Michael Isaacson

Nonlinear-wave effects on fixed and floating bodies

A numerical method for calculating the interaction of steep (nonlinear) ocean waves with large fixed or floating structures of arbitrary shape is described. The interaction is treated as a transient problem with known initial conditions corresponding to still water in the vicinity of the structure and a prescribed incident waveform approaching it. The development of the flow, together with the associated fluid forces and structural motions, are obtained by a time-stepping procedure in which the flow at each time step is calculated by an integral-equation method based on Greens theorem. A few results are presented for two reference situations and these serve to illustrate the effects of nonlinearities in the incident waves.

Wave interactions with double slotted barriers

The present article outlines the numerical calculation of wave interactions with a pair of thin vertical slotted barriers extending from the water surface to some distance above the seabed, and describes laboratory tests undertaken to assess the numerical model. The numerical model is based on an eigenfunction expansion method and utilizes a boundary condition at the surface of each barrier which accounts for energy dissipation within the barrier. Comparisons with experimental measurements of the transmission, reflection, and energy dissipation coefficients for partially submerged slotted barriers show excellent agreement and indicate that the numerical method is able to adequately account for the energy dissipation by the barriers.

Waves in a harbour with partially reflecting boundaries

Abstract The present paper describes a method based on linear diffraction theory for predicting the wave field in a harbour containing partially reflecting boundaries. The method utilizes a point source representation of the harbour boundaries and a matching boundary which separates regions interior and exterior to the harbour, and involves the application of a partial reflection boundary condition. Numerical results are presented for the wave field within a rectangular harbour with a pair of symmetrical breakwaters, for cases of fully absorbing, fully reflecting, and partially reflecting boundaries. The method appears to be able to account adequately for the effects of wave diffraction and partial reflections, and to predict the wave field realistically.

WAVE LOADS AND MOTIONS OF LONG STRUCTURES IN DIRECTIONAL SEAS.

The present paper deals with the effects of wave directionality on the loads and motions of long structures. A numerical procedure based on Greens theorem is developed to compute the exciting forces and hydrodynamic coefficients due to the interaction of a regular oblique wave train with an infinitely long, semi-immersed floating cylinder of arbitrary shape. The linear transfer function approach is used to determine the wave loads and motions of a structure of finite length in short-crested seas. The effect of wave directionality is expressed as a frequency-dependent, directionally averaged reduction factor for the wave loads and a response ratio for the body motions. Numerical results are presented for the force reduction factor and response ratio of a long floating box subject to a directional wave spectrum with a cosine-power-type energy spreading function.

Second order wave diffraction around two-dimensional bodies by time-domain method*

A time-domain second order method is developed to study the nonlinear wave forces and runupon a surface piercing body of arbitrary shape in two dimensions. The free surface boundary conditions and the radiation condition are satisfied to second order by a numerical integration in time and the field solution at each time step is obtained by an integral equation method based on Greens theorem. The solution is separated into a known incident potential and a scattered potential. The initial condition corresponds to a Stokes second order wave field in the domain, and the scattered potential is allowed to develop in time and space. The stability and numerical accuracy of the proposed solution and the treatment of the radiation condition to second order are discussed. Comparisons of wave forces are made with previous theoretical and experimental results for the case of a semi-circular cylinder with axis at the still water level and a favourable agreement is indicated.

Time-domain solution for wave-current interactions with a two-dimensional body

The effects of a current on the radiation and diffraction of regular waves around a two-dimensional body are examined by a time-domain method. The Froude number is assumed to be small so that the steady wave system associated with the current is insignificant. The boundary-value problem is then separated into a steady current problem with a rigid-wall condition applied at the still water level and an unsteady wave problem with modified free surface boundary conditions accounting for the disturbed current field. The boundary conditions for the unsteady problem are satisfied to first order in wave amplitude by a time-stepping procedure, and the field solution at each time step is obtained by an integral equation based on Greens theorem. For the case of a semi-circular cylinder with axis at the still water level, the wave amplitudes, the first-order oscillatory forces and the second-order steady forces at various values of Froude number are presented, and the effects of the current on the solution are discussed. Comparisons are also made with previous numerical results and good agreement is indicated.

FLOATING BREAKWATER RESPONSE TO WAVE ACTION

The Labrador Sea Extreme Waves Experiment (LEWEX), is an international basic research programme concerned with full-scale measurements, analysis, modelling and simulation in test basins of 3-dimensional seas. The research is carried out in order to assess the significance of 3-dimensional sea states in engineering applications. The first phase of the programme full scale wave measurements in the North Atlantic Ocean was performed at a site and time that had a high probability of encountering severe sea states. The present publication shows examples of measured bi-modal directional sea spectra obtained with the WAVESCAN buoy and directional sea spectra measured with an airborne Synthetic Aperture Radar (SAR). Directional spectra of gravity waves are obtained with the SAR both in open waters and below an ice cover. Further work is needed in order to verify SAR-measurements with in-situ observations. In-situ measured directional spectra are also compared with hindcast spectra from the 3G-WAM model. Hindcast significant wave heights were found to be lower than the in-situ measurements.The littoral drift model developed at DHI and ISVA, see Deigaard et al. (1986b) has been extended to include the effects of the irregularity of the waves, of a coastal current and a wind acting on the surf zone. Further, a mathematical model to simulate the near-shore current pattern along a barred coast with rip channels has been developed. The influence on the littoral drift of the irregularity of waves, wind, coastal current, and rip channels is discussed. It is concluded that irregularity of waves and presence of rip channels must be considered while coastal current and wind action are of minor importance.At present, the Prodhoe Bay oil field in Alaska contributes a substantial amount of the domestic oil production of the United States. Oil is also expected to be present on the continental shelf of Alaska, and it is estimated that approximatedly 28 percent of the total U. S. reserve is located beneath the shallow ice covered seas of the Alaskan continental shelf. To expolre and to exploit these oil rich resources, engineers are confronted with hostile oceanographic conditions such as high tides, waves, strong currents and sea ice. The same area is also rich in fishery resources. Being one of the most productive fishing grounds in the nothern Pacific, the potential ecological impact due to an oil spill is of a major concern. This paper describes the methologies used for the development of a modeling system for the oil risk analysis. The system is designed with generality in mind so it can be used for other coastal areas. The development of three dimensional models used in the modeling system described here have been published in the earlier International Coastal Engineering Conferences (Liu and Leendertse, 1982, 1984, 1986) and a report published recently by RAND (Liu and Leendertse, 1987). In the oil-spill risk analysis, these three dimensional hydrodynamic models are coupled to a two-dimensional stochastic weather model and an oil weathering model.The two projects (LUBIATOWO 79 and LUBIATOWO 86) were aimed at study pore pressure behaviour in natural sand bed in the coastal zone of the Baltic sea under the action of storm waves. During both projects, the wave induced pore pressures at the various levels in the sea bed were measured. The collected data were used to verify the applicability of the various theoretical approaches. In the conclusion, the range of the application of the particular analytical method is given.The rapid recession of the shingle bank of Hurst Beach (up to 3.5m/yr) makes it an excellent natural laboratory for the study of the factors which influence the stability of shingle beaches. Studies have included: the significance of long period, high energy, swell waves the classification and quantification of overwash processes run-up and seepage characteristics the effect of settlement of the underlying strata and the implications for practices in shingle nourishment. The studies have revealed the distinctive character of shingle beaches as compared with the more fully researched sand beaches. More detailed research on shingle beaches is justified particularly in relation to (i) the run-up characteristics including its interaction with swash cusps and (ii) the influence of the subsidiary sand fraction on the beach characteristics.Environmental assessment, engineering studies and designs were completed for a new 26.5 m3/s seawater intake system in the Persian Gulf. The original intake facility consisted of a curved, 60m breakwater with one end attached to the shoreline, a settling basin immediately adjacent to the shoreline and dredged to a maximum depth of approximately 5m, and a pumphouse structure located on shore such that the seaward wall formed one side of the settling basin. The facility located on an island in the Gulf, which served multiple seawater uses, had experienced both structural and operational problems, the latter consisting principally of excessive ingestion of sediment and seaweed. These factors plus the requirement for additional demands for seawater beyond plant capacity caused the owner to initiate a study of alternative intake systems, produce a design for the most effective solution and construct the new intake system.A two-dimensional wave prediction model suitable for use on personal computers is described. The model requires the twodimensional time-dependent wind field as input. Output consists of wave height, wave period, and wave direction estimates at all grid points on a computational grid representing an enclosed or semi-closed basin. Model predictions compare favorably with observations from a wave research tower in Lake Erie. A formula is provided to estimate how long a model simulation would take on a personal computer given the surface area of the computational domain, the grid size, and the computer clock speed.Cullera Bay is a neritic ecosystem placed on the Spanish Mediterranean Littoral largely influenced by the Jucar River, that brings about lower salinities than surrounding waters, and broad variations of its values. An extensive research, with 9 samplings throughout the year, was carried out, measuring both physical and chemical parameters, and the planktonic communities. The trophic status of the ecosystem, the spatial and temporal variations of the nutrients and the planktonic communities were studied, evaluating the influence of the river loads and the littoral dynamics. Some essential basis to allow a suitable emplacement of waste waters disposals along the Valencian littoral are set up in order to minimize the gradual eutrophication of this coast.In the last two years a whole of studies was realized in order to determine precise solutions to the regeneration of Villajoyosas beach, in the Spanish mediterranean coast. Investigations were carried out to the surrounding coastal areas based in field investigations and laboratory analyses of the beaches materials.

Modelling of iceberg drift motions near a large offshore structure

Abstract The drift motions of icebergs driven by waves and currents toward a large offshore structure are examined. Results from a series of experiments with various iceberg sizes and environmental conditions are presented and compared with predictions of a corresponding numerical model. The influence of the structure on the flow field and on associated iceberg motions is shown to be significant for wave-driven drift motions when the iceberg diameter is less than approximately half the structure diameter. Agreement between the physical and numerical models is found to be reasonable, with the exception of certain cases where negative wave-drift forces act on icebergs in front of the structure.

The second approximation to mass transport in cnoidal waves

A second approximation is developed for the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport profiles through the boundary layer are obtained by considering terms of up to third order in the perturbation parameter. A comparison with results based on a first approximation indicates that the effect of the third-order terms is to predict a smaller mass-transport velocity and that this difference is generally significant, particularly for waves extending to the intermediate depth range. The predicted correction to the first approximation is qualitatively supported by experimental evidence.

Wave Diffraction Around Three-Dimensional Bodies in a Current

The effects of a collinear current on the diffraction of regular waves around three-dimensional surface-piercing bodies are examined. With the current speed assumed to be small, the boundary-value problem is separated into a steady current problem with a rigid wall condition applied at the still water level and a linear wave propagation problem in the resulting current field. The boundary conditions of the wave propagation problem are satisfied by a time-stepping procedure and the field solution is obtained by an integral equation method. Free surface profiles, runup, and wave forces are described for a vertical circular cylinder in combined waves and a current. The current is shown to affect significantly the steady drift force and runup predictions. Comparisons of the computed wave forces are made with a previous numerical solution involving a semi-immersed sphere in deep water, and indicate good agreement.