Wavemaker theories for acoustic–gravity waves over a finite depth
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Author(s)
Tian, Miao
Kadri, Usama
Date Issued
May 2017
Journal
Journal of Engineering Mathematics
Publisher
Springer Netherlands
Citation
Tian, Miao, and Usama Kadri. “Wavemaker Theories for Acoustic–gravity Waves over a Finite Depth.” Journal of Engineering Mathematics, vol. 108, no. 1, Feb. 2018, pp. 25–35.
Version
Author's final manuscript
Abstract
Acoustic–gravity waves (hereafter AGWs) in ocean have received much attention recently, mainly with respect to early detection of tsunamis as they travel at near the speed of sound in water which makes them ideal candidates for early detection of tsunamis. While the generation mechanisms of AGWs have been studied from the perspective of vertical oscillations of seafloor and triad wave–wave interaction, in the current study, we are interested in their generation by wave–structure interaction with possible implication to the energy sector. Here, we develop two wavemaker theories to analyse different wave modes generated by impermeable (the classic Havelock’s theory) and porous (porous wavemaker theory) plates in weakly compressible fluids. Slight modification has been made to the porous theory so that, unlike the previous theory, the new solution depends on the geometry of the plate. The expressions for three different types of plates (piston, flap, and delta-function) are introduced. Analytical solutions are also derived for the potential amplitudes of the gravity, acoustic–gravity, evanescent waves, as well as the surface elevation, velocity distribution, and pressure for AGWs. Both theories reduce to previous results for incompressible flow when the compressibility is neglected. We also show numerical examples for AGWs generated in a wave flume as well as in deep ocean. Our current study sets the theoretical background towards remote sensing by AGWs, for optimised deep ocean wave-power harnessing, among others.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10665-017-9902-1
