Related papers: A forced Boussinesq model with a sponge layer
This paper studies analytically the stability of solitary waves in a generalized Boussinesq equation with quadratic-cubic nonlinearity. For general values of two parameters a and b determining the system, unstable waves may occur. If…
We consider the Boussinesq-Peregrine (BP) system as described by Lannes [Lannes, D. (2013). The water waves problem: mathematical analysis and asymptotics (Vol. 188). American Mathematical Soc.], within the shallow water regime, and study…
In this paper, we develop computer-assisted techniques for the analysis of periodic orbits of ill-posed partial differential equations. As a case study, our proposed method is applied to the Boussinesq equation, which has been investigated…
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…
In this chapter, we illustrate the advantage of variational principles for modeling water waves from an elementary practical viewpoint. The method is based on a `relaxed' variational principle, i.e., on a Lagrangian involving as many…
We numerically study nonlinear phenomena related to the dynamics of traveling wave solutions of the Serre equations including the stability, the persistence, the interactions and the breaking of solitary waves. The numerical method utilizes…
The nonlinear stage of the modulational (Benjamin - Feir) instability of unidirectional deep water surface gravity waves is simulated numerically by the firth-order nonlinear envelope equations. The conditions of steep and breaking waves…
The existence of multi-speed solitary waves for the one-dimensional good Boussinesq equation with a power nonlinearity is proven. These solutions are shown to behave at large times as a pair of scalar solitary waves traveling at different…
We consider a simplified physics of the could interface where condensation, evaporation and radiation are neglected and momentum, thermal energy and water vapor transport is represented in terms of the Boussinesq model coupled to a passive…
The propagation of focused wave groups in intermediate water depth and the shoaling zone is experimentally and numerically considered in this paper. The experiments are carried out in a two-dimensional wave flume and wave trains derived…
We analyze the spectral stability of small-amplitude, periodic, traveling-wave solutions of a Boussinesq-Whitham system. These solutions are shown numerically to exhibit high-frequency instabilities when subject to bounded perturbations on…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
We investigate the instabilities and transition mechanisms of Boussinesq stratified boundary layers on sloping boundaries when subjected to oscillatory body forcing parallel to the slope. Such conditions are typical of the boundary layers…
Waves in excitable media can be treated by a simple geometric theory. The propagation velocity is assumed known and evolution of wave fronts is determined by elementary physical principles (Fermat's principle, Huygens' principle). Based on…
A major drawback of Boussinesq-type subgrid-scale stress models used in large-eddy simulations is the inherent assumption of alignment between large-scale strain rates and filtered subgrid-stresses. A priori analyses using direct numerical…
Modeling mass flows is classically based on hydrostatic balance equations. However, if momentum transfers scale similarly in slope parallel and flow depth directions, then the gravity and acceleration can have the same order of magnitude…
The mild-slope equation and its various modifications aim to model, with varying degrees of success, linear water wave propagation over sloping or undulating seabed topography. However, despite multiple modifications and attempted…
The numerical simulation of nonlinear dispersive waves is a central research topic of many investigations in the nonlinear wave community. Simple and robust solvers are needed for numerical studies of water waves as well. The main…
Moist stratified turbulence is studied in a two-dimensional Boussinesq system influenced by condensation and evaporation. The problem is set in a periodic domain and employs simple evaporation and condensation schemes, wherein both the…
We undertake a systematic review of some results concerning local well-posedness of the Cauchy problem for certain systems of nonlinear wave equations, with minimal regularity assumptions on the initial data. Moreover we provide a…