On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves

From MaRDI portal
Publication:4318522

DOI10.1017/S0022112094004350zbMath0815.76016MaRDI QIDQ4318522

V. P. Krasitskij

Publication date: 10 July 1995

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




Related Items (83)

The nonlinear Benjamin–Feir instability – Hamiltonian dynamics, discrete breathers and steady solutionsModulational instability of two obliquely interacting waves in presence of a thin pycnoclineA Hamiltonian Dysthe equation for deep-water gravity waves with constant vorticityOn coupled envelope evolution equations in the Hamiltonian theory of nonlinear surface gravity wavesThird-order theory for multi-directional irregular wavesThe Zakharov equation with separate mean flow and mean surfaceOn a random time series analysis valid for arbitrary spectral shapeFourth-order nonlinear evolution equations for a capillary-gravity wave packet in the presence of another wave packet in deep waterOn some consequences of the canonical transformation in the Hamiltonian theory of water wavesEvolution of statistically inhomogeneous degenerate water wave quartetsOn the relation between two numerical methods for the computation of random surface gravity wavesSpectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulationsEvolution of wide-spectrum unidirectional wave groups in a tank: an experimental and numerical studyNew solutions of the C. S. Y. equation reveal increases in freak wave occurrenceGlobal well-posedness and scattering for the Dysthe equation in \(L^2(\mathbb{R}^2)\)On the initial evolution of the weak turbulence spectrum in a system with a decay dispersion relationThree- and four-wave resonances in the nonlinear quadratic Kelvin latticeApparent singularities of the finite-depth Zakharov equationInstability of waves in deep water -- a discrete Hamiltonian approachThe localized Zakharov equation: derivation and validationThreshold model on the evolution of Stokes wave side-band instabilityHamiltonian higher-order nonlinear Schrödinger equations for broader-banded waves on deep waterA note on an alternative derivation of the Benney equations for short wave-long wave interactionsDeterministic and stochastic theory for a resonant triadParametrization of sea surface skewness and kurtosis with application to crest distributionsOn the non-uniqueness of the kernel of the Zakharov equation in intermediate and shallow water: the connection with the Davey–Stewartson equationOn elementary four-wave interactions in dispersive mediaSpectral inversion of second order Volterra models based on the blind identification of Wiener modelsDiscrete resonant Rossby/drift wave triads: explicit parameterisations and a fast direct numerical search algorithmExact discrete resonances in the Fermi-Pasta-Ulam-Tsingou systemFIFTH-ORDER EVOLUTION EQUATION OF GRAVITY–CAPILLARY WAVESThe most unstable conditions of modulation instabilityNonlinear evolution equations of co-propagating waves over finite depth fluidPhysical mechanisms of the rogue wave phenomenon.Unitary transformations in weakly nonideal Bose gasesWater waves in a deep square basinEffective five-wave Hamiltonian for surface water waves.Resonant triad dynamics in weakly damped Faraday waves with two-frequency forcingNonlinear Wave Interaction in Coastal and Open Seas: Deterministic and Stochastic TheoryEfficiency of exponential time differencing schemes for nonlinear Schrödinger equationsTwo-dimensional resonant triad interactions in a two-layer systemThe water wave problem and Hamiltonian transformation theoryOn Zakharov's kernel and the interaction of non-collinear wavetrains in finite water depthStatistics of surface gravity wave turbulence in the space and time domainsWeakly nonlinear statistics of high random wavesCrest speeds of unsteady surface water wavesExtreme wave events in directional, random oceanic sea statesAn experimental and numerical study of the spatial evolution of unidirectional nonlinear water-wave groupsThree-dimensional surface gravity waves of a broad bandwidth on deep waterPhase-averaged equation for water wavesAsymptotics for the long-time evolution of kurtosis of narrow-band ocean wavesOn an eddy viscosity model for energetic deep-water surface gravity wave breakingCan swell increase the number of freak waves in a wind sea?Large-time evolution of statistical moments of wind–wave fieldsProgress in ocean wave forecastingOn certain properties of the compact Zakharov equationOn the Badulin, Kharif and Shrira model of resonant water wavesOn the predictability of evolution of surface gravity and gravity-capillary wavesOn the interaction of four water-wavesDiscreteness and its effect on water-wave turbulenceA numerical study on statistical characteristics of amplitude fluctuations in a wave turbulenceNew insight into classical equilibrium solutions of kinetic equationsFive-wave interaction on the surface of deep fluidEffects of three-wave interactions in the gravity-capillary range of wind wavesFour-wave resonant interactions in the classical quadratic Boussinesq equationsResonant interactions between Kelvin ship waves and ambient wavesThe evolution of large non-breaking waves in intermediate and shallow water. I. Numerical calculations of uni-directional seasPhysical mechanisms for sporadic wind wave horse-shoe patternsGlobal dynamics in the simplest models of three-dimensional water-wave patternsSpatial evolution of young wind waves: numerical modelling verified by experimentsModelling statistical wave interferences over shear currentsUniversal route to thermalization in weakly-nonlinear one-dimensional chainsKinematics of fluid particles on the sea surface: Hamiltonian theoryNormal form transformations and Dysthe's equation for the nonlinear modulation of deep-water gravity wavesOn weakly turbulent scaling of wind sea in simulations of fetch-limited growthHamiltonian form of the modified nonlinear Schrödinger equation for gravity waves on arbitrary depthStability of bichromatic gravity waves on deep waterFourth-order coupled nonlinear Schrödinger equations for gravity waves on deep waterKinetic equations in a third-generation spectral wave modelExperimental investigation on the evolution of the modulation instability with dissipationSpecial solutions to a compact equation for deep-water gravity wavesHamiltonian Dysthe Equation for Three-Dimensional Deep-Water Gravity WavesOn the highest non-breaking wave in a group: fully nonlinear water wave breathers versus weakly nonlinear theory



Cites Work


This page was built for publication: On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves