The diffraction of an obliquely incident surface wave by a vertical barrier of finite depth

1966 ◽  
Vol 62 (4) ◽  
pp. 829-838 ◽  
Author(s):  
T. R. Faulkner
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Deep Sea ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Finite Depth ◽  
Two Dimensional ◽  
Obliquely Incident ◽  
Vertical Barrier

The effect of a vertical barrier, fixed in an infinitely deep sea, on normally incident surface waves of small amplitude was first considered by Ursell (1) and generalizations which retain the two-dimensional aspects of the problem have subsequently been considered by John (2) and Lewin (3). The fluid motion due to the flexural vibrations of a barrier of finite depth has been considered by Alblas (4), the motion in this case being three-dimensional.

A porous-wavemaker theory

1983 ◽  
Vol 132 ◽  
pp. 395-406 ◽  
Author(s):  
Allen T. Chwang
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Small Amplitude ◽  
Vertical Plate ◽  
Hydrodynamic Pressure ◽  
Finite Depth ◽  
Wave Profile ◽  
Total Force ◽  
Wave Effect ◽  
Effect Parameter

A porous-wavemaker theory is developed to analyse small-amplitude surface waves on water of finite depth, produced by horizontal oscillations of a porous vertical plate. Analytical solutions in closed forms are obtained for the surface-wave profile, the hydrodynamic-pressure distribution and the total force on the wavemaker. The influence of the wave-effect parameter C and the porous-effect parameter G, both being dimensionless, on the surface waves and on the hydrodynamic pressures is discussed in detail.

The radiation and scattering of surface waves by vertical barriers

1974 ◽  
Vol 63 (4) ◽  
pp. 625-634 ◽  
Author(s):  
D. Porter
Keyword(s):  
Boundary Value Problem ◽  
Surface Waves ◽  
Incident Wave ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Vertical Plane ◽  
Wave Radiation ◽  
Two Dimensional ◽  
Radiation Problem ◽  
Vertical Barriers

A train of small-amplitude surface waves is incident normally on an arbitrary arrangement of thin barriers lying in a vertical plane in deep water. Each barrier is allowed to make small rolling or swaying oscillations of the same frequency as that of the incident wave. The boundary-value problem for the consequent fluid motion, assumed two-dimensional, is solved exactly using a technique which enables the amplitudes of the scattered waves far from the barriers to be readily determined. Reference is made to the associated wave radiation problem and to the calculation of forces and moments on the barriers.

The transmission of surface waves through a gap in a vertical barrier

1972 ◽  
Vol 71 (2) ◽  
pp. 411-421 ◽  
Author(s):  
D. Porter
Keyword(s):  
Surface Waves ◽  
Velocity Potential ◽  
Hilbert Problem ◽  
Fluid Motion ◽  
Two Dimensional ◽  
Reduction Procedure ◽  
Vertical Barrier ◽  
Integral Equation Formulation ◽  
Gap Width ◽  
Riemann Hilbert Problem

AbstractThe two-dimensional configuration is considered of a fixed, semi-infinite, vertical barrier extending downwards from a fluid surface and having, at some depth, a gap of arbitrary width. A train of surface waves, incident on the barrier, is partly transmitted and partly reflected. The velocity potential of the resulting fluid motion is determined by a reduction procedure and also by an integral equation formulation. It is shown that the two methods lead to the same Riemann–Hilbert problem. Transmission and reflexion coefficients are calculated for several values of the ratio gap width/mean gap depth.

scholarly journals On the Potential of 3D Transdimensional Surface Wave Tomography for Geothermal Prospecting of the Reykjanes peninsula

2021 ◽  
Author(s):  
Amin Rahimi Dalkhani ◽  
Xin Zhang ◽  
Cornelis Weemstra
Keyword(s):  
Surface Wave ◽  
Surface Waves ◽  
Velocity Structure ◽  
Voronoi Tessellation ◽  
Three Dimensional ◽  
Seismic Network ◽  
Two Dimensional ◽  
Travel Times ◽  
Model Resolution ◽  
Reykjanes Peninsula

Seismic travel time tomography using surface waves is an effective tool for three-dimensional crustal imaging. Historically, these surface waves are the result of active seismic sources or earthquakes. More recently, however, also surface waves retrieved through the application of seismic interferometry are exploited. Conventionally, two-step inversion algorithms are employed to solve the tomographic inverse problem. That is, a first inversion results in frequency-dependent, two-dimensional maps of phase velocity, which then serve as input for a series of independent, one-dimensional frequency-to-depth inversions. As such, a two-dimensional grid of localized depth-dependent velocity profiles are obtained. Stitching these separate profiles together subsequently yields a three-dimensional velocity model. Relatively recently, a one-step three-dimensional non-linear tomographic algorithm has been proposed. The algorithm is rooted in a Bayesian framework using Markov chains with reversible jumps, and is referred to as transdimensional tomography. Specifically, the three-dimensional velocity field is parameterized by means of a polyhedral Voronoi tessellation. In this study, we investigate the potential of this algorithm for the purpose of recovering the three-dimensional surface-wave-velocity structure from ambient noise recorded on and around the Reykjanes Peninsula, southwest Iceland. To that end, we design a number of synthetic tests that take into account the station configuration of the Reykjanes seismic network. We find that the algorithm is able to recover the 3D velocity structure at various scales in areas where station density is high. In addition, we find that the standard deviation on the recovered velocities is low in those regions. At the same time, the velocity structure is less well recovered in parts of the peninsula sampled by fewer stations. This implies that the algorithm successfully adapts model resolution to the density of rays. Also, it adapts model resolution to the amount of noise on the travel times. Because the algorithm is computationally demanding, we modify the algorithm such that computational costs are reduced while sufficiently preserving non-linearity. We conclude that the algorithm can now be applied adequately to travel times extracted from (time-averaged) station-station cross correlations by the Reykjanes seismic network.

On the evolution of packets of long surface waves

1975 ◽  
Vol 344 (1638) ◽  
pp. 427-433 ◽  
Keyword(s):  
Nonlinear Waves ◽  
Small Amplitude ◽  
Vries Equation ◽  
Three Dimensional ◽  
Finite Depth ◽  
Two Dimensional ◽  
Direction Transverse ◽  
Amplitude Parameter ◽  
First Approximation ◽  
Poisson Type

Three dimensional inviscid nonlinear waves on the surface of water of finite depth are examined in the limit of long waves. It is shown that small amplitude waves having a suitably slow variation in the direction transverse to that of propagation satisfy a two dimensional analogue of the well known Korteweg-de Vries equation when the parameter Δ =ε /h 2 k 2 is finite; where ε is an amplitude parameter, h is the depth and k is the wavenumber. When Δ is small this analogue is reduced, to first approximation, to a scaled form of the nonlinear Schrödinger-Poisson type equations adumbrated by Davey & Stewartson (1974).

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

Steady State Motion and Surface Waves

1996 ◽  
Author(s):  
T. T. C. Ting
Keyword(s):  
Steady State ◽  
Surface Wave ◽  
Surface Waves ◽  
Existence And Uniqueness ◽  
Wave Speed ◽  
Wave Theory ◽  
Two Dimensional ◽  
Elastic Materials ◽  
Steady State Motion ◽  
Anisotropic Elastic

The Stroh formalism for two-dimensional elastostatics can be extended to elastodynamics when the problem is a steady state motion. Most of the identities in Chapters 6 and 7 remain applicable. The Barnett-Lothe tensors S, H, L now depend on the speed υ of the steady state motion. However S(υ), H(υ), L(υ) are no longer tensors because they do not obey the laws of tensor transformation when υ≠0. Depending on the problems the speed υ may not be prescribed arbitrarily. This is particularly the case for surface waves in a half-space where υ is the surface wave speed. The problem of the existence and uniqueness of a surface wave speed in anisotropic materials is the crux of surface wave theory. It is a subject that has been extensively studied since the pioneer work of Stroh (1962). Excellent expositions on surface waves for anisotropic elastic materials have been given by Farnell (1970), Chadwick and Smith (1977), Barnett and Lothe (1985), and more recently, by Chadwick (1989d).

scholarly journals Bilge-Keel Influence on Free Decay of Roll Motion of a Realistic Hull1

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Yichen Jiang ◽  
Ronald W. Yeung
Keyword(s):  
Free Surface ◽  
Fluid Motion ◽  
Three Dimensional ◽  
Vortex Method ◽  
Roll Motion ◽  
Two Dimensional ◽  
Desktop Computer ◽  
Roll Damping ◽  
Discrete Vortex ◽  
Bilge Keel

The prediction of roll motion of a ship with bilge keels is particularly difficult because of the nonlinear characteristics of the viscous roll damping. Flow separation and vortex shedding caused by bilge keels significantly affect the roll damping and hence the magnitude of the roll response. To predict the ship motion, the Slender-Ship Free-Surface Random-Vortex Method (SSFSRVM) was employed. It is a fast discrete-vortex free-surface viscous-flow solver developed to run on a standard desktop computer. It features a quasi-three-dimensional formulation that allows the decomposition of the three-dimensional ship-hull problem into a series of two-dimensional computational planes, in which the two-dimensional free-surface Navier–Stokes solver Free-Surface Random-Vortex Method (FSRVM) can be applied. In this paper, the effectiveness of SSFSRVM modeling is examined by comparing the time histories of free roll-decay motion resulting from simulations and from experimental measurements. Furthermore, the detailed two-dimensional vorticity distribution near a bilge keel obtained from the numerical model will also be compared with the existing experimental Digital Particle Image Velocimetry (DPIV) images. Next, we will report, based on the time-domain simulation of the coupled hull and fluid motion, how the roll-decay coefficients and the flow field are altered by the span of the bilge keels. Plots of vorticity contour and vorticity isosurface along the three-dimensional hull will be presented to reveal the motion of fluid particles and vortex filaments near the keels.

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