Characteristics of abnormal waves in North Sea storm sea states

A data set of storm wave records from the North Sea is analysed. Using current definitions of abnormal waves, eight of the largest wind waves are defined as abnormal waves. Twenty-four of the largest waves in time series, with a height larger than 10 m and with big vertical asymmetry are chosen for further analysis. Their individual characteristics are investigated and related to the global sea state characteristics. A comparison between measured data, second-order theory predictions and offshore basin data is made. The results for the chosen waves do not coincide with predictions of second-order theory. Considering that wind wave is second- and third-order non-linear, a new relationship between skewness and kurtosis is proposed for the sea states in which extremely asymmetric large waves have occurred. Another relationship between kurtosis and abnormality index of maximum waves is proposed too.     

Estimation of the bispectra and phase distribution of storm sea states with 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.].     

Loads on a 3D body due to second-order waves and a current

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.     

Second-order wavemaker theory for multidirectional waves

The present paper develops the complete second-order wavemaker theory for the generation of multidirectional waves in a semi-infinite basin. The theory includes superharmonics and subharmonics and is valid for a rotational as well as a translatory serpent-type wave-board motion. The primary goal is to obtain the second-order motion of the wave paddles required to get a prescribed multidirectional irregular wave field correct to second order, i.e. to suppress spurious free-wave generation. The wavemaker theory is a 3D extension of the full second-order wavemaker theory for wave flumes by Schäffer (1996).     

On the growth of ocean waves

The availability of 10 h of continuous, uninterrupted field measurements of wind waves recorded in the western Pacific and containing a complete wave growth episode, has provided a distinct opportunity for us to make a novel, unprecedented examination of detailed wave growth processes. We found that the significance of the size of data used in the measurement, which can only be addressed with continuous and uninterrupted measurements, reflected the ineptness of the conventional approach toward further detailed understanding of realistic wave growth processes, as the conventional 20 min data size essentially stamped out any dynamics with time scale below 20 min. While our conventional understanding and modeling were generally operative and useful, they left no real vestige on time localized mechanisms such as wave grouping or wave breaking processes all with time scales much less than 20 min.     

Water levels in a dual-basin harbour in response to infragravity and edge waves

Seiche modes in a compound harbour (an “Outer Harbour” connected both to the sea and to an “Inner Harbour”) were studied using water level data and a numerical model. A variety of harbour oscillations are present, with periods up to 67 min. Periods longer than 25 min exceed resonant modes of the harbour. This paper addresses the characteristics and causes of the open-basin modes. The dual harbour open-basin mode is modified by constriction at the connection between harbours, by partial reflection at the antinode, and by the geometry of the entrance. The single-harbour open-basin mode excites the dual harbour closed-basin mode, which has nearly the same period. This forcing moves the closed-basin antinode and slightly changes the modal period, but the coupling permits the amplitude to increase through the closed-basin resonance. The water level response to wind stress is weak, but significant residual currents can occur, which take the form of clockwise gyres in each basin. Energetic peaks in the water level spectrum at 26, 35, and 67 min are shown to correspond to possible edge waves on the local shelf. The work has practical implications to port design, e.g. towards minimisation of ship ranging while at anchor.     

On generation source sites of internal waves in the Luzon Strait

This effort aims to determine the generation source sites in the Luzon Strait for energetic, long-crest, transbasin internal waves （IW） observed in the northern South China Sea （NSCS）. The roles of islands distributed on eastern side of the strait, Kuroshio, submarine ridges, shoaling thennocline, and strait configuration played in the IW generation are examined using the cruise data analysis, satellite data interpretation, and dynamical analysis. The islands and channels on eastern side of the strait are excluded from a list of possible IW source sites owing to their unmatched horizontal dimensions to the scale of IW crest line length, and the relative low Reynolds number. The Kuroshio has a potential to be a radiator for the long-crest IW disturbances, meanwhile, the Kurosbio west （east） wing absorbs the eastward （westward） propagating IW disturbance. Namely, the Kuroshio blockades the outside west-east propagating IW disturbances. The 3-D configuration of the Luzon Strait is characterized by a sudden, more than one order widening of the cross-section areas at the outlets on both sides, providing a favorable condition for IW type initial disturbance formation. In the Luzon Strait, the thermocline is featured by a westward shoaling all the year around, providing the dynamical conditions for the amplitude growth （declination） to the westward （eastward） propagating IW type disturbance. Thus, the west slope of western submarine ridge at the western outlet of the Luzon Strait is a high possibility source sites for energetic, long-crest, transbasin IWs in the NSCS. The interpretation results of satellite SAR images during a 13 a period from 1995 to 2007 provide the convincing evidence for the conclusions.     

Michell and Hogner models of far-field ship waves

The far-field waves, and the related far-field wave drag, predicted by the Michell or Hogner theories are considered. These two classical theories are found to predict nearly identical transverse waves for all practical cases. However, the Michell and Hogner models predict divergent waves—dominant at high Froude numbers—that can differ significantly. Differences between the far-field waves predicted by the Michell and Hogner models are much smaller for catamarans, for which lateral interferences between the twin hulls overwhelm lateral interferences between the port and starboard sides of the hulls, than for monohull ships. Moreover, differences between the divergent waves predicted by the Michell and Hogner theories are larger for higher Froude numbers, bigger beam/length ratios, smaller draft/length ratios, or larger separation distances between the twin hulls of a catamaran.     

Run-up on a body in waves and current. Fully nonlinear and finite-order calculations

Run-up on a large fixed body in waves and current have been calculated using both a fully nonlinear time-domain boundary element model and a finite-order time-domain boundary element model, the latter being correct to second order in the wave steepness and to first-order in the current strength. The results from the two models agree well in the low Froude number and low wave steepness regime. This serves as a cross-validation of the two boundary element models. Furthermore, the two sets of data provide an excellent method for examining the domain of validity for the second-order method. Such limits are, for the case studied, given in terms of maximum Froude number and maximum wave steepness.     

Idealised flow models to predict alluvial sandstone body distribution in the Middle Jurassic Yorkshire Basin

Prediction of the subsurface position of alluvial channel sandstones is of great importance in the search for potential hydrocarbon reservoirs. For maximum production at minimum expense, wells need to be sited where there is abundant sandstone and, for enhanced oil recovery, detailed knowledge of sandstone-body geometry and connectivity is desirable. Attempts to predict the position of sandstone-bodies in the subsurface have included theoretical computer simulation and detailed empirical modelling of alluvial architecture (three-dimensional rock type distributions). Up to now, no reliable predictive method has been developed and any improvement is of significance.The method presented here combines the theoretical approach to tectonic control of alluvial architecture with the available geological data to predict subsurface concentrations and orientations of alluvial sandstone bodies.     

Internal solitary waves shoaling onto a shelf: Comparisons of weakly-nonlinear and fully nonlinear models for hyperbolic-tangent stratifications

In this study the evolution of internal solitary waves shoaling onto a shelf is considered. The results of high resolution two-dimensional numerical simulations of the incompressible Euler equations are compared with the predictions of several weakly-nonlinear shoaling models of the Korteweg–de Vries family including the Gardner equation and the cubic regularized long wave (or Benjamin–Bona–Mahoney) equation. Wave models in both physical x–t space and in s–x space are considered where s is a commonly used characteristic time variable. The effects of rotation, background currents and damping are ignored. The Boussinesq and rigid lid approximations are also used. The shoaling internal solitary waves generally fission into several waves. Reflected waves are negligible in the cases considered here. Several hyperbolic tangent stratifications are considered with and without a critical point. Among the equations in x–t space the cubic regularized long wave equation gives the best predictions. The Gardner equation in s–x space gives the best predictions of the shape of the leading waves on the shelf, but for many stratifications it predicts a propagation speed that is too large.     

On the tuning of a wave-energy driven oscillating-water-column seawater pump to polychromatic waves

Performance of wave-energy devices of the oscillating water column (OWC) type is greatly enhanced when a resonant condition with the forcing waves is maintained. The natural frequency of such systems can in general be tuned to resonate with a given wave forcing frequency. In this paper we address the tuning of an OWC sea-water pump to polychromatic waves. We report results of wave tank experiments, which were conducted with a scale model of the pump. Also, a numerical solution for the pump equations, which were proven in previous work to successfully describe its behavior when driven by monochromatic waves, is tested with various polychromatic wave spectra. Results of the numerical model forced by the wave trains measured in the wave tank experiments are used to develop a tuning criterion for the sea-water pump.     

On the structure and propagation of internal solitary waves generated at the Mascarene Plateau in the Indian Ocean

Analysis of a comprehensive dataset of Synthetic Aperture Radar (SAR) images acquired over the sea area around the Mascarene Plateau in the western Indian Ocean reveals, for the first time, the full two-dimensional spatial structure of internal solitary waves in this region of the ocean. The satellite SAR images show that powerful internal waves radiate both to the west and east from a central sill near 12.5°S, 61°E between the Saya de Malha and Nazareth Banks. To first order, the waves appear in tidally generated packets on both sides of the sill, and those on the western side have crest lengths in excess of 350 km, amongst the longest yet recorded anywhere in the world's oceans. The propagation characteristics of these internal waves are well described by first mode linear waves interacting with background shear taken from the westward-flowing South Equatorial Current (SEC), a large part of which flows through the sill in question. Analysis of the timings and locations of the packets indicates that both the westward- and eastward-traveling waves are generated from the western side of the sill at the predicted time of maximum tidal flow to the west. The linear generation mechanism is therefore proposed as the splitting of a large lee wave that forms on the western side of the sill, in a similar manner to that already identified for the shelf break generation of internal waves in the northern Bay of Biscay. While lee waves should form on either side of the sill in an oscillatory tidal flow, that on the western side would be expected to be much larger than that on the eastern side because of a superposition of the tidal flow and the steady westward flow of SEC. The existence of a large lee wave at the right time in the tidal cycle is then finally confirmed by direct observations. Our study also confirms the existence of second mode internal waves that form on the western side of the sill and travel across the sill towards the east.     

An explicit approximation to the wavelength of nonlinear waves

An explicit and concise approximation to the wavelength in which the effect of nonlinearity is involved and presented in terms of wave height, wave period, water depth and gravitational acceleration. The present approximation is in a rational form of which Fenton and Mckee's (1990, Coastal Engng 14, 499–513) approximation is reserved in the numerator and the wave steepness is involved in the denominator. The rational form of this approximation can be converted to an alternative form of a power-series polynomial which indicates that the wavelength increases with wave height and decreases with water depth. If the determined coefficients in the present approximation are fixed, the approximating formula can provide a good agreement with the wavelengths numerically obtained by Rienecker and Fenton's (1981, J. Fluid Mech. 104, 119–137) Fourier series method, but has large deviations when waves of small amplitude are in deep water or all waves are in shallow water. The present approximation with variable coefficients can provide excellent predictions of the wavelengths for both long and short waves even, for high waves.     

Intercomparison of wave-driven current models

Seven numerical models which simulate waves and currents in the surf-zone are tested for the case of a reduced-scale detached breakwater subjected to the action of regular waves with normal incidence. The computed wave heights, water levels and velocities are compared with measurements collected in an experimental wave basin. The wave height decay in the surf-zone is predicted reasonably well. Set-up and currents appear to be less well predicted. This intercomparison exercise shows that radiation stresses are systematically overestimated by formulations used in the models, mean bottom shear stresses are not always co-linear with the mean bottom velocity vector in shallow water, and turbulence modelling in the surf-zone requires a sophisticated     

Approximation to the hydrodynamics of floating pontoons under oblique waves

The hydrodynamic properties of long rigid floating pontoon interacting with linear oblique waves in water of finite arbitrary depth are examined theoretically. The flow is idealized as linearized, velocity potentials are expressed in the form of eigen-function expansions with unknown coefficients. The fluid domain is split into three regions, region (1) wave-ward of the structure, region (2) in the lee of the structure, and region (3) beneath the structure. The different hydrodynamic quantities of interest such as the exciting forces, added mass and damping coefficients, reflection and transmission coefficients were studied for an applicable range of wave/structure parameters. Assuming rigid body motions, dynamic responses of the moored structure is approximately calculated through three equations of motion. Floating pontoons proved to be a convenient alternative for protection from waves in shallow water. The present method of solution was found to be computationally efficient, and results are comparable to those obtained through other techniques.     

稳恒水波的Fourier近似解研究

A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton＇s iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that （1） the set-up and the set-down are both non-monotonic quantities with the wave steepness, and （2） the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.     

New modified gradient models for MPS method applied to free-surface flow simulations

In this paper, two modified pressure gradient models based on Taylor series expansion are proposed to enhance the higher order source term MPS (MPS-HS) method. The modified models consist of gradient correction matrices applied to the existing (base) pressure gradient models. To validate the modified pressure gradient models first hydrostatic pressure test is simulated and compared to both the base and modified MPS methods. Using the modified models are shown to reduce unphysical pressure oscillations observed in the base models. Second, an evolution of an elliptical drop in a 2D flow field is examined and shown to verify the models. Third, the proposed models illustrated appropriate stability and consistency properties against analytical solutions when an altered gravitational acceleration was superimposed to the hydrostatic pressure test. In addition, an improved performance is observed when Higher order Laplacian (HL) and Error-Compensating Source (ECS) of the Poisson Pressure Equation (PPE) schemes are coupled with the modified pressure gradient models compared to coupling them with the base gradient models. Finally, the modified MPS methods enhanced performances are validated in a free-surface flow simulation for a dam break problem with impact pressure, and a violent sloshing flow in a rectangular tank when compared to the base MPS methods against an existing experimental data.     

Seabed shear stresses under irregular waves plus current from Monte Carlo simulations of parameterized models

Shear stresses on a rough seabed under irregular waves plus current are calculated. Parameterized models valid for regular waves plus current have been used in Monte Carlo simulations, assuming the wave amplitudes to be Rayleigh-distributed. Numerical estimates of the probability distribution functions are presented. For waves only, the shear stress maxima follow a Weibull distribution, while for waves plus current, both the maximum and time-averaged shear stresses are well represented by a three-parameter Weibull distribution. The behaviour of the maximum shear stresses under a wide range of wave-current conditions has been investigated, and it appears that under certain conditions, the current has a significant influence on the maximum shear stresses. Results of comparison between predictions and measurements of the maximum bottom shear stresses from laboratory and field experiments are presented.