Resonant interactions of rotational water waves in the equatorial f-plane approximation

DOI10.1063/1.5027027zbMath1402.76025OpenAlexW2896910728MaRDI QIDQ4556640

Calin Iulian Martin, Biswajit Basu

Publication date: 16 November 2018

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5027027

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Hydrology, hydrography, oceanography (86A05) Vortex flows for incompressible inviscid fluids (76B47) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Capillarity (surface tension) for incompressible inviscid fluids (76B45) Boundary values of solutions to elliptic equations and elliptic systems (35J67) Resonance in context of PDEs (35B34) Stability and instability of geophysical and astrophysical flows (76E20) Traveling wave solutions (35C07)

Related Items (9)

On three-dimensional geophysical capillary-gravity water flows with constant vorticity ⋮ Constant vorticity equatorial flows beneath surface solitary waves with centripetal forces ⋮ Constant vorticity water flows in the equatorial \(\beta\)-plane approximation with centripetal forces ⋮ Expressions and evolution of traveling wave solutions in a generalized two-component rotation b-family system ⋮ Resonances for water waves over flows with piecewise constant vorticity ⋮ Constant vorticity water flows with full Coriolis term ⋮ On constant vorticity water flows in the -plane approximation ⋮ A cylindrical coordinates approach to constant vorticity geophysical waves with centripetal forces at arbitrary latitude ⋮ Exponential profiles producing genuine three-dimensional nonlinear flows relevant for equatorial ocean dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the pressure transfer function for solitary water waves with vorticity
• On equatorial wind waves.
• Analyticity of periodic traveling free surface water waves with vorticity
• Periodic traveling gravity water waves with discontinuous vorticity
• Two-dimensionality of gravity water flows of constant nonzero vorticity beneath a surface wave train
• The trajectories of particles in Stokes waves
• Exact equatorial water waves in the \(f\)-plane
• On the interaction of four water-waves
• Nonlinear resonances of water waves
• Stability of bichromatic gravity waves on deep water
• Weak turbulent approach to the wind-generated gravity sea waves
• Two-dimensionality of gravity water flows governed by the equatorial \(f\)-plane approximation
• Resonant interactions of capillary-gravity water waves
• Turbulence of capillary waves -- theory and numerical simulation
• Estimation of wave heights from pressure data at the bed in the presence of uniform underlying currents
• Global bifurcation of steady gravity water waves with critical layers
• Equatorial wind waves with capillary effects and stagnation points
• Small-amplitude equatorial water waves with constant vorticity: dispersion relations and particle trajectories
• On the existence of equatorial wind waves
• Nonlinear Resonance Analysis
• Exact steady periodic water waves with vorticity
• Wave height estimates from pressure and velocity data at an intermediate depth in the presence of uniform currents
• Capturing the flow beneath water waves
• Shallow water equations for equatorial tsunami waves
• Prediction of the free-surface elevation for rotational water waves using the recovery of pressure at the bed
• Dynamic-pressure distributions under Stokes waves with and without a current
• Large gyres as a shallow-water asymptotic solution of Euler’s equation in spherical coordinates
• Non-existence of three-dimensional travelling water waves with constant non-zero vorticity
• Pressure beneath a Stokes wave
• A Penalization Method for Calculating the Flow Beneath Traveling Water Waves of Large Amplitude
• Gerstner waves in the presence of mean currents and rotation
• Recovery of steady periodic wave profiles from pressure measurements at the bed
• On Constant Vorticity Flows Beneath Two-Dimensional Surface Solitary Waves
• The dynamics of waves interacting with the Equatorial Undercurrent

This page was built for publication: Resonant interactions of rotational water waves in the equatorial f-plane approximation