spectrum of wind excited waves, assuming two inviscid fluids (air and water) and no surface tension, an approximation valid at large speeds. In this limit there exists an unique (small) dimensionless…

This is a study of two-dimensional steady periodic travelling waves on the surface of an infinitely deep irrotational ocean, when the top streamline is in contact with a membrane which has a nonlinear response to stretching and bending, and…

Euler's equations govern the behavior of gravity waves on the surface of an incompressible, inviscid, and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes…

In order to describe the dynamics of monochromatic surface waves in deep water, we derive a nonlinear and dispersive system of equations for the free surface elevation and the free surface velocity from the Euler equations in infinite…

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…

In order to obtain quite precise information about the shape of the particle paths below small-amplitude gravity waves travelling on irrotational deep water, analytic solutions of the nonlinear differential equation system describing the…

This paper investigates the stability of traveling wave solutions to the free boundary Euler equations with a submerged point vortex. We prove that sufficiently small-amplitude waves with small enough vortex strength are conditionally…

This paper considers two-dimensional steady continuous stratified periodic water waves. Firstly, we prove that each streamline must be symmetric about the crest line when it is strictly monotonous between troughs and crests by exploiting…

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…

Wave steepness is a key geometric variable for describing breaking occurrence and its consequences, including energy dissipation and air entrainment. Using three laboratory campaigns under varying spectral conditions and co-flowing wind…

The paper contains an analysis of the conditions for the existence of elastic versus non-elastic wave superpositions governed by the Euler system in (1+1)-dimensions. A review of recently obtained results is presented, including the…

It is shown that spatially periodic one-dimensional surface waves in shallow water behave almost linearly, provided large part of the energy is contained in sufficiently high frequencies. The amplitude is not required to be small (apart…

Sufficient conditions for wave breaking are found for the short-pulse equation describing wave packets of few cycles on the ultra-short pulse scale. The analysis relies on the method of characteristics and conserved quantities of the…

We prove local higher-order asymptotics for extreme water waves with vorticity near stagnation points. We obtain that the behaviour of solutions and their regularity depend substantially on the vorticity. In particular, we show that extreme…

We study traveling wave solutions of an equation for surface waves of moderate amplitude arising as a shallow water approximation of the Euler equations for inviscid, incompressible and homogenous fluids. We obtain solitary waves of…

Two-dimensional periodic surface waves propagating under the combined influence of gravity and surface tension on water of finite depth are considered. Within the framework of small-amplitude waves, we find the exact solutions of the…