Extended time-dependent mild-slope and wave-action equations for wave–bottom and wave–current interactions

DOI10.1098/rspa.2011.0377zbMath1243.76018OpenAlexW2114495716MaRDI QIDQ2901829

Aron Roland, Yaron Toledo, Tai-Wen Hsu

Publication date: 31 July 2012

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

Full work available at URL: https://doi.org/10.1098/rspa.2011.0377

zbMATH Keywords

water waveswave-current interactionsmild-slope equationswave-action equations

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15)

Related Items (2)

On the model formulations for the interaction of nonlinear waves and current ⋮ Modeling of Wave-Induced Oscillation in Pohang New Harbor by Using Hybrid Finite Element Model

Cites Work

• Reflection in variational models for linear water waves
• A scalar form of the complementary mild-slope equation
• A coupled-mode model for the scattering of water waves by shearing currents in variable bathymetry
• Measurement of wave scattering by topography in the presence of currents
• Energy transport in a nonlinear and inhomogeneous random gravity wave field
• The mild-slope equations
• A new complementary mild-slope equation
• The modified mild-slope equation
• Extensions of the mild-slope equation
• A complementary mild-slope equation derived using higher-order depth function for waves obliquely propagating on sloping bottom
• Approximations to the scattering of water waves by steep topography
• Wavetrains in Inhomogeneous Moving Media
• On slowly-varying Stokes waves
• On the predictability of evolution of surface gravity and gravity-capillary waves

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