New exact relations for steady irrotational two-dimensional gravity and capillary surface waves

DOI10.1098/rsta.2017.0220zbMath1404.76037arXiv1712.04768OpenAlexW3099689768WikidataQ47579672 ScholiaQ47579672MaRDI QIDQ4561750

Didier Clamond

Publication date: 13 December 2018

Published in: Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1712.04768

zbMATH Keywords

capillary wavesgravity wavesexact equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45)

Related Items (6)

Recovery of steady rotational wave profiles from pressure measurements at the bed ⋮ Nonlinear water waves: introduction and overview ⋮ Accurate fast computation of steady two-dimensional surface gravity waves in arbitrary depth ⋮ General procedure for free-surface recovery from bottom pressure measurements: application to rotational overhanging waves ⋮ On the construction of traveling water waves with constant vorticity and infinite boundary ⋮ Extreme water-wave profile recovery from pressure measurements at the seabed

Uses Software

• DLMF

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The trajectories of particles in Stokes waves
• Steady periodic hydroelastic waves
• Accurate calculations of Stokes water waves of large amplitude
• The regularity and local bifurcation of steady periodic water waves
• Mean velocities in a Stokes wave
• Global bifurcation of steady gravity water waves with critical layers
• Remarks on Bernoulli constants, gauge conditions and phase velocities in the context of water waves
• Numerical verification of solutions of Nekrasov's integral equation
• A variational principle for waves of infinite depth
• A plethora of generalised solitary gravity–capillary water waves
• An exact integral equation for solitary waves (with new numerical results for some ‘internal’ properties)
• Steady water waves
• Gravity–Capillary Free-Surface Flows
• Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth
• New integral relations for gravity waves of finite amplitude
• Capillary–gravity waves of solitary type on deep water
• Integral properties of periodic gravity waves of finite amplitude
• Some New Relations Between Stokes's Coefficients in the Theory of Gravity Waves
• Cnoidal-type surface waves in deep water
• Numerical Solution of Nekrasov's Equation in the Boundary Layer Near the Crest for Waves Near the Maximum Height
• Steady finite-amplitude waves on a horizontal seabed of arbitrary depth
• The flow beneath a periodic travelling surface water wave
• On asymmetric generalized solitary gravity–capillary waves in finite depth
• Recovery of steady periodic wave profiles from pressure measurements at the bed
• New exact relations for easy recovery of steady wave profiles from bottom pressure measurements
• On the Lagrangian description of steady surface gravity waves
• T<scp>HE</scp> O<scp>RIGINS OF</scp> W<scp>ATER</scp> W<scp>AVE</scp> T<scp>HEORY</scp>

This page was built for publication: New exact relations for steady irrotational two-dimensional gravity and capillary surface waves