The Wiener–Hopf and residue calculus solutions for a submerged semi-infinite elastic plate

Williams, Timothy; Meylan, Michael H.

doi:10.1007/s10665-011-9518-9

Cited by 34 publications

(26 citation statements)

References 37 publications

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“…In both cases, (35) and 37, the wave height and wave number are independent of each other; the wave number can be specified arbitrarily.…”

Section: Incident Impulse Wavesmentioning

confidence: 99%

Solitary Waves Incident on a Submerged Horizontal Plate

Liu

2014

J. Waterway, Port, Coastal, Ocean Eng.

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Wave scattering of a solitary wave traveling over a submerged horizontal plate was studied. Experiments for normal incidence were conducted in a wave flume with a horizontal plate suspended at two different depths in the middle of the flume. Gauge pressures above and underneath the plate, surface elevations on and near the plate, and flow velocities at three representative fields of view were measured. The flow underneath the plate was found to behave almost like a plug flow, driven by the time-dependent, spatially uniform pressure gradient between the two openings. Complex vortices formed near the two edges of the plate as the plate acted like a flow divider. A numerical model based on 2D Navier-Stokes equations was used to further confirm the main features captured by the experimental measurements. Analytical solutions based on the linear long wave theory, which admits a "soliton-like" impulse wave solution, were also derived. The linear theory was applicable for obliquely incident impulse waves. When the analytical solutions were applied to the wave conditions used in the experiments, it was found that the theory described pressure and surface elevation satisfactorily when the non-linearity is insignificant. Based on the pressure distribution above and beneath the plate the total vertical force and moment exerted on the plate were calculated. As the wave passed over the plate, the plate first experienced a lift, followed by a force in the downward direction, and then a lift again. As a result a non-zero time-varying moment existed. The analytical solution was also utilized to examine the effects of relative plate width on the transmitted and reflected waves. The effects of the angle of incidence

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“…In both cases, (35) and 37, the wave height and wave number are independent of each other; the wave number can be specified arbitrarily.…”

Section: Incident Impulse Wavesmentioning

confidence: 99%

Solitary Waves Incident on a Submerged Horizontal Plate

Liu

2014

J. Waterway, Port, Coastal, Ocean Eng.

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“…This sophisticated method gives identical results to those found from the Wiener-Hopf technique when applied to the problem of a semi-infinite plate where solutions are explicit (e.g. Greene & Heins [4], Heins [5]); this equivalence is explicitly demonstrated in Williams & Meylan [6].…”

Section: Introductionmentioning

confidence: 55%

Linearised water wave problems involving submerged horizontal plates

Porter

2015

Applied Ocean Research

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“…As discussed below, we demonstrate here that the presence of poroelasticity in the submerged plate can strongly suppress one of the transmitted waves (the plate-interaction wave), leaving only one significant transmitted surface wave that attenuates slowly. The solution for the semi-infinite submerged elastic plate was found first using the eigenfunction matching method [13] and later by the Wiener-Hopf method [14]. In the water-wave context, horizontal submerged plates are particularly popular for dissipating water-wave energy, e.g.…”

Section: Introductionmentioning

confidence: 99%

On the Wiener–Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate

et al. 2020

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A solution to the problem of water-wave scattering by a semi-infinite submerged thin elastic plate, which is either porous or non-porous, is presented using the Wiener–Hopf technique. The derivation of the Wiener–Hopf equation is rather different from that which is used traditionally in water-waves problems, and it leads to the required equations directly. It is also shown how the solution can be computed straightforwardly using Cauchy-type integrals, which avoids the need to find the roots of the highly non-trivial dispersion equations. We illustrate the method with some numerical computations, focusing on the evolution of an incident wave pulse which illustrates the existence of two transmitted waves in the submerged plate system. The effect of the porosity is studied, and it is shown to influence the shorter-wavelength pulse much more strongly than the longer-wavelength pulse.

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The Wiener–Hopf and residue calculus solutions for a submerged semi-infinite elastic plate

Cited by 34 publications

References 37 publications

Solitary Waves Incident on a Submerged Horizontal Plate

Solitary Waves Incident on a Submerged Horizontal Plate

Linearised water wave problems involving submerged horizontal plates

On the Wiener–Hopf solution of water-wave interaction with a submerged elastic or poroelastic plate

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