Waveform of gravity and capillary-gravity waves over a bathymetry

Jie Yu
Phys. Rev. Fluids 4, 014806 – Published 22 January 2019

Abstract

We examine the waveforms of linear waves over a fully submerged, arbitrarily periodic bed, using the recent Floquet theory for gravity waves and extending it to the regime of capillary-gravity waves. The exact solutions illustrate the complex features of waveform geometry that are frequency dependent, including the modulation of propagating waveforms in space-time, spatially modulated standing waveforms, asymmetric waveforms over a symmetric bed profile, and high-curvature wave-crest forms. These features are in contrast to the trivial and invariant sinusoidal waveform of the ordinary linear waves on a flat bed, but reminiscent of nonlinear waveforms. The effect of surface tension is seen to counteract wave scattering by topography, tending to restore the waveform towards a symmetric and sinusoidal geometry. These features are the general characteristics of linear waves over a periodic bed since they are the properties of eigenmodes, and can inspire and guide applications.

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  • Received 27 September 2018

DOI:https://doi.org/10.1103/PhysRevFluids.4.014806

Published by the American Physical Society

Physics Subject Headings (PhySH)

Fluid Dynamics

Authors & Affiliations

Jie Yu*

  • Naval Research Laboratory, Stennis Space Center, Mississippi 39529, USA

  • *Jie.Yu@nrlssc.navy.mil

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Vol. 4, Iss. 1 — January 2019

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