A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions

DOI10.1017/S0022112082001141zbMath0512.76024MaRDI QIDQ3657606

Publication date: 1982

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

free surface nonlinear interaction truncated Fourier series two dimensional irrotational surface displacement full nonlinear equations solitary waves overtaking one another and meeting from opposite directions

Mathematics Subject Classification ID

Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Solitary waves for incompressible inviscid fluids (76B25) Basic methods in fluid mechanics (76M99)

Related Items

On the calculation of the water particle kinematics arising in a directionally spread wavefield. ⋮ Head-on collision between capillary-gravity solitary waves ⋮ Interaction between a vertical wall and a wave propagating in a channel of parabolic cross section ⋮ Surface water waves and tsunamis ⋮ A non-linear wave decomposition model for efficient wave-structure interaction. part A: formulation, validations and analysis ⋮ Variational space-time (dis)continuous Galerkin method for nonlinear free surface water waves ⋮ Computing unstable periodic waves at the interface of two inviscid fluids in uniform vertical flow ⋮ Development and validation of a non-linear spectral model for water waves over variable depth ⋮ Error propagation when approximating multi-solitons: The KdV equation as a case study ⋮ Hamiltonian finite element discretization for nonlinear free surface water waves ⋮ On the change of amplitude of interacting solitary waves ⋮ Localization for spatial-spectral implementations of 1D analytic Boussinesq equations ⋮ A Numerical Study of the Exact Evolution Equations for Surface Waves in Water of Finite Depth ⋮ The reflection of nonlinear irregular surface water waves ⋮ A Boussinesq system for two-way propagation of nonlinear dispersive waves ⋮ Numerical simulation of a solitonic gas in KdV and KdV-BBM equations ⋮ Efficient computation of steady solitary gravity waves ⋮ The reflection of a solitary wave by a vertical wall ⋮ Boundary approximation methods for potential problems associated with moving boundary problems ⋮ Dispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat Space ⋮ Variational Boussinesq model for kinematics calculation of surface gravity waves over bathymetry ⋮ Numerical Modelling of Surface Water Wave Interaction with a Moving Wall ⋮ Rational approximation schemes for unstable Hele-Shaw flows ⋮ Time behaviour of the error when simulating finite-band periodic waves. The case of the KdV equation ⋮ Boundary Perturbation Methods for Water Waves ⋮ Fast accurate computation of the fully nonlinear solitary surface gravity waves ⋮ The evolution of large ocean waves: the role of local and rapid spectral changes ⋮ Solitary water wave interactions ⋮ On the efficient numerical simulation of directionally spread surface water waves ⋮ The swash of solitary waves on a plane beach: flow evolution, bed shear stress and run-up ⋮ The evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seas ⋮ A non-periodic spectral method with application to nonlinear water waves ⋮ Non‐linear time‐domain models for irregular wave diffraction about offshore structures ⋮ Harmonic stability of standing water waves ⋮ A stability analysis of a Eulerian solution method for moving boundary problems in electrochemical machining ⋮ A unified model for the evolution of nonlinear water waves ⋮ Localization in Spatial-Spectral Method for Water Wave Applications ⋮ Velocity and pressure in rear-end collisions between two solitary waves with and without an underlying current ⋮ Numerical analysis on the generation, propagation and interaction of solitary waves by a harmonic polynomial cell method ⋮ Modeling extreme waves based on equations of potential flow with a free surface ⋮ Weak oblique collisions of interfacial solitary waves ⋮ Analytical study of the head-on collision process between hydroelastic solitary waves in the presence of a uniform current ⋮ Numerical analysis of the transformation of a solitary wave reflected by a vertical wall

Cites Work