Numerical simulation of solitary wave scattering by a circular cylinder array

The interaction of a solitary wave with an array of surface-piercing vertical circular cylinders is investigated numerically. The wave motion is modeled by a set of generalized Boussinesq equations. The governing equations are discretized using a finite element method. The numerical model is validated against the experimental data of solitary wave reflection from a vertical wall and solitary wave scattering by a vertical circular cylinder respectively. The predicted wave surface elevation and the wave forces on the cylinder agree well with the experimental data. The numerical model is then employed to study solitary wave scattering by arrays of two circular cylinders and four circular cylinders respectively. The effect of wave direction on the wave forces and the wave runup on the cylinders is quantified.     

A comparison of several wave spectra for the random wave diffraction by a semi-infinite breakwater

A comparison of the diffraction of multidirectional random waves using several selected wave spectrum models is presented in this paper. Six wave spectrum models, Bretschneider, Pierson–Moskowitz, ISSC, ITTC, Mitsuyasu, and JONSWAP spectrum, are considered. A discrete form for each of the given spectrum models is used to specify the incident wave conditions. Analytical solutions based on both the Fresnel integrals and polynomial approximations of the Fresnel integrals and numerical solutions of a boundary integral approach have been used to obtain the two-dimensional wave diffraction by a semi-infinite breakwater at uniform water depth. The diffraction of random waves is based on the cumulative superposition of linear diffraction solution. The results of predicted random wave diffraction for each of the given spectrum models are compared with those of the published physical model presented by Briggs et al. [1995. Wave diffraction around breakwater. Journal of Waterway, Port, Coastal and Ocean Engineering—ASCE 121(1), 23–35]. Reasonable agreement is obtained in all cases. The effect of the directional spreading function is also examined from the results of the random wave diffraction. Based on these comparisons, the present model for the analysis of various wave spectra is found to be an accurate and efficient tool for predicting the random wave field around a semi-infinite breakwater or inside a harbor of arbitrary geometry in practical applications.     

Numerical simulation of the hydrodynamic behaviour of submerged plane nets in current

The aim of this paper is to investigate the shape and tension distribution of fishing nets in current. A numerical model is developed, based on lumped mass method to simplify the net. The motion equation is set up for each lumped mass. The Runge–Kutta–Verner fifth-order and sixth-order method is used to solve these simultaneous equations, and then the displacement and tension of each lumped mass are obtained. In order to verify the validity of the numerical method, model tests have been carried out. The results by the numerical simulation agree well with the experimental data.     

Depth- and current-induced effects on wave propagation into the Altamaha River Estuary, Georgia

A study of sea surface wave propagation and its energy deformation was carried out using field observations and numerical experiments over a region spanning the midshelf of the South Atlantic Bight (SAB) to the Altamaha River Estuary, GA. Wave heights on the shelf region correlate with the wind observations and directional observations show that most of the wave energy is incident from the easterly direction. Comparing midshelf and inner shelf wave heights during a time when there was no wind and hence no wave development led to an estimation of wave energy dissipation due to bottom friction with corresponding wave dissipation factor of 0.07 for the gently sloping continental shelf of the SAB. After interacting with the shoaling region of the Altamaha River, the wave energy within the estuary becomes periodic in time showing wave energy during flood to high water phase of the tide and very little wave energy during ebb to low water. This periodic modulation inside the estuary is a direct result of enhanced depth and current-induced wave breaking that occurs at the ebb shoaling region surrounding the Altamaha River mouth at longitude 81.23°W. Modelling results with STWAVE showed that depth-induced wave breaking is more important during the low water phase of the tide than current-induced wave breaking during the ebb phase of the tide. During the flood to high water phase of the tide, wave energy propagates into the estuary. Measurements of the significant wave height within the estuary showed a maximum wave height difference of 0.4 m between the slack high water (SHW) and slack low water (SLW). In this shallow environment these wave–current interactions lead to an apparent bottom roughness that is increased from typical hydraulic roughness values, leading to an enhanced bottom friction coefficient.     

A General Linear Wave Theory for Water Waves Propagating over Uneven Porous Bottoms

Starting from the widespread phenomena of porous bottoms in the near shore region, considering fully the diversity of bottom topography and wave number variation, and including the effect of evanescent modes, a general linear wave theory for water waves propagating over uneven porous bottoms in the near shore region is established by use of Green‘s scond identity. This theory can be reduced to a number of the most typical mild-slope equations curreutly in use and provide a reliable research basis for follow-up development of nonlinear water wave theory involving porous bottoms.     

Mach Effect of Oblique Nonlinear Irregular Waves Interacting with Vertical Walls

Based on Hong‘s theory, previous random models, and a generalized expression suitable for FIT calculation, the interaction between irregular waves and vertical walls is numerically simulated. The results of simulation demonstrate that the wave energy changes with the incidence angle and the distance from the wall. Particularly, the Mach effect and the combined wave spectrum characteristics are analyzed in detail, which are significant in both theory and practice.     

Probabilistic Models for the Probability of Wave Breaking and Whitecap Coverage Based on Kinematic Breaking Criterion

More and more researches show that neither the critical downward acceleration nor the critical slope of water waves is a universal constant. On the contrary, they vary with particular wave conditions. This fact moders the models either for the probability of wave breaking B or for the whitecap coverage W based on these criteria difficult to apply. In this paper and the one which follows we seek to develop models for the prediction of both B and W based on the kinematical criterion. First, several joint probabihstic distribution functions (PDFs) of wave characteristics are derived, based on which the breaking properties B and W are estimated. The estimation is made on the assumption that a wave breaks ff the horizontal velocity of water particles at its crest exceeds the local wave celerity, and whitecapping occurs in regions of fluid where water particles travel faster than the waves. The consequent B and W depend on wave spectral moments of orders 0 to 4.Then the JONSWAP spectrum is used to represent the fetch-limited sea waves in deep water, so as to relate the probahility of wave breaking and the whitecap coverage with wind parameters. To this end, the time-averaging technique proposed by Glazman (1986) is applied to the estimation of the spectral moments involved, and furthermore, the theoretical models are compared with available observations collected from published literature. From the comparison, the averaging time scale is determined. The final models show that the probability of wave breaking as well as the whitecap coverage depends on the dimensionless fetch. The agreement between these models and the database is reasonable.     

Artificial Upwelling of Deep Seawater Using the Perpetual Salt Fountain for Cultivation of Ocean Desert

Deep seawater in the ocean contains a great deal of nutrients. Stommel et al. have proposed the notion of a “perpetual salt fountain” (Stommel et al., 1956). They noted the possibility of a permanent upwelling of deep seawater with no additional external energy source. If we can cause deep seawater to upwell extensively, we can achieve an ocean farm. We have succeeded in measuring the upwelling velocity by an experiment in the Mariana Trench area using a special measurement system. A 0.3 m diameter, 280 m long soft pipe made of PVC sheet was used in the experiment. The measured data, a verification experiment, and numerical simulation results, gave an estimate of upwelling velocity of 212 m/day. This revised version was published online in July 2006 with corrections to the Cover Date.     

Influence of Rhodolith-Forming Species and Growth-Form on Associated Fauna of Rhodolith Beds in the Central-West Gulf of California, México

Abstract.  Rhodoliths provide a stable and three-dimensional habitat to which other seaweeds and invertebrates can attach. Although ecological factors affecting rhodolith beds have been studied, little is known about the effect of rhodolith species and growth-form on associated fauna. Experiments were conducted at three rhodolith beds in the central-west Gulf of California. Faunal abundance differed significantly in relation to rhodolith-forming species, but no significant differences were observed between different growth-forms. Rhodolith structure differs between the species Lithophyllum margaritae and Neogoniolithon trichotomum , and the combination of structure differences and rhodolith abundances may be responsible of the significant differences in faunal abundance and richness. Crustaceans, polychaetes and molluscs were the most important taxa in all three rhodolith beds. The amphipod species Pontogeneia nasa and the cnidarian Aiptasia sp. were dominant in both rhodolith beds, El Requesón and Isla Coyote, in Bahía Concepción. The Isla Coronados rhodolith bed was dominated by an unidentified harpacticoid copepod (Copepoda sp.1). Rhodolith species is more important than growth-form in determining abundance and richness of the associated fauna. Nevertheless, factors such as wave motion, depth, bioturbation and others should be considered when studying organisms associated with rhodolith beds.     

Roles of Continental Shelves and Marginal Seas in the Biogeochemical Cycles of the North Pacific Ocean

Most marginal seas in the North Pacific are fed by nutrients supported mainly by upwelling and many are undersaturated with respect to atmospheric CO₂ in the surface water mainly as a result of the biological pump and winter cooling. These seas absorb CO₂ at an average rate of 1.1 ± 0.3 mol C m⁻²yr⁻¹ but release N₂/N₂O at an average rate of 0.07 ± 0.03 mol N m⁻²yr⁻¹. Most of primary production, however, is regenerated on the shelves, and only less than 15% is transported to the open oceans as dissolved and particulate organic carbon (POC) with a small amount of POC deposited in the sediments. It is estimated that seawater in the marginal seas in the North Pacific alone may have taken up 1.6 ± 0.3 Gt (10¹⁵ g) of excess carbon, including 0.21 ± 0.05 Gt for the Bering Sea, 0.18 ± 0.08 Gt for the Okhotsk Sea; 0.31 ± 0.05 Gt for the Japan/East Sea; 0.07 ± 0.02 Gt for the East China and Yellow Seas; 0.80 ± 0.15 Gt for the South China Sea; and 0.015 ± 0.005 Gt for the Gulf of California. More importantly, high latitude marginal seas such as the Bering and Okhotsk Seas may act as conveyer belts in exporting 0.1 ± 0.08 Gt C anthropogenic, excess CO₂ into the North Pacific Intermediate Water per year. The upward migration of calcite and aragonite saturation horizons due to the penetration of excess CO₂ may also make the shelf deposits on the Bering and Okhotsk Seas more susceptible to dissolution, which would then neutralize excess CO₂ in the near future. Further, because most nutrients come from upwelling, increased water consumption on land and damming of major rivers may reduce freshwater output and the buoyancy effect on the shelves. As a result, upwelling, nutrient input and biological productivity may all be reduced in the future. As a final note, the Japan/East Sea has started to show responses to global warming. Warmer surface layer has reduced upwelling of nutrient-rich subsurface water, resulting in a decline of spring phytoplankton biomass. Less bottom water formation because of less winter cooling may lead to the disappearance of the bottom water as early as 2040. Or else, an anoxic condition may form as early as 2200 AD. This revised version was published online in July 2006 with corrections to the Cover Date.