Semi-analytical solution of cnoidal wave diffraction around a double-layer arc-shaped vertical porous breakwater

The analytical solutions for the diffraction of the short-crested wave, the cnoidal wave, and the solitary wave incident on a composite bucket foundation of an offshore wind turbine are derived in this paper. The analytical expressions for the pressure, wave run-up, and wave force on the composite bucket foundation are obtained. Based on the numerical results, it is found that the short-crested wave run-up is affected by the wave phase, the cnoidal wave run-up is affected by the wave parameter λ, and the solitary wave run-up is affected by the wave parameter χ. For a composite bucket foundation, the long-crested wave force is larger than the short-crested wave force and the solitary wave force is larger than cnoidal wave force in certain shallow water conditions. Moreover, the short-crested wave force may first increase and then decrease with the increase in the water depth, while the cnoidal wave force and the solitary wave force monotonically increase with the increase in the water depth. In the design of the offshore wind turbine with composite bucket foundation, it will be more conservative if the formula derived from the plane waves is used as design criteria in a short-crested sea, and the wave force in shallow water should be determined by the solitary wave and the cnoidal wave together.

Fluid resonance in the narrow gap of a box-wall system under cnoidal wave action

Discussion of “A function to determine wavelength from deep in to shallow water based on the length of the cnoidal wave at breaking” by J.P. Le Roux

Analytical and experimental studies on Bragg scattering of water waves by multiple submerged perforated semi-circular breakwaters

A study, using potential water wave theory, is conducted on the oblique water wave motion over two fixed submerged rectangular blocks (breakwaters) placed over a finite step bottom. We have considered infinite and semi-infinite fluid domains. In both domains, the Fourier expansion method is employed to obtain the velocity potentials explicitly in terms of the infinite Fourier series. The unknown coefficients appearing in the velocity potentials are determined by the eigenfunction expansion matching method at the interfaces. The derived velocity potentials are used to compute the hydrodynamic horizontal and vertical forces acting on the submerged blocks for different values of block thickness, gap spacing between the two blocks, and submergence depth of the upper block from the mean free surface. In addition, the wave load on the vertical wall is computed in the case of the semi-infinite fluid domain for different values of blocks width and the incident wave angle. It is observed that the amplitudes of hydrodynamic forces are negligible for larger values of the wavenumber. Furthermore, the upper block experiences a higher hydrodynamic force than the lower block, regardless of the gap spacing, submergence depth, and block thickness.

Hydrodynamic interaction with an array of porous circular cylinders

: A method is presented for calculating the distribution of force and overturning moment resulting from incident water waves moving along the axis of a groin or jetty with vertical sides. Wave height at the structure is determined from experimental data on Mach-stem reflection. The distribution of force is assumed to be in proportion to the nonlinear shallow-water wave profile given by either the cnoidal or stream-function wave theory. An example problem demonstrates how the cnoidal theory may be used to estimate the wave force and overturning moment distribution along a structure.

Hydrodynamic interactions of cnoidal waves with a vertical cylinder

<p>Deformation bands are sub-seismic brittle structures found in granular materials. These structures exhibit two spatial distributions: [1] non-linear decay of spacing associated with the damage zone of a fault, and [2] periodic, constant spacing not associated with faults. Periodically spaced deformation bands are of interest as they can be pervasive through porous (>5% φ) formations and are known to impact fluid flow. Bands can act as conduits or barriers to fluid flow and are commonly identified in petroleum reservoirs. An understanding of the factors controlling their distribution is therefore of great importance.</p><p>Here, we test a novel mathematical theory postulating that material instabilities in solids with internal mass transfer associated with volumetric deformation are due to elastoviscoplastic p-waves termed cnoidal waves. The stationary cnoidal wave model for periodic compaction bands predicts that their spacing is controlled by important material properties: the permeability of the weak phase in the pores, the viscosity of the weak phase, and the inelastic volumetric viscosity (strength) of the solid grains. A semi-analytical parametric study of the dimensional non-linear governing equations yields a surprisingly simple scaling relationship, which requires testing in the field. Stronger units with higher permeability are predicted to exhibit a wider spacing between deformation bands.</p><p>We test the cnoidal-wave model on natural deformation bands from Castlepoint, North Island, New Zealand. These bands are hosted by Miocene turbidites of the Whakataki formation, which formed in tectonically controlled trench-slope basins associated with the onset of subduction of the Pacific plate beneath the Zealandian plate along the Hikurangi subduction margin. Adjacent sand- and siltstone beds exhibit significant differences in deformation band spacing. Spacing statistics derived from field mapping and laboratory measurements of host-rock permeability and strength are employed to test the scaling relation predicted by the cnoidal wave model. Inconsistencies between theoretical and observed spacing are discussed critically.</p>

Severe water waves can induce seabed liquefaction and do harm to marine structures. Dynamic response of seabed with definite thickness induced by cnoidal water waves is investigated numerically. Biot’s consolidation equations are employed to model the seabed response. Parametric studies are carried out to examine the influence of the air content in the pore water and the soil hydraulic conductivity. It has been shown that the air content and soil hydraulic conductivity can significantly affect the pore pressure in seabed. An increase of air content and/or a decrease of soil hydraulic conductivity can change the pore pressure gradient sharply.

ABSTRACTResearch on the response of random wave on offshore structures has received great deal of attention of many researchers and engineers in the design of marine structures. Most previous investigations have been limited to the regular waves. In this paper, based on Longuet–Higgins random wave theory and finite element method, a numerical model for random wave-induced seabed response is established. The seabed is treated as poroelastic medium and characterized by Biot’s partly dynamic equations (u–p model). The JONSWAP spectrum is adopted in Longuet–Higgins model, which is based on the cumulative superposition of linear diffraction solution. Based on the numerical results, the effects of random wave on seabed response are investigated by comparing with the corresponding Stokes wave and cnoidal wave. Then, a parametric study is conducted to examine the effect of wave and soil characteristic on the seabed.

Wave loads on large vertical cylinders: A design method

A novel semi-analytical approach based on scaled boundary finite element method for fluid-structure coupling analysis of liquid sloshing in 3D containers

Very little quantitative information exists on growth of wind waves in waters where relatively shallow depth could influence wave growth; results of laboratory investigation of growth of waves in shallow water is presented, showing experimental relationships between wind velocity, fetch, and wave parameters for two different water depths.

Trapping of oblique surface gravity waves by dual porous barriers near a wall is studied in the presence of step type varying bottom bed that is connected on both sides by water of uniform depths. The porous barriers are assumed to be fixed at a certain distance in front of a vertical rigid wall. Using linear water wave theory and Darcy's law for flow past porous structure, the physical problem is converted into a boundary value problem. Using eigenfunction expansion in the uniform bottom bed region and modified mild-slope equation in the varying bottom bed region, the mathematical problem is handled for solution. Moreover, certain jump conditions are used to account for mass conservation at slope discontinuities in the bottom bed profile. To understand the effect of dual porous barriers in creating tranquility zone and minimum load on the sea wall, reflection coefficient, wave forces acting on the barrier and the wall, and surface wave elevation are computed and analyzed for different values of depth ratio, porous-effect parameter, incident wave angle, gap between the barriers and wall and slope length of undulated bottom. The study reveals that with moderate porosity and suitable gap between barriers and sea wall, using dual barriers an effective wave trapping system can be developed which will exert less wave force on the barriers and the rigid wall. The proposed wave trapping system is likely to be of immense help for protecting various facilities/ infrastructures in coastal environment.