scholarly journals Trapping of water waves by freely floating structures in a channel

2011 ◽  
Vol 467 (2136) ◽  
pp. 3613-3632 ◽  
Author(s):  
Sergey A. Nazarov ◽  
Juha H. Videman
Keyword(s):  
Spectral Problem ◽  
Water Waves ◽  
Variational Principles ◽  
Water Channel ◽  
Coupled System ◽  
Wave Theory ◽  
Operator Pencil ◽  
Geometric Condition ◽  
Trapped Modes ◽  
Floating Structures

This article is concerned with the existence of rigid freely floating structures capable of supporting trapped modes (time-harmonic water waves of finite energy in an unbounded domain). Under the usual assumptions of linear water-wave theory, a condition guaranteeing the existence of trapped modes is derived, and structures satisfying this geometric condition are shown to exist in a three-dimensional water channel. The sufficient condition arises from the application of variational principles to a conveniently formulated linear spectral problem, the main effort being the construction of a reduction scheme that turns the quadnic operator pencil associated with the original coupled system into a linear self-adjoint spectral problem. An example of floating bodies supporting at least four trapped modes is given.

scholarly journals Trapped modes around freely floating bodies in a two-layer fluid channel

2014 ◽  
Vol 470 (2170) ◽  
pp. 20140396 ◽  
Author(s):  
Filipe S. Cal ◽  
Gonçalo A. S. Dias ◽  
Juha H. Videman
Keyword(s):  
Spectral Problem ◽  
Water Waves ◽  
Adjoint Operator ◽  
Trapped Modes ◽  
Floating Bodies ◽  
Floating Structures ◽  
Nonlinear Spectral Problem ◽  
Time Harmonic ◽  
Fluid Channel ◽  
Elimination Scheme

Unlike the trapping of time-harmonic water waves by fixed obstacles, the oscillation of freely floating structures gives rise to a complex nonlinear spectral problem. Still, through a convenient elimination scheme the system simplifies to a linear spectral problem for a self-adjoint operator in a Hilbert space. Under symmetry assumptions on the geometry of the fluid domain, we present conditions guaranteeing the existence of trapped modes in a two-layer fluid channel. Numerous examples of floating bodies supporting trapped modes are given.

DISPERSION IN SEISMIC SURFACE WAVES

Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Milton B. Dobrin
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Seismic Refraction ◽  
Wave Theory ◽  
Wave Dispersion ◽  
Surface Zone ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Arrival Times ◽  
Ground Roll

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.

Trapped modes and resonances for water waves over a slightly perturbed bottom

2010 ◽  
Vol 17 (3) ◽  
pp. 307-327 ◽  
Author(s):  
M. I. Romero Rodríguez ◽  
P. Zhevandrov
Keyword(s):  
Water Waves ◽  
Trapped Modes

Reflection of water waves in a channel with corrugated bed

1987 ◽  
Vol 185 ◽  
pp. 249-274 ◽  
Author(s):  
T. Brooke Benjamin ◽  
B. Boczar-Karakiewicz ◽  
W. G. Pritchard
Keyword(s):  
Experimental Study ◽  
Surface Waves ◽  
Water Waves ◽  
Bragg Reflection ◽  
Water Channel ◽  
Sand Bars ◽  
Multiple Processes ◽  
Linearized Theory ◽  
Coastal Sand ◽  
Frictional Effects

Intended as a contribution towards understanding the multiple processes entailed in the development of coastal sand bars due to wave action, this theoretical and experimental study deals with the Bragg reflection of long-crested surface waves in a water channel whose bed is corrugated sinusoidally. The present findings complement and in a few respects improve upon those in previous investigations, particularly Davies & Heathershaw (1984).In §2 a linearized theory is presented, being directed to the elucidation of experimental situations where monochromatic waves propagate into a channel with a limited stretch of corrugations on its bed and an imperfectly absorbing beach at its far end. Allowance is made fully for dispersive effects (§2.2) and approximately for small frictional effects (§2.3). Points of interpretation (§2.4) include accounts of degenerate but non-trivial solutions that apply at frequencies terminating the stopping band, wherein the spatial wavefield has an exponential envelope. The experimental results presented in §4 derive from measurements of the wavefield over a stretch of 24 corrugations, at various frequencies both inside and outside the stopping band. Quantitative comparisons (§4.2 and 4.3) demonstrate close agreements with the theory.

A Study on Predictions of Fully Nonlinear Motion Aircushion Type Floating Structures Using 2D MPS Method

2008 ◽  
Author(s):  
Mitsuhiro Masuda ◽  
Tomoki Ikoma ◽  
Koichi Masuda ◽  
Hisaaki Maeda
Keyword(s):  
Water Waves ◽  
Theoretical Calculations ◽  
Numerical Technique ◽  
Ocean Waves ◽  
Nonlinear Phenomena ◽  
Linear Potential ◽  
Floating Structure ◽  
Fully Nonlinear ◽  
Floating Structures ◽  
Mps Method

Very large floating structures (VLFSs) have been proposed for new ocean space utilization and many researches have been carried out. VLFSs are elastically deformed due to ocean waves because the rigidity of the structure decreases relatively. The authors examine the aircushion type floating structure in order to reduce hydroelastic motion. An aircushion type floating structure to which air-chambers are installed can reduce the wave drifting force and hydroelastic motion at the same time. Most theoretical calculations of motion of aircushion type floating structures in water waves have been done based on a linear potential theory so far. As a result, the utility of the aircushion has been proved. However fully nonlinear phenomena such as deck wetness, slamming and air-leakage cannot be investigated by using existing calculations based on the linear theory. In this study, a computer program code of the two-dimensional MPS method that can consider fully nonlinear influence is developed and then the air layer inside an aircushion is expressed with particles of the MPS. Moreover, the numerical technique for introducing directly the mooring force into the motion equation of the particle is developed. Motion response of aircushion type floating structures in a billow is computed. As a result, the usefulness of this numerical calculation method is confirmed.

scholarly journals Scattering of gravity waves by a periodically structured ridge of finite extent

2019 ◽  
Vol 871 ◽  
pp. 350-376 ◽  
Author(s):  
Agnès Maurel ◽  
Kim Pham ◽  
Jean-Jacques Marigo
Keyword(s):  
Gravity Waves ◽  
Time Domain ◽  
Water Waves ◽  
Classical Result ◽  
Water Channel ◽  
Three Dimensional ◽  
Dimensional Problem ◽  
Homogenized Model ◽  
The Time Domain ◽  
Finite Extent

We study the propagation of water waves over a ridge structured at the subwavelength scale using homogenization techniques able to account for its finite extent. The calculations are conducted in the time domain considering the full three-dimensional problem to capture the effects of the evanescent field in the water channel over the structured ridge and at its boundaries. This provides an effective two-dimensional wave equation which is a classical result but also non-intuitive transmission conditions between the region of the ridge and the surrounding regions of constant immersion depth. Numerical results provide evidence that the scattering properties of a structured ridge can be strongly influenced by the evanescent fields, a fact which is accurately captured by the homogenized model.

Dynamic Response of a Porous Seabed and an Offshore Pile to Linear Water Waves

2008 ◽  
Author(s):  
Jian-Fei Lu ◽  
Dong-Sheng Jeng
Keyword(s):  
Dynamic Response ◽  
Water Waves ◽  
Coupled Model ◽  
Expansion Method ◽  
Wave Theory ◽  
Horizontal Displacement ◽  
Element Model ◽  
Wave Force ◽  
Acoustic Medium ◽  
Linear Wave

In this study, a coupled model is proposed to investigate dynamic response of a porous seabed and an offshore pile to ocean wave loadings. Both the offshore pile and the porous seabed are treated as a saturated poro-elastic medium, while the seawater is considered as a conventional acoustic medium. The coupled boundary element model is established by the continuity conditions along the interfaces between the three media. In the system, wave force is considered as an external load and it is evaluated via the wave function expansion method in the context of a linear wave theory. Numerical results show that the increase of the modulus ratio between the pile and the seabed can reduce the horizontal displacement of the pile and the pore pressures of the seabed around the pile. Furthermore, the maximum pore pressure of the seabed usually occurs at the upper part of the seabed around the pile.

scholarly journals Trapped modes around a row of circular cylinders in a channel

1999 ◽  
Vol 386 ◽  
pp. 259-279 ◽  
Author(s):  
T. UTSUNOMIYA ◽  
R. EATOCK TAYLOR
Keyword(s):  
Expansion Method ◽  
Wave Theory ◽  
Multipole Expansion ◽  
Circular Cylinders ◽  
Large Radius ◽  
Trapped Modes ◽  
Resonant Phenomenon ◽  
Trapped Mode ◽  
Linear Water Wave Theory ◽  
Multipole Expansion Method

Trapped modes around a row of bottom-mounted vertical circular cylinders in a channel are examined. The cylinders are identical, and their axes equally spaced in a plane perpendicular to the channel walls. The analysis has been made by employing the multipole expansion method under the assumption of linear water wave theory. At least the same number of trapped modes is shown to exist as the number of cylinders for both Neumann and Dirichlet trapped modes, with the exception that for cylinders having large radius the mode corresponding to the Dirichlet trapped mode for one cylinder will disappear. Close similarities between the Dirichlet trapped modes around a row of cylinders in a channel and the near-resonant phenomenon in the wave diffraction around a long array of cylinders in the open sea are discussed. An analogy with a mass–spring oscillating system is also presented.

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