On the theory of water waves

From MaRDI portal
Publication:4041241

DOI10.1098/rspa.1974.0072zbMath0289.76010OpenAlexW2116250046MaRDI QIDQ4041241

N. Laws, A. E. Green, P. M. Naghdi

Publication date: 1974

Published in: Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.1974.0072




Related Items

Conservative discontinuous Galerkin methods for the nonlinear Serre equationsExistence of a regular solution for 1D Green-Naghdi equations with surface tension at a large time instantThe water wave equationSmooth and singular traveling wave solutions for the Serre-Green-Naghdi equationsHyperbolic relaxation technique for solving the dispersive Serre-Green-Naghdi equations with topographyExact closed-form solutions of a fully nonlinear asymptotic two-fluid modelModelling turbulence generation in solitary waves on shear shallow water flowsMathematical modeling and numerical analysis for the higher order Boussinesq systemParticle trajectories in the Serre equationsHyperbolic approximation of the BBM equationAnalysis and computation with stratified fluid modelsLarge time existence for 1D Green-Naghdi equationsDerivation and well-posedness of the extended Green-Naghdi equations for flat bottoms with surface tensionTime domain simulation of focused waves by high-level irrotational Green-Naghdi equations and harmonic polynomial cell methodHamiltonian Structure and Linear Stability of Solitary Waves of the Green-Naghdi EquationsError Estimates for Galerkin Approximations of the Serre EquationsDirected fluid sheets and gravity waves in compressible and incompressible fluidsPerfectly matched layers methods for mixed hyperbolic-dispersive equationsWell-balanced second-order convex limiting technique for solving the Serre-Green-Naghdi equationsSteady solutions of high-level irrotational Green-Naghdi equations for strongly nonlinear periodic wavesA thermodynamic viscous interface theory and associated stability problemsExtended Lagrangian approach for the numerical study of multidimensional dispersive waves: applications to the Serre-Green-Naghdi equationsImproved local existence result of the Green-Naghdi equations with the Coriolis effectThe validity of two-dimensional models of a rotating shallow fluid layerHigh order ADER-DG schemes for the simulation of linear seismic waves induced by nonlinear dispersive free-surface water wavesNon-dispersive conservative regularisation of nonlinear shallow water (and isentropic Euler equations)Three‐Dimensional Nonlinear Dispersive Waves on Shear FlowsPractical use of variational principles for modeling water wavesStationary shock-like transition fronts in dispersive systemsRobust explicit relaxation technique for solving the Green-Naghdi equationsA CDG-FE method for the two-dimensional Green-Naghdi model with the enhanced dispersive propertyHyperbolicity of the modulation equations for the Serre-Green-Naghdi modelOn the regularity of the Green–Naghdi equations for a rotating shallow fluid layerAn explicit solution with correctors for the Green-Naghdi equationsSOME TRAVELING WAVE SOLITONS OF THE GREEN–NAGHDI SYSTEMSmooth Exact Traveling Wave Solutions Determined by Singular Nonlinear Traveling Wave Systems: Two ModelsThe symmetry analysis and analytical studies of the rotational GreenNaghdi (R-GN) equationDispersive Shallow Water Wave Modelling. Part I: Model Derivation on a Globally Flat SpaceDispersive Shallow Water Wave Modelling. Part II: Numerical Simulation on a Globally Flat SpaceDispersive Shallow Water Wave Modelling. Part III: Model Derivation on a Globally Spherical GeometryLong Wave Interaction with a Partially Immersed Body. Part I: Mathematical ModelsLarge time existence for 3D water waves and asymptoticsWaves caused by a moving disturbance in a shallow channel of finite widthEquivalence of ordinary differential equations \(y = R(x, y)y^{\prime 2} + 2Q(x, y)y' +P(x, y)\)Conservative modified Serre-Green-Naghdi equations with improved dispersion characteristicsAsymptotic dynamics of monochromatic short surface wind wavesAn energy-consistent depth-averaged Euler system: derivationA numerical scheme for the Green-Naghdi modelVariational water-wave model with accurate dispersion and vertical vorticityUniqueness and continuous dependence for water wavesAn integrable equation governing short waves in a long-wave modelTheory of small aspect ratio waves in deep waterDifferent approximations of shallow fluid flow over an obstacleA comparative study of diffraction of shallow-water waves by high-level IGN and GN equationsDepth-integrated wave–current models. Part 1. Two-dimensional formulation and applicationsA mathematical analysis of nonlinear waves in a fluid filled visco- elastic tubeOn the Green-Naghdi equations with surface tension in the Camassa-Holm scaleNonhydrostatic two-layer models of incompressible flowBifurcations of Traveling Wave Solutions for Fully Nonlinear Water Waves with Surface Tension in the Generalized Serre–Green–Naghdi EquationsAn extension of the Boussinesq-type models to weakly compressible flowsExact Traveling Wave Solutions and Bifurcations of Classical and Modified Serre Shallow Water Wave EquationsA rapid numerical method for solving Serre–Green–Naghdi equations describing long free surface gravity wavesLarge-time existence for one-dimensional Green-Naghdi equations with vorticityOn the geophysical Green-Naghdi systemWell-posedness and derivative blow-up for a dispersionless regularized shallow water systemTRAVELING WAVE SOLUTIONS OF THE GREEN–NAGHDI SYSTEMHydrodynamic models and confinement effects by horizontal boundariesLong, intermediate and short-term well-posedness of high precision shallow-water models with topography variationsThe Kelvin-Helmholtz instability for a viscous interfaceSingular solutions of the BBM equation: analytical and numerical studyFinite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equationsOn the Galilean Invariance of Some Nonlinear Dispersive Wave EquationsA direct theory of viscous fluid flow in channels