Related papers: Long Wave Dynamics along a Convex Bottom
Existing theoretical results for attenuation of surface waves propagating on water of random fluctuating depth are shown to over predict the rate of decay due to the way in which ensemble averaging is performed. A revised approach is…
We study the Korteweg-de Vries-type equation dt u=-dx(dx^2 u+f(u)-B(t,x)u), where B is a small and bounded, slowly varying function and f is a nonlinearity. Many variable coefficient KdV-type equations can be rescaled into this equation. We…
In this article we deal with a class of geometric inverse problem for bottom detection by one single measurement on the free surface in water--waves. We found upper and lower bounds for the size of the region enclosed between two different…
The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable…
This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric…
Since the pioneering work of Kelvin on Laplace tidal equations, a zoology of trapped waves have been found in the context of coastal dynamics. Among them, the one originally computed by Kelvin plays a particular role, as it is an…
In this paper, we study the motion of the free surface of a body of fluid over a variable bottom, in a long wave asymptotic regime. We assume that the bottom of the fluid region can be described by a stationary random process $\beta(x,…
We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute…
We address various issues concerning the Cauchy problem for the Zakharov-Rubenchik system (known as the Benney-Roskes system in water waves theory), which models the interaction of short and long waves in many physical situations. Motivated…
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…
We consider wave maps on $(1+d)$-dimensional Minkowski space. For each dimension $d\geq 8$ we construct a negatively curved, $d$-dimensional target manifold that allows for the existence of a self-similar wave map which provides a stable…
Many important physical situations such as fluid flows, marine environment, solid-state physics and plasma physics have been represented by shallow water wave equation. In this article, we construct new solitary wave solutions for the…
In this paper, we study the Cauchy problem for the four-wave kinetic equation describing the weak turbulence of gravity water waves. The mathematical challenges of this analysis stem primarily from two interrelated aspects: (1) the extreme…
Steady-state and transient antiplane dynamic processes in a structured solids consisting of uniform periodic square-cell lattices connected by a lattice layer of different bond stiffnesses and point masses are analyzed. A semi-infinite…
We report experimental observations of traveling waves in a pure fluid with a free surface situated in a long container submitted to a horizontal temperature gradient perpendicular to its large extension. Above a critical value of the…
Dispersive shock waves (DSW) are a salient feature of long water waves often observed in tidal bores and tsunami/meteotsunami contexts. Their interaction with bathymetry is poorly understood. The shoreline hazard from tsunamis and…
This is a study of the Euler equations for free surface water waves in the case of varying bathymetry, considering the problem in the shallow water scaling regime. In the case of rapidly varying periodic bottom boundaries this is a problem…
We develop a weakly nonlinear model to study the spatiotemporal manifestation and the dynamical behavior of surface waves in the presence of an underlying interfacial solitary wave in a two-layer fluid system. We show that interfacial…
The instability and nonlinear evolution of directional ocean waves is investigated numerically by means of simulations of the governing kinetic equation for narrow-band surface waves. Our simulation results reveal the onset of the…
We study the waves at the interface between two thin horizontal layers of immiscible fluids subject to high-frequency horizontal vibrations. Previously, the variational principle for energy functional, which can be adopted for treatment of…