Short-crested Waves Research Articles

Hydrodynamic load modeling and analysis of a floating bridge in homogeneous wave conditions

The Norwegian Public Road Administration (NPRA) is currently developing the E39 ferry-free project, in which several floating bridges will be built across deep and wide fjords. In this study, we consider the floating bridge that was an early concept for crossing the Bjørnafjorden with a width of about 4600 m and with a depth of more than 500 m. The floating bridge concept is a complex end-anchored curve bridge, consisting of a cable-stayed high bridge part and a low bridge part supported by 19 pontoons. It has a number of eigen-modes, which can be excited by wave loads. Wave loads and their effects should thus be properly modeled and assessed. Therefore, the effect of hydrodynamic load modeling are investigated in homogeneous wave conditions, including varying water depth at the ends of the bridge, viscous drag force on pontoons, short-crestedness and second order wave loads. It is found that the varying water depth has negligible effect, while the other features are important to consider. Second order difference-frequency wave loads contribute significantly to sway motion, axial force and strong axis bending moments along the bridge. However, these effects can be reduced by viscous drag forces, which implies that an appropriate model of viscous drag force effect on the pontoons is important. short-crested waves greatly affect the heave motion and weak axis bending moment. All these considerations on hydrodynamic load modeling are further applied to analyze the wave load effect of a floating bridge in a fjord considering inhomogeneous waves [1].

Short-crested wave breaking

Peregrine (1998, 1999), in discussing the effect of local variations of wave energy dissipation as a generation mechanism for vorticity at the scale of individual waves, spurred a wave of study of vorticity dynamics and mixing processes in the wave-driven ocean. In deep water, the limited depth of penetration of breaking effects leads to the conceptual forcing of a smoke-ring resulting from the localized cross-section of impulsive forcing, as elaborated by Pizzo and Melville (2013). In shallow water, depth limitations favor the generation of a quasi-two-dimensional field of vertical vortex structures, with a resulting inverse cascade of energy to low wavenumbers and the evolution of flows such as transient rip currents (Johnson and Pattiaratchi, 2006). In this presentation, we consider vorticity-generating mechanisms ranging from the generation of patterns of vertical vorticity in 2D, depth-averaged flows, to a more detailed picture of the vorticity field evolving during a localized breaking event. Using an LES/VOF model (Derakhti and Kirby, 2014), we examine the evolution of coherent vortex structures whose initial scales are determined by the width of the breaking region, and are much larger than the locally-controlled reverse horseshoe structures seen in typical studies of along-crest uniform breaking. We study the persistence of three-dimensionality of these structures and their contribution to the development of depth-integrated vertical vorticity, but also point out the persistent presence of both components of horizontal vorticity as a result of the isolated breaking event.

SPH MODELING OF VORTICITY GENERATION BY SHORT-CRESTED WAVE BREAKING

This study investigates vorticity generation by short-crested wave breaking by using the mesh-free Smoothed Particle Hydrodynamics model, GPUSPH. The short-crested waves are created by generating intersecting wave trains in a numerical wave basin with a beach. The capability of GPUSPH to simulate short-crested waves is first validated by laboratory measurements. Then we examine short-crested wave breaking with two incident wave heights H = 0.2 m and 0.3 m. The larger incident wave breaks at the toe of the planar beach, while the smaller incident wave breaks above the planar beach. The breaking wave profile, current field, nearshore circulation pattern, and vertical vorticity field due to short-crested wave breaking are carefully compared between two incident waves.

Global motion and airgap computations for semi-submersible floating production unit in waves

We study the global hydrodynamic performance of a semi-submersible floating platform unit in order to optimize the hull form in the future. The hydrodynamic problem is solved by employing potential flow theory and Morison equation for modelling of the viscous effects. The added mass and damping coefficients, as well as the first-order motion responses, second-order mean drift forces, diffracted and radiated wave field, and airgap are computed to examine the hydrodynamic behavior of the floating production unit. The computational results show that the motion responses in short-crested waves are mostly smaller than those in long-crested waves. The maximum wave elevation occurs at WP45 in 45° wave heading in long-crested waves. In addition, the minimum airgap occurs at AG45 in 45° wave heading in linear waves, while the worst airgap point in nonlinear waves is AG0 in 0° wave heading.Extensive parametric studies have been performed to examine the dependence of the motion responses and the other key design criteria on the principal dimensions including hull draft, column width, column spacing, column corner radius, pontoon height, pontoon width, and the size of cakepiece. By comprehensive and systematic hydrodynamic computations and analyses, it is revealed that the combined vertical motion at the worst airgap location is almost in phase with the wave elevation in extreme wave condition with a peak wave period around 14–15s. Moreover, it is found that the most efficient way to reduce the motion is to increase the hull draft, though the airgap may also decrease. Besides, reducing the pontoon height can achieve better motion performance and larger airgap simultaneously. This paper aims to provide a benchmark for future studies on automatic hull form optimization.

Surface wave predictions in weakly nonlinear directional seas

We have employed laboratory and numerical experiments in order to investigate propagation of waves in both long and short-crested wave fields in deep water. For long-crested waves with steepness, ϵ=kcac=0.1 (a fairly extreme case), reliable prediction can be performed with the modified nonlinear Schrödinger equation up to about 40 characteristic wavelengths. For short-crested waves the accuracy of prediction is strongly reduced with increasing directional spread.

Prediction formula for the spectral wave period Tm-1,0 on mildly sloping shallow foreshores

During the last decades, the spectral wave period Tm-1,0 has become accepted as a characteristic wave period when describing the hydraulic attack on coastal structures, especially over shallow foreshores. In this study, we derive an empirical prediction formula for Tm-1,0 on shallow to extremely shallow foreshores with a mild slope. The formula was determined based on flume tests and numerical calculations, mainly for straight linear foreshore slopes. It is shown that the wave period increases drastically when the water depth decreases; up to eight times the offshore value. The bed slope angle influences the wave period slightly. For short-crested wave fields, the strong increase of Tm-1,0 starts closer to shore (at smaller water depths) than for long-crested wave fields.

Experimental Investigation of Hydrodynamic Coefficients for Short-Crested Waves

Objectives: To determine the hydrodynamic coefficients; drag (Cd) and inertia (Cm), for short-crested waves exerted on vertical cylinder. Methods/Statistical Analysis: An experimental study on hydrodynamic coefficients of the top-fitted vertical cylinder subjected to short-crested waves is presented. The model tests were carried out in the wave tank of Offshore Laboratory of University Technology PETRONAS, Malaysia. In this study, the model testwas conducted by using two sets of vertical cylinder with diameter, 16 mm and 48 mm, which were subjected to four series of short-crested waves based on four different locations in Malaysian offshore region.The wave forces acting on the cylinder were recorded by using wave force sensor. The post processing data was carried outby considering The Least Square Method. The results were compared with the existing recommended hydrodynamic coefficients in the PETRONAS Technical Standard (PTS). Findings: The hydrodynamic coefficients for short-crested wave of a vertical cylinderwere obtained. The results showed that the experimental hydrodynamic coefficient values are 30 % to 45 % lowerthan the recommended hydrodynamic coefficients adopted by PTS. Application/Improvements: The hydrodynamic coefficients values obtained from this experimental investigationhave ensured the possibility of designing an economical and optimum design of offshore platforms could be achieved.

Analysis of Lifting Operation of a Monopile Considering Vessel Shielding Effects in Short-crested Waves

Analysis of Lifting Operation of a Monopile Considering Vessel Shielding Effects in Short-crested Waves

Hydroelectromechanical modelling of a piezoelectric wave energy converter

We investigate the hydroelectromechanical-coupled dynamics of a piezoelectric wave energy converter. The converter is made of a flexible bimorph plate, clamped at its ends and forced to motion by incident ocean surface waves. The piezoceramic layers are connected in series and transform the elastic motion of the plate into useful electricity by means of the piezoelectric effect. By using a distributed-parameter analytical approach, we couple the linear piezoelectric constitutive equations for the plate with the potential-flow equations for the surface water waves. The resulting system of governing partial differential equations yields a new hydroelectromechanical dispersion relation, whose complex roots are determined with a numerical approach. The effect of the piezoelectric coupling in the hydroelastic domain generates a system of short- and long-crested weakly damped progressive waves travelling along the plate. We show that the short-crested flexural wave component gives a dominant contribution to the generated power. We determine the hydroelectromechanical resonant periods of the device, at which the power output is significant.

A consistent collinear triad approximation for operational wave models

In shallow water, the spectral evolution associated with energy transfers due to three-wave (or triad) interactions is important for the prediction of nearshore wave propagation and wave-driven dynamics. The numerical evaluation of these nonlinear interactions involves the evaluation of a weighted convolution integral in both frequency and directional space for each frequency-direction component in the wave field. For reasons of efficiency, operational wave models often rely on a so-called collinear approximation that assumes that energy is only exchanged between wave components travelling in the same direction (collinear propagation) to eliminate the directional convolution. In this work, we show that the collinear approximation as presently implemented in operational models is inconsistent. This causes energy transfers to become unbounded in the limit of unidirectional waves (narrow aperture), and results in the underestimation of energy transfers in short-crested wave conditions. We propose a modification to the collinear approximation to remove this inconsistency and to make it physically more realistic. Through comparison with laboratory observations and results from Monte Carlo simulations, we demonstrate that the proposed modified collinear model is consistent, remains bounded, smoothly converges to the unidirectional limit, and is numerically more robust. Our results show that the modifications proposed here result in a consistent collinear approximation, which remains bounded and can provide an efficient approximation to model nonlinear triad effects in operational wave models.

On the superharmonic instability of nonlinear three-dimensional interfacial waves of two infinite layers

Linear superharmonic stability analysis of nonlinear short-crested gravity interfacial waves between two semi-infinite fluids is numerically investigated. Like short-crested free surface waves, superharmonic instabilities correspond to the harmonic resonance phenomenon. The basic flow is calculated with a perturbation method and expansions are summed using Padé approximants. It is found that these instabilities develop near the poles due to harmonic resonance. The obtained results show that the instability of maximal growth rate develops for a density ratio μ=0.08 and occurs sporadically. In addition, for μ=0.34, the maximum growth rate is negligible and hence, for this value the short-crested interfacial waves are stable to superharmonic perturbations.

Stability of cube armoured roundheads exposed to long crested and short crested waves

The paper presents an update of the stability formulae by Maciñeira and Burcharth (2007) for cube armoured roundheads exposed to long- and short-crested waves. Reanalysis of former model test results and supplementary new model tests leads to a more precise set of formulae covering long-crested and short-crested waves. The formulae are valid for two layers of randomly placed cubes, ranges of head diameter, slope, cube mass density and wave steepness.

Development and application of a semi-analytical method with diagonal coefficient matrices for analysis of wave diffraction around vertical cylinders of arbitrary cross-sections

This paper proposes a semi-analytical method for modeling short-crested wave diffraction around a vertical cylinder of arbitrary cross-section, in an unbounded domain. In this method, only the boundaries of domain are discretized using special sub-parametric elements. The formulation of elements is constructed by employing higher-order Chebyshev mapping functions and special shape functions. The shape functions are introduced to satisfy Kronecker Delta property for the potential function and its derivative, corresponding to the governing Helmholtz equation of the problem. Furthermore, the first derivative of shape functions of any given control point are set to zero. By implementing weighted residual method and using Clenshaw–Curtis numerical integration, the coefficient matrices of equations system become diagonal, yielding a set of decoupled governing Bessel differential equations for the whole system. In other words, the governing equation for each degree of freedom (DOF) is independent of other DOFs of the domain. Accuracy and efficiency of present method are fully demonstrated through three short-crested wave diffraction problems which are successfully modeled using a few numbers of DOFs (or nodes), with excellent agreements between the results of the present method and those of other analytical/numerical solutions.

An alternative portable dynamic positioning system on a barge in short-crested waves using the fuzzy control

The paper described the nonlinear dynamic motion behavior of a barge equipped with the portable outboard Dynamic Positioning (DP) control system in short-crested waves. The DP system based on the fuzzy theory is applied to control the thrusters to optimally adjust the ship position and heading in waves. In addition to the short-crested waves, the current, wind and nonlinear drifting force are also included in the calculations. The time domain simulations for the six degrees of freedom motions of the barge with the DP system are solved by the 4th order Runge-Kutta method. The results show that the position and heading deviations are limited within acceptable ranges based on the present control method. When the dynamic positioning missions are needed, the technique of the alternative portable DP system developed here can serve as a practical tool to assist those ships without equipping with the DP facility.

Suspended sediments due to random waves including effects of second order wave asymmetry and boundary layer streaming

The paper provides a practical stochastic method by which the suspended sediment concentration due to long-crested (2D) and short-crested (3D) nonlinear random waves can be calculated. The approach is based on assuming the waves to be a stationary narrow-band random process, and by using the parameterized formulas valid for regular waves presented in Soulsby, R.L., 1997. Dynamics of Marine Sands. Thomas Telford, London. The Forristall, G.Z., 2000. Journal of Physical Oceanography. 30, 1931–1943. wave crest height distribution representing both 2D and 3D nonlinear random waves is also adopted. The model covers sediment suspension over rippled beds and for sheet flow. Comparisons are made with random wave data from Thorne, P.D., Williams, J.J., Davies, A.G., 2002. Journal of Geophysical Research. 107 (C8), 3178 for flow over rippled beds. An example for sheet flow using data typical to field conditions is also included to illustrate the approach.

Homotopy-based analytical approximation to nonlinear short-crested waves in a fluid of finite depth

A nonlinear short-crested wave system, consisting of two progressive waves propagating at an oblique angle to each other in a fluid of finite depth, is investigated by means of an analytical approach named the homotopy analysis method (HAM). Highly convergent series solutions are explicitly derived for the velocity potential and the surface wave elevation. We find that, at every value of water depth, there is little difference between the kinetic energy and the potential energy for nonlinear waves. The nonlinear short-crested waves with a larger angle of incidence always contain the more potential wave energy. With the aid of the HAM, we obtain the dispersion relation for nonlinear short-crested waves. Furthermore, it is shown that the wave elevation tends to be smoothened at the crest and be sharpened at the trough as the water depth increases, and the wave pressure crests and troughs become steeper with increasing incident wave steepness.

An Experimental Investigation of the Responses of Classic Spar Platform Subjected to Bi-directional Waves

The effect of the bi-directional short-crested waves on the dynamic motion responses of the moored classic spar is demonstrated from the results of the models test in this study. Practically in the design of offshore structures, long-crested or 2-dimensional wave properties that propagated to one direction are considered. Even though such long-crested wave is widely used for the design purposes, it is hardly determined in the real sea. The wind generated sea state in the real sea conditions are indeed well represented by the short-crested waves. Short-crested waves are defined as linear summation of long-crested wave series that propagated to different directions. Hence, the motions of the model were investigated experimentally by conducting the wave tank tests in the wave tank of Offshore Laboratory of Universiti Teknologi PETRONAS. Five groups of bi-directional wave series were defined and exerted on the classic spar model, which fabricated by using steel with scaling factor of 1:100. From the results measured, it was found that similar trends of the responses in term of Response Amplitude Operator (RAO) for surge, heave and pitch motions were obtained. Maximum responses of surge, heave and pitch were found due to wave crossing angle 90°, while minimum response was found due to wave crossing angle 135°, respectively. It could be concluded that the wave crossing angle 90° (BD3) gives the widest spreading for short crested waves, while the wave crossing angle 135° (BD4) gives the narrowest spreading for short crested waves.

On the existence of steady-state resonant waves in experiments

AbstractThis paper describes an experimental investigation of steady-state resonant waves. Several co-propagating short-crested wave trains are generated in a basin at the State Key Laboratory of Ocean Engineering (SKLOE) in Shanghai, and the wavefields are measured and analysed both along and normal to the direction of propagation. These steady-state resonant waves are first calculated theoretically under the exact resonance criterion with sufficiently high nonlinearity, and then are generated in the basin by means of the main wave components that contain at least 95 % of the wave energy. The steady-state wave spectra are quantitatively observed within the inherent system error of the basin and identified by means of a contrasting experiment. Both symmetrical and anti-symmetrical steady-state resonant waves are observed and the experimental and theoretical results show excellent agreement. These results offer the first experimental evidence of the existence of steady-state resonant waves with multiple solutions.

MODELLING OF WAVE ATTENUATION INDUCED BY MULTI-PURPOSE FLOATING STRUCTURES USED FOR POWER SUPPLY AND COASTAL PROTECTION

Experiments have been performed in the Shallow Water Wave Basin of DHI (Horsholm, Denmark) within the EU FP7 Hydralab Programme, on large farms of up to 25 heaving point absorber type Wave Energy Converters (WECs). For a range of geometric lay-out configurations and wave conditions (regular, polychromatic, long- and short-crested irregular waves), WEC response and modification of the wave field have been measured to provide data for the understanding of WEC farm interactions and for the evaluation of farm interaction numerical models. A first extensive wave farm database is established. The experimental arrangement and the obtained database are presented, as well as results for wave height attenuation downwave of the farms. For long-crested irregular waves, up to 18.1 % and 20.8 % reduction in significant wave height is observed downwave of the 5x5-WEC rectilinear and staggered farm, respectively. Wave height attenuation is expected to be larger, since in practical wave farm applications WECs will be controlled to extract a large amount of power from the waves, and therefore the array will cause larger wave height dissipation. These findings present the ability to combine the harvesting of energy from sea waves with coastal defence systems, resulting in cost reduction for both applications when WECs operate as multi-purpose devices.

Response of Saturated Porous Seabed under Combined Short-Crested Waves and Current Loading

ABSTRACT Wen, F.; Wang, J.H., and Zhou, X.L. 2016. Response of saturated porous seabed under combined short-crested waves and current loading. Ocean currents and waves generally coexist in a real ocean environment. However, most previous investigations have only considered wave loading or have been limited to two-dimensional cases. In this study, first we derive interaction of short-crested waves and uniform currents. Then, based on Biot's consolidation (i.e. quasi-static) theory, we establish a numerical model integrating a three-dimensional model of the seabed with combined short-crested waves and current loading. Applying the proposed numerical model, we examine the influence of current on seabed response. Numerical results reveal that current has a significant effect on seabed response. For example, a following current (current in the x direction, U1 > 0) will increase pore pressure, while an opposing current (current in the x direction, U1 < 0) will decrease pore pressure. The maximum relative differ...