On the particle paths in solitary water waves

DOI10.1090/S0033-569X-09-01166-1zbMath1185.35182OpenAlexW2028194950MaRDI QIDQ5305322

Adrian Constantin

Publication date: 22 March 2010

Published in: Quarterly of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: http://www.ams.org/distribution/qam/2010-68-01/S0033-569X-09-01166-1/home.html

zbMATH Keywords

Euler equationsfree boundaryconformal mapparticle trajectory

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Solitary waves for incompressible inviscid fluids (76B25) Free-surface potential flows for incompressible inviscid fluids (76B07) Euler equations (35Q31)

Related Items

Extrema of the dynamic pressure in an irrotational Stokes wave with underlying currents and infinite depth ⋮ Constant vorticity equatorial flows beneath surface solitary waves with centripetal forces ⋮ Smooth stationary water waves with exponentially localized vorticity ⋮ Recovering surface profiles of solitary waves on a uniform stream from pressure measurements ⋮ Solitary waves on constant vorticity flows with an interior stagnation point ⋮ Particle trajectories for waves on a linear shear current ⋮ On the steady solitary-wave solution of the Green-Naghdi equations of different levels ⋮ Theoretical considerations, flow visualization and pressure measurements for rear-end collisions of two unequal solitary waves ⋮ Particle paths in small amplitude solitary waves with negative vorticity ⋮ Regularity and symmetry properties of rotational solitary water waves ⋮ Velocity and pressure in rear-end collisions between two solitary waves with and without an underlying current ⋮ Velocity field and pressure analysis of equatorial flows beneath solitary water waves

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The hydrodynamical relevance of the Camassa-Holm and Degasperis-Procesi equations
• The trajectories of particles in Stokes waves
• Exact solitary water waves with vorticity
• Small-amplitude Stokes and solitary gravity water waves with an arbitrary distribution of vorticity
• Bounds for water waves
• On solitary water-waves of finite amplitude
• Stokes waves
• Symmetry of steady periodic gravity water waves with vorticity
• On the deep water wave motion
• Stability properties of steady water waves with vorticity
• On the streamlines and particle paths of gravitational water waves
• On Some Properties of Traveling Water Waves with Vorticity
• Symmetry of solitary waves
• On periodic water-waves and their convergence to solitary waves in the long-wave limit
• The existence of solitary water waves
• A Modern Introduction to the Mathematical Theory of Water Waves
• Exact steady periodic water waves with vorticity
• Edge waves along a sloping beach
• Non–existence of solitary water waves in three dimensions
• Pressure beneath a Stokes wave
• Rotational steady water waves near stagnation
• The Classical Problem of Water Waves: a Reservoir of Integrable and Nearly-Integrable Equations
• On the Non-Dimensionalisation, Scaling and Resulting Interpretation of the Classical Governing Equations for Water Waves
• On Gerstner's Water Wave
• Propagation of very long water waves, with vorticity, over variable depth, with applications to tsunamis
• Particle trajectories in solitary water waves
• T<scp>HE</scp> O<scp>RIGINS OF</scp> W<scp>ATER</scp> W<scp>AVE</scp> T<scp>HEORY</scp>
• The existence of solitary waves