Related papers: Local Runup Amplification By Resonant Wave Interac…
The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of shallow water theory. The wave shoaling in bays, when the depth varies smoothly along the channel axis,…
In this work we derive evolution equations for the nonlinear behavior of a coasting beam under the influence of a resonator impedance. Using a renormalization group approach we find a set of coupled nonlinear equations for the beam density…
The estimate of individual wave run-up is especially important for tsunami warning and risk assessment as it allows to evaluate the inundation area. Here as a model of tsunami we use the long single wave of positive polarity. The period of…
The paper deals with blow--up for the solutions of wave equation with nonlinear source and nonlinear boudary damping terms, posed in a bounded and regular domain. The initial data are posed in the energy space. The aim of the paper is to…
Historically the finite volume methods have been developed for the numerical integration of conservation laws. In this study we present some recent results on the application of such schemes to dispersive PDEs. Namely, we solve numerically…
We derive and analyze well-posed, energy- and entropy-stable boundary conditions (BCs) for the two-dimensional linear and nonlinear rotating shallow water equations (RSWE) in vector invariant form. The focus of the study is on subcritical…
Travelling waves of densities of binary fluid mixtures are investigated near a critical point. The free energy is considered in a non-local form taking account of the density gradients. The equations of motions are applied to a universal…
Long waves in shallow water propagating over a background shear flow towards a sloping beach are being investigated. The classical shallow-water equations are extended to incorporate both a background shear flow and a linear beach profile,…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
We study the boundary value problem for nonlinear fourth-order partial differential equation with jumping nonlinearity which can serve, e.g., as a model of an asymmetrically supported bending beam. We focus on a special type of solutions,…
Weakly nonlinear internal wave-wave interaction is a key mechanism that cascades energy from large to small scales, leading to ocean turbulence and mixing. Oceans typically have a non-uniform density stratification profile; moreover,…
The propagation and transformation of water waves over varying bathymetries is a subject of fundamental interest to ocean, coastal and harbor engineers. The specific bathymetry considered in this paper consists of one or two, naturally…
Rogue waves are known to occur on the ocean surface leading to significant damage to marine installations and compromising ship safety. Understanding the physical mechanisms responsible for extreme wave focusing is crucial in order to…
In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear…
Studies in the literature on plane turbulent wall jets on flat surfaces, have invariably considered either the nozzle initial conditions or the asymptotic conditions far downstream, as scaling parameters for the streamwise variations of…
The propagation of surface water waves interacting with a current and an uneven bottom is studied. Such a situation is typical for ocean waves where the winds generate currents in the top layer of the ocean. The role of the bottom…
Wave shoaling of water waves over mild bottom slopes is well described by linearized theories. However, the analytical treatment of nonlinear wave shoaling subject to rapidly varying bottoms has proven to be elusive in the past decades. As…
We study the initial-value problem for a general class of nonlinear nonlocal coupled wave equations. The problem involves convolution operators with kernel functions whose Fourier transforms are nonnegative. Some well-known examples of…
The problem of blow up of solutions to the initial boundary value problem for non-autonomous semilinear wave equation with damping and accelerating terms under the Robin boundary condition is studied. Sufficient conditions of blow up in a…
Dispersive averaging effects are used to show that KdV equation with periodic boundary conditions possesses high frequency solutions which behave nearly linearly. Numerical simulations are presented which indicate high accuracy of this…