Ocean Engineering

This paper considers acoustic plane wave scattering from a rough seabed on a transition sediment layer overlying an elastic sea basement. The transition sediment layer is assumed to be fluid-like, with density and sound speed distributions behaving as generalized-exponential and inverse-square functions, respectively. This specific class of density and sound speed profiles deserves special attentions not only because it is geologically realistic, but also renders analytical solutions to the Helmholtz equation, making it particularly useful in the study of ocean and seabed acoustics. Based upon a boundary perturbation approach, the computational algorithm for the spatial spectrum in terms of the power spectral density of the scattered field has been developed and implemented. The results have shown that, while the coherent field mainly depends upon the gross structure of the seabed roughness, e.g., RMS roughness, the scattered field is significantly affected by the details of the roughness distributions specialized by the roughness power spectrum and the spatial correlation length of the rough surface. The dependence of the power spectral density of the scattered field on the various types of sediment stratifications, including the constant and the k²-linear sound speed distributions, is also included in the analysis.

This paper presents soft computing approach for estimation of missing wave heights at a particular location on a real-time basis using wave heights at other locations. Six such buoy networks are developed in Eastern Gulf of Mexico using soft computing techniques of Artificial Neural Networks (ANN) and Genetic Programming (GP). Wave heights at five stations are used to estimate wave height at the sixth station. Though ANN is now an established tool in time series analysis, use of GP in the field of time series forecasting/analysis particularly in the area of Ocean Engineering is relatively new and needs to be explored further. Both ANN and GP approach perform well in terms of accuracy of estimation as evident from values of various statistical parameters employed. The GP models work better in case of extreme events. Results of both approaches are also compared with the performance of large-scale continuous wave modeling/forecasting system WAVEWATCH III. The models are also applied on real time basis for 3 months in the year 2007. A software is developed using evolved GP codes (C++) as back end with Visual Basic as the Front End tool for real-time application of wave estimation model.

The interaction between current and flexural gravity waves generated due to a floating elastic plate is analyzed in two dimensions under the assumptions of linearized theory. For plane flexural gravity waves, explicit expressions for the water particle dynamics and trajectory are derived. The effect of current on the wavelength, phase velocity and group velocity of the flexural gravity waves is analyzed. Variations in wavelength and wave height due to the changes in current speed and direction are analyzed. Effects of structural rigidity and water depth on wavelength are discussed in brief. Simple numerical computations are performed and presented graphically to explain most of the theoretical findings in a lucid manner.

A 1:50 scale physical model was constructed for the 17th Street Canal region, New Orleans, on the southern coast of Lake Pontchartrain, as part of the Interagency Performance Evaluation Task Force (IPET) study of Hurricane Katrina. The purpose of the 1350 m2 physical model that represented about 3.4 km2 of the local area was to aid in defining wave and water velocity conditions in the 17th Street Canal during the time period leading up to the breaching of the floodwall within the Canal. In the immediate period following this disaster, there were many hypothesis of failure put forth in the media. Some of these hypothesis indicated wave action may have been the underlying cause of the failure of the 17th Street Canal floodwall. Some performed numerical work with inappropriate boundary conditions, which indicated strong wave-generated currents may have caused erosion along the floodwalls. This physical model study indicated a number of wave-attenuating processes occurring as waves approached the location of the breach. Wave height reduction resulted due to: (1) refraction of wave energy over the shallower submerged land areas surrounding the harbor away from the canal; (2) reflection of energy off vertical walls in the region between the entrance to the canal near the Coast Guard Harbor and the bridge; and (3) interaction of the wave with the Hammond Highway bridge, including reflection and transmission loss. Wave heights near the lakeside of the bridge were 0.3–0.9 m in height, reduced from 1.8 to 2.7 m wave heights in the open lake. Waves on the south side of the bridge, near the breach, were further reduced to heights below 0.3 m. These results supported the conclusion that waves were not a significant factor for the 17th Street Canal floodwall failure. Other IPET investigations determined floodwall failure was of a geotechnical nature due to the high surge water level. The physical model also provided calibration information for numerical wave models. The effects of debris on flow and waves after the breach was formed were also investigated.

This paper describes a new numerical algorithm for solving 2.5D hydrodynamic theory, which is based on the high-speed slender body assumptions where the free-surface condition is 3D but the control equation and body surface condition are 2D. This numerical algorithm is accomplished using boundary integral equations formed in the inner fluid field domain and outer fluid field domain and matched on a fixed control surface. Theoretically predicted vertical hydrodynamic coefficients by this method is verified by the theoretical results computed by 2.5D theory based on time domain boundary integral equations. This paper also shows that the matched boundary integral equations can be used to calculate the hydrodynamic characteristics of high-speed displacement vessels with a large flare.

A review is made of linear slender-body methods for predicting the squat of a ship in shallow open water, dredged channels or canals. The results are summarized into a general formula based on Fourier transforms, and the method is extended to cater to stepped canals. An approximate solution for canals of arbitrary cross-section is proposed.

Research was conducted to study the hydrodynamic efficiency of a foil with aft-swept wing tips. A potential flow based time domain panel method was formulated to predict the performance of a lunate and rectangular foil in large amplitude, unsteady motion. Skin drag was approximated and boundary layer growth and separation were also estimated. Hydrodynamic efficiency was evaluated in terms of propulsive efficiency and thrust coefficient of the foil. Results are presented for a lunate shaped planform and for a rectangular foil. Predictions show that the lunate shaped planform has a substantially higher propulsive efficiency (13% higher) than the rectangular foil under heavy load conditions when the feathering parameter is zero, throughout a range of reduced frequencies (0.2 to 1.8). Under a medium load condition, however, the rectangular foil gave a higher propulsive efficiency at reduced frequencies less than 0.5 and the same efficiency value at a reduced frequency of 1.8. For a practical range of reduced frequencies between 0.5 and 1.0, the lunate tail gave higher propulsive efficiency. The lunate planform gave a lower thrust coefficient at a heavy load and higher thrust at a medium load condition than the rectangular planform for all reduced frequencies.

Nonlinear interactions between large waves and freely floating bodies are investigated by a 2D fully nonlinear numerical wave tank (NWT). The fully nonlinear 2D NWT is developed based on the potential theory, MEL/material-node time-marching approach, and boundary element method (BEM). A robust and stable 4th-order Runge–Kutta fully updated time-integration scheme is used with regriding (every time step) and smoothing (every five steps). A special φn-η type numerical beach on the free surface is developed to minimize wave reflection from end-wall and wave maker. The acceleration-potential formulation and direct mode-decomposition method are used for calculating the time derivative of velocity potential. The indirect mode-decomposition method is also independently developed for cross-checking. The present fully nonlinear simulations for a 2D freely floating barge are compared with the corresponding linear results, Nojiri and Murayama’s (Trans. West-Jpn. Soc. Nav. Archit. 51 (1975)) experimental results, and Tanizawa and Minami’s (Abstract for the 6th Symposium on Nonlinear and Free-surface Flow, 1998) fully nonlinear simulation results. It is shown that the fully nonlinear results converge to the corresponding linear results as incident wave heights decrease. A noticeable discrepancy between linear and fully nonlinear simulations is observed near the resonance area, where the second and third harmonic sway forces are even bigger than the first harmonic component causing highly nonlinear features in sway time series. The surprisingly large second harmonic heave forces in short waves are also successfully reproduced. The fully updated time-marching scheme is found to be much more robust than the frozen-coefficient method in fully nonlinear simulations with floating bodies. To compare the role of free-surface and body-surface nonlinearities, the body-nonlinear-only case with linearized free-surface condition was separately developed and simulated.

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.

A finite differences (FD) solution method is proposed for the numerical treatment of the dynamic equilibrium problem of 2D catenary risers. The method is based on the so-called Box approximation, which in the scope of the present contribution is applied to the complete nonlinear model as well as to the reduced linearized formulation. The application of the Box method transforms the original governing systems into convenient sets of algebraic equations, which in turn are solved efficiently by the relaxation method. Extensive numerical calculations are presented that describe the dynamic behaviour of the structure and evaluate the amplification in loading due to the dynamic components. The effect of the geometric nonlinearities is assessed through comparative calculations that concern both mathematical formulations examined in the present, i.e. the complete nonlinear, and the reduced linearized model. Special attention is paid to the heave excitations as they amplify significantly the magnitudes of the loading components.

In addition to reducing the incoming wave energy, submerged breakwaters also cause a setup of the sea level in the protected area, which is relevant to the whole shadow zone circulation, including alongshore currents and seaward flows through the gaps. This study examines such a leading hydraulic parameter under the simplified hypothesis of 2D motion and presents a prediction model that has been validated by a wide ensemble of experimental data. Starting from an approach originally proposed by Dalrymple and Dean [(1971). Piling-up behind low and submerged permeable breakwaters. Discussion note on Diskin et al. (1970). Journal of Waterways and Harbors Division WW2, 423–427], the model splits the rise of the mean water level into two contributions: one is due to the momentum flux release forced by wave breaking on the structure, and the other is associated with the mass transport process. For the first time, the case of random wave trains has been explicitly considered.

Non-linear loads on a fixed body due to waves and a current are investigated. Potential theory is used to describe the flow, and a three-dimensional (3D) boundary element method (BEM), combined with a time-stepping procedure, is used to solve the problem. The exact free-surface boundary conditions are expanded about the still-water level by Taylor series so that the solution is evaluated on a time-invariant geometry. A formulation correct to second order in the wave steepness and to first order in the current speed is used. Numerical results are obtained for the first-order and the second-order oscillatory forces and for the second-order mean force on a fixed vertical circular cylinder in waves and a current. The second-order oscillatory forces on the body in waves and current are new results, while the remaining force components are verified by comparison with established numerical and analytical models. It is shown that the current can have a significant influence on the forces, and especially on the amplitude of the second-order oscillatory component.

Interactions between water waves and non-wall-sided cylinders are analyzed based on velocity potential theory with fully nonlinear boundary conditions on the free surface and the body surface. The finite element method (FEM) is adopted together with a 3D mesh generated through an extension of a 2D Delaunay grid on a horizontal plane along the depth. The linear matrix equation for the velocity potential is constructed by imposing the governing equation and boundary conditions through the Galerkin method and is solved through an iterative method. By imposing the gradient of the potential equal to the velocity, the Galerkin method is used again to obtain the velocity field in the fluid domain. Simulations are made for bottom mounted and truncated cylinders with flare in a numerical tank. Periodic waves and wave groups are generated by a piston type wave maker mounted on one end of the tank. Results are obtained for forces, wave profiles and wave runups. Further simulations are made for a cylinder with flare subjected to forced motion in otherwise still open water. Results are provided for surge and heave motion in different amplitudes, and for a body moving in a circular path in the horizontal plane. Comparisons are made in several cases with the results obtained from the second order solution in the time domain.

A three-dimensional (3D) numerical model of fixed Oscillating Water Column system (OWC) is presented and validated. The steady-state potential flow boundary value problem due to regular wave interaction with the OWC is solved by a first order mixed distribution panel method. Ocean response predictions are derived using a deterministic statistical model based on a spectral analysis method. The model validation focusses on diffraction predictions and involves convergence tests and numerical comparisons with independent potential flow computations. Predictions of both regular and irregular wave responses are also compared against experimental results. Sample results including the yearly-averaged power conversion efficiency are presented in the final section to illustrate the method’s suitability to a 3D hydrodynamic design optimisation.

In this paper, a novel high order panel method based on doublet distribution and Gaussian quadrature was adopted to deal with the potential flow problem. In the geometry representation we employed both the exact surface and NURBS surface form to construct the surface panel. These data were calculated directly from the mathematical shape definition. Furthermore, no fixed order of doublet density distribution was assumed on each panel. Not only the number of panels could be chosen, but also the Gaussian order of each panel. The numerical results for sphere, ellipsoid and Wigley hull demonstrated here indicated that the present method was adapted to the potential flow problem. Moreover, the NURBS surface geometry representation was capable of further potential flow optimal calculation.

A new three-dimensional, non-hydrostatic free surface flow model is presented. For simulating water wave motions over uneven bottoms, the model employs an explicit project method on a Cartesian the staggered gird system to solve the complete three-dimensional Navier–Stokes equations. A bi-conjugated gradient method with a pre-conditioning procedure is used to solve the resulting matrix system. The model is capable of resolving non-hydrostatic pressure by incorporating the integral method of the top-layer pressure treatment, and predicting wave propagation and interaction over irregular bottom by including a partial bottom-cell treatment. Four examples of surface wave propagation are used to demonstrate the capability of the model. Using a small of vertical layers (e.g. 2–3 layers), it is shown that the model could effectively and accurately resolve wave shoaling, non-linearity, dispersion, fission, refraction, and diffraction phenomena.

The oscillating flow around an infinite array of circular cylinders at low Keulegan-Carpenter numbers and Reynolds numbers is investigated numerically using a 3D mathematical model. Three different regimes of the Tatsuno and Bearman (1990) map are investigated; the first one is a 2D symmetric regime, whereas the second and the third are asymmetric and 3D. In each regime, the gap between two neighboring cylinders has been varied in a very wide range, from the case of practically isolated cylinder to the case of very strong interference.As regards the isolated cylinder, the mean value of the inertia coefficient is much more affected by the 3D effects than that of the drag coefficient. Conversely, the variation along the axial direction of the sectional drag coefficient is much stronger than that found for the sectional inertia coefficient.In all cases investigated, the reduction of the gap between cylinders has two main effects: first, it causes the reduction of the Morison coefficients; second, in the 3D regimes, the gap enhances 3D motion in the range of moderate values due to the interaction between vortex structures released by two neighboring cylinders, whereas a further reduction of the gap in the range of small values tends to reduce the three-dimensionality of flow field up to a complete suppression occurring for very small values of the gap.Finally, we propose a very simple parameterization that gives the Morison coefficients as a function of the gap once the values for the case of isolated cylinder are known.

This work provides a general hydrodynamic circulation model that can be used to understand density driven flows, which may arise in the case of suspension of fine-grained materials. The research is expected to provide a better understanding of the characteristics of spatial and temporal variability of current, which is associated with the period of ebb and flood tidal cycles.The model development includes extending the existing three-dimensional (3D) ADCIRC model with (1) baroclinic forcing term and (2) transport module of suspended and soluble materials. The transport module covers the erosion, material suspension and deposition processes for cohesive type sediment. In the case of an idealized tidal inlet in stratified water, the inclusion of baroclinic term can demonstrate the prevailing longshore sediment transport. It is shown that the model has application to the transport of the cohesive sediments from the mouth of the Mississippi River along the north shore of the Gulf of Mexico towards and along the Texas coast.

The submerged 3D turbulent jet flow behavior around a pile on a rigid bed and on a scoured bed was studied experimentally and numerically. ADV was used to obtain the jet velocity distributions and Realizable k–ε turbulence model was used for the prediction of flow field around a pile. The jet flow area was three-dimensional and thus numerical model was a three-dimensional model. The numerical results were used to predict the velocity close to the pile and bed shear stress on the bed. In general, the results indicated that the flow field was also in agreement with the findings of previous experiments in literature and the related principles in the subject area. The experimental results demonstrated that Acoustic Doppler Velocimeter (ADV) measurements were almost identical with the Realizable k–ε turbulence model results for turbulence intensity I=10%.

The purpose of the present paper is to develop a potential-based panel method for determining the steady potential flow about three-dimensional hydrofoil under free surface. The method uses constant-strength doublets and source density distribution over the foil body surface and thereby Dirichlet-type boundary condition is used instead of Neumann-type condition. On the undisturbed free surface source density is used to meet the free surface condition that is linearised in terms of double-body model approach and is discretised by a one-side, upstream, four-point finite difference operator. After solving the doublets on the foil and sources on the free surface, the numerical results of pressure, lift and resistance coefficients and also wave profiles can then be calculated for different Froude number and depth of submergence to demonstrate the influence of free surface and aspect ratio effects on performance of the hydrofoil.

Time-domain computations of 3D ship motions with forward speed are presented in this paper. The method of computation is based upon transient Green function. Both linear and nonlinear (large-amplitude) computations are performed where the included nonlinearities are those arising from the incident wave, but the diffraction and radiation forces are otherwise retained as linear. The incident wave can be described by any explicit nonlinear model. Computations over a variety of wave and speed parameters establish the robustness of the algorithm, which include high speed and following waves. Comparison of linear and nonlinear computations show that nonlinearities have a considerable influence on the results, particularly in predicting the instantaneous location of the hull in relation to the wave, which is crucial in determining forefoot emergence and deck wetness.

During laboratory tests designed to measure the torque required to actuate the emergency forebody release device of the research submersible Alvin, the coefficient of static friction was determined for the contacting metals, Monel K-500 and phosphor bronze A. Three conditions were investigated: surfaces clean and dry, surfaces immersed in seawater, and surfaces greased. Coefficient values fell in the range 0.12–0.24.

The paper is intended to extend the investigations about the nature of abnormal waves that have been reported in the work of Guedes Soares et al. (Characteristics of abnormal waves in North Sea states. Applied Ocean Research 25, [337–344]). The same dataset gathered at the oil platform North Alwyn in the North Sea during the November storm in 1997 is used along with the time series from the Draupner platform, in which an abnormal wave occurred. The data are reanalyzed from the viewpoint of the applicability of second-order models to fit large waves. The observed results confirm that the second-order approximation is not adequate to describe highly asymmetric and abnormal waves.

This work deals with the estimation of the bispectrum of wind waves during severe storms containing abnormal or freak waves. It presents the basic definitions of higher-order spectra and of the bispectra in particular and further suggests how to interpret some of the results to identify non-linearity in the wave time series. Different estimation methods are used and compared so as to identify the differences in the estimated bispectra that results from the estimation procedure and the ones that result from the physics of the sea states. It is found that as a result of the second-order self-coupling the phase distribution of the wind wave during the severe storms differs from the uniform one and is well approximated by the distribution proposed by Tayfun and Lo [1989. Envelope, phase and narrow-band models of sea waves. Journal of Waterway Port Coast and Ocean Engineering 115(5), 594–613.].

Regular waves were applied in a laboratory flume to investigate the evolutions of the velocity fields near above a fine sandy bed (d50=0.073 mm) during fluidized responses. Measurements of 2D velocity components and suspended sediment concentration (SSC) at 1 cm above the bed in addition to water surface displacements and sub-soil pore pressures were carried out with an acoustic Doppler velocimeter and an optical probe. The results have shown similar three typical soil responses including one unfluidized and two fluidized responses to previous report in other fine-grained soil beds. In the post- and pre-fluidized stages of a resonantly fluidized response, amplitudes of horizontal velocity component can be decreased by a maxima value of 50% while vertical components can be amplified up to 5 times larger. The developments of near-bed velocity field become less significant in consecutive non-resonantly fluidized responses. Particularly, the evolutions of the velocity field are closely dependent on the deepening of fluidized surface soil layers df and the characteristics of soil fluidization responses. The amplified vertical velocity components are clearly contradictory to the dissipated overloading waves near above a fluidized bed but are critical to much drastic sediment suspensions by interactions between overloading waves and fluidized bed soils.