The elemination of re-reflected waves by a porous medium of finite thickness

The elimination of re-reflected waves in a wave channel by installing a porous medium in front of the wavemaker is investigated. The thickness of the porous wall required to eliminate the re-reflected waves is shown to be related to th porosity, friction coefficient, and wave period, as well as to both the positions of the porous medium and the test structure. However, this study indicates that the goal of eliminating re-reflected waves can be achieved by simply varying the thickness of the porous medium according to the wave period, with all the other factors arbitrarily selected.Assuming that the oscillation amplitude of the wavemaker board is constant, the primitive wave amplitude, before reaching the porous medium, becomes smaller as the wave period is increased. In addition, the study found that the required thickness of the porous medium for eliminating the re-reflected wave becomes larger as the wave period is increased. This results in a trend which further reduces the wave amplitude after the wave passes through the porous medium. In consequence, the oscillation amplitude of a wavemaker board has to be adjusted in a larger scale if the wave period is to be increased.     

An original method for characterizing internal waves

This study consisted in the characterization of internal waves in the south of the Strait of Messina (Italy). The observational data consisted in thermistor string profiles from the Coastal Ocean Acoustic Changes at High frequencies (COACH06) sea trial.An empirical orthogonal function analysis is applied to the data. The first two spatial empirical modes represent over 99% of the variability, and their corresponding time-dependent expansion coefficients take higher absolute values during internal wave events. In order to check how the expansion coefficients vary during an internal wave event, their time derivative, called here changing rates, are computed. It shows that each wave of an internal wave train is characterized by a double oscillation of the changing rates. At the front of the wave, both changing rates increase in absolute value with opposite sign, and then decrease to become null at the maximum amplitude of the wave. At the rear of the wave, the changing rates describe another period, again with opposite sign. This double oscillation can be used as a detector of internal waves, but it can also give information on the width of the wave, by measuring the length of the oscillation, as this information may sometimes be hard to read straight out of the data. When plotting the changing rates one versus another, the resulting scatter diagram puts on a butterfly shape that illustrates well this behaviour.     

An efficient focusing model for generation of freak waves

Based on the Longuet-Higgins wave model theory, the previews studies have shown that freak waves can be generated in finite space and time successfully. However, as to generating high nonlinear freak waves, the simulation results will be unrealistic. Therefore, a modified phase modulation method for simulating high nonlinear freak waves was developed. The surface elevations of some wave components at certain time and place are positive by modulating the corresponding random initial phases, then the total surface elevation at the focused point is enhanced and furthermore a freak wave event is generated. The new method can not only make the freak wave occur at certain time and place, but also make the simulated wave surface time series satisfy statistical properties of the realistic sea state and keep identical with the target wave spectrum. This numerical approach is of good precision and high efficiency by the comparisons of the simulated freak waves and the recorded freak waves.     

Model tree approach for prediction of pile groups scour due to waves

Scour around piles could endanger the stability of the structures placed on them. Hence, an accurate estimation of the scour depth around piles is very important in coastal and marine engineering. Due to the complex interaction between the wave, seabed and pile group; prediction of the scour depth is not an easy task and the available empirical formulas have limited accuracy. Recently, soft computing methods such as Artificial Neural Networks (ANNs) and Support Vector Machines (SVMs) have been used for the prediction of the scour depth. However, these methods do not give enough insight about the process and are not as easy to use as the empirical equations. In this study, new formulas are given that are easy to use, accurate and physically sound. Available empirical equations for estimating the pile group scour depth such as those of Sumer et al. (1992) and Bayram and Larson (2000), are less accurate compared to the given equations. These equations are as accurate as other soft computing methods such as ANN and SVM. Moreover, in this study, safety factors are given for different levels of acceptable risks, which can be so useful for engineers.     

On a near-optimal control approach for a wave energy converter in irregular waves

Real-time smooth reactive control and optimal damping of wave energy converters in irregular waves is difficult in part because the radiation impulse response function is real and causal, which constrains the frequency-dependent added mass and radiation damping according to the Kramers–Kronig relations. Optimal control for maximum energy conversion requires independent synthesis of the impulse response functions corresponding to these two quantities. Since both are non-causal (one being odd and other even), full cancellation of reactive forces and matching of radiation damping requires knowledge or estimation of device velocity into the future. To address this difficulty and the non-causality of the exciting force impulse response function, this paper investigates the use of propagating-wave surface elevation up-wave of the device to synthesize the necessary forces. Long-crested waves are assumed, and the approach is based on the formulations of Naito and Nakamura [2] and Falnes [22]. A predominantly heaving submerged device comprised of three vertically stacked discs driving a linear power take-off is studied. The overall formulation leads to smooth control that is near-optimal, given the approximations involved in the time-shifting of the non-causal impulse response functions and the consequent up-wave distances at which wave surface elevation is required. Absorbed power performance with the near-optimal approach is compared with two other cases, (i) when single-frequency tuning is used based on non-real time adjustment of the reactive and resistive loads to maximize conversion at the spectral peak frequency, and (ii) when no control is applied with damping set to a constant value. Simulation results for wave spectra over a range of energy periods and significant wave heights are compared for the three situations studied. While practical implementation presents engineering challenges, in terms of time-averaged absorbed power, unconstrained near-optimal control is found to perform significantly better than single-frequency tuning in the spectra with longer energy periods (>10 s for the present device), and somewhat better in the spectra with shorter energy periods (here ≤10 s).     

An efficient approach for characterizing basin-scale hydrodynamics

As the upstream oil and gas sector continues to use more groundwater resources for their operations, a comprehensive understanding of formation fluids at the sedimentary basin scale is required to inventory and manage available groundwater resources. Basin-scale fluid flow is often simplified to only assess pre-development groundwater conditions without understanding how large-scale hydrocarbon development might be changing regional flow patterns. This study focuses on two aspects of hydrogeological mapping for characterizing basin-scale hydrodynamics: (1) assessing the influence of hydrocarbon production and injection on pressure measurements used to map hydraulic heads and infer groundwater conditions; and (2) determining the effects of variable density groundwater on understanding the magnitude and direction of flow primarily in saline formation water aquifers. Drillstem Tests (DST's) are transient pressure tests that are used to infer regional groundwater flow, but they can be strongly affected when the sample location is located within the vicinity of a hydrocarbon production or injection well. To identify production and injection influences this study implements a Cumulative Interference Index (CII) methodology. This implementation can be used to map pre-development groundwater flow conditions and evaluate regional changes or effects due to historical oil and gas activity. Density effects are often neglected and can have considerable effect on groundwater flow in cases where aquifers contain dense brines, are inclined and sloping, or possess weaker hydraulic gradients than the buoyancy force potential. This study implements a vectorial analysis to identify flow directions in regions where density driven flow is important and can change the inferred magnitude and direction of flow. Two case studies are presented to demonstrate the effectiveness of these methodologies at evaluating basin-scale hydrodynamics.     

On the internal generation of waves: control volume approach

The literature contains theoretical derivation of the internal wave generation techniques by using control volume approach. The source term in three-dimensional continuity equation is derived by Reynolds transport theorem. The source term in two-dimensional wave model is derived by work-energy equation. The results confirmed that the appropriate velocity to be included in the source term is physically the group velocity which is the energy velocity for a wave model.     

Tentative engineering approach to scour around breakwaters in random waves

An approach by which the scour depth and protection layer width around the head of vertical-wall breakwaters, the scour and deposition depths as well as the protection layer widths at the round head of rubble-mound breakwaters in random waves can be derived is presented. Here the formulas for scour depth by Sumer and Fredsøe (1997) for vertical-wall breakwaters for regular waves and Fredsøe and Sumer (1997) for rubble-mound breakwaters for irregular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and deposition depths as well as protection layer widths in random waves. Comparisons are made between the present approach and the Fredsøe and Sumer (1997) random wave scour data for rubble-mound breakwaters.     

A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH

The transformation of irrotational surface gravity waves in an inviscid fluid can be studied by time stepping the kinematic and dynamic surface boundary conditions. This requires a closure providing the normal surface particle velocity in terms of the surface velocity potential or its tangential derivative. A convolution integral giving this closure as an explicit expression is derived for linear 1D waves over a mildly sloping bottom. The model has exact linear dispersion and shoaling properties. A discrete numerical model is developed for a spatially staggered uniform grid. The model involves a spatial derivative which is discretized by an arbitrary-order finite-difference scheme. Error control is attained by solving the discrete dispersion relation a priori and model results make a perfect match to this prediction. A procedure is developed by which the computational effort is minimized for a specific physical problem while adapting the numerical parameters under the constraint of a predefined tolerance of damping and dispersion error. Two computational examples show that accurate irregular-wave transformation on the kilometre scale can be computed in seconds. Thus, the method makes up a highly efficient basis for a forthcoming extension that includes nonlinearity at arbitrary order. The relation to Boussinesq equations, mild-slope wave equations, boundary integral equations and spectral methods is briefly discussed.     

一个波浪破碎散射模型的改进

为了得到与实测数据更为一致的散射模型,对KHCC03散射模型进行了改进.研究了考虑波浪破碎影响的KHCC03散射模型的适用范围.研究结果表明,KHCC03散射模型在入射角为25°～40°范围内,模型结果与实测数据吻合较好,在入射角小于25°和入射角大于40°的情况下,模型结果与实测数据差异较大.针对这一问题,对KHCC03模型进行了改进,结果表明:与原KHCC03模型相比,改进后的模型结果与实测数据吻合程度明显提高.     

An extension of the Airy theory for linear waves into shallow water

As a fully developed (Airy) wave propagates from deep into shallow water, its crest becomes more peaked while the trough flattens out. The median crest diameter MCD, defined as the distance between the wave flanks under the crest at a level halfway between the crest and trough, therefore decreases relative to the similarly defined median trough diameter MTD, which remains constant up to the breaking point. The MCD is directly related to other wave characteristics, which enables water particle velocities to be calculated for any water depth without having to recur to more complex, higher-order Stokes, cnoidal or Fenton theories. Over a nearly horizontal bottom, most fully developed wave characteristics can be expressed as functions of the wave period T_w. It is shown that the horizontal particle velocity at the bottom under the breaker crest is at least 9 times faster than under the breaker trough, which explains why sediment is transported landward under fair weather conditions. The proposed equations also shed new light on the formation of spilling, plunging and surging/collapsing breakers.     

An iterative procedure for the diffraction of water waves by multiple cylinders

Diffraction of water waves by an array of vertical cylinders of circular cross section is studied. In order to account for first order interaction among the cylinders, the body boundary condition is satisfied for each cylinder considering the scattered wave field from other cylinders in an iterative way. After each iteration, coefficients in the partial wave decomposition of the wave potential are modified. Convergence is fast for the whole range of frequencies and for a large number of bodies, compared with exact algebraic methods of Linton and Evans [J. Fluid Mech. 46 (1990) 549] and Kagemoto and Yue [J. Fluid Mech. 166 (1) (1986) 189].     

Tentative engineering approach to scour around spherical bodies in random waves

An approach by which the scour depth around a spherical body and the self-burial depth of such a body in random waves can be derived is presented. Here the formulas for scour and self-burial depths of a spherical body by Truelsen et al. [Truelsen C, Sumer BM, Fredsøe J. Scour around spherical bodies and self- burial. ASCE J Waterway Port Coast Ocean Eng 2005;131(1):1–13] for regular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and self-burial depths in random waves.     

An extended verification technique for solving problems of numerical modeling of wind waves

Based on different modifications of the source function in the WAM(C4) wind-wave model, a large series of verification calculations aimed at increasing the quality of the numerical model (with respect to the parameters of accuracy and performance) is performed. We propose a methodology allowing us to solve the following fundamental and practical problems of numerical modeling: (1) determining the minimum interval of verification of numerical wind-wave models, (2) finding a criterion for choosing the best model out of all models subjected to verification, and (3) formulating the accuracy requirement for specifying the input field necessary for the given accuracy of wind-wave field calculations. Particularly, we have found that (a) the minimum term of verification calculations for numerical wind-wave models is three months; (b) according to our criterion, the proposed modification of the WAM model impartially is “essentially preferable” to the original model; and (c) the relative errors (yielded by the proposed version of the WAM model) in the calculated wave heights ρH _s and average periods ρT _m for different levels of the relative error of the input wind-wave field ρW make it possible to solve the third problem mentioned above.     

An unconventional approach for assimilating aliased radar radial velocities

An aliasing operator is introduced to mimic the effect of aliasing that causes discontinuities in radial-velocity observations, and to modify the observation term in the costfunction for direct assimilations of aliased radar radial-velocity observations into numerical models. It is found that if the aliasing operator is treated as a part of the observation operator and applied to the analysed radial velocity in a conventional way, then the analysis is not ensured to be aliased (or not aliased) in consistency with the aliased (or not aliased) observation at every observation point. Thus, the analysis-minus-observation term contains a large alias error whenever an inconsistency occurs at an observation point. This causes fine-structure discontinuities in the costfunction. An unconventional approach is thus introduced to apply the aliasing operator to the entire analysis-minus-observation term at each observation point in the observation term of the costfunction. With this approach, the costfunction becomes smooth and concave upwards in the vicinity of the global minimum. The usefulness of this approach for directly assimilating aliased radar radial-velocity observations under certain conditions is demonstrated by illustrative examples.     

An optimization approach for fairing of ship hull forms

This paper presents a numerical fairing procedure to be used at the preliminary design stage to create high-quality ship hull form geometry. The procedure is based on a variational optimization approach in which a fairness measure related to the surface curvature is the objective function to be minimized subject to a set of geometric constraints to ensure that the final form has the required geometric characteristics. The optimization variables are selected as the control points of a B-spline surface representing the initial hull form. A nonlinear direct search technique is employed to solve the problem. The methodology is applied for typical ship forms to indicate that, provided that the designer can specify appropriate design objectives and geometric constraints, the methodology can produce alternative hull forms with significantly improved fairing characteristics. The choice of the fairness objective function is shown to have a crucial effect on the quality of the hull surface. Highly nonlinear exact fairness functionals yield surfaces of high quality at the expense of high-computerized effort.     

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.     

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.     

An integrated numerical method for simulation of drifted objects trajectory under real-world tsunami waves

The present study focused on tracing tsunami-drifted objects under a real tsunami based on an integrated numerical method. Instead of a solitary wave that is much shorter and steeper than real-world tsunami waves, an extra-long tsunami wave is represented here in a nearshore region using a new approach. To this end, propagation of a seismic tsunami from the source to the nearshore region was simulated using two-dimensional depth-averaged equations. When the waves reached the target coastal area, the time series of the free surface of the tsunami was approximated by a theoretical relation based on a combination of several solitons, which were then used to solve the linearized trajectory equation of the wave-maker to generate the intended time series of the tsunami wave. Finally, in a nearshore model, the movement of drifted bodies under the generated tsunami wave was simulated based on the smoothed-particle hydrodynamics (SPH) method. In order to verify the accuracy of the proposed method in tracing the drifted bodies under a real tsunami, the giant fish-oil tank, which was transported about 300 m during the 2011 Tohoku tsunami of Japan, was selected as the benchmark. The results demonstrate that the time series of the long tsunami wave was successfully generated by the piston wave-maker in the GPU-based SPH model, and the proposed approach can be regarded as a suitable alternative for reproduction of a real tsunami. The results also showed that the simulated fish-oil tank properly followed the estimated trajectory in Ishinomaki but it was transported more than the reported distance, which was expected due to absence of a holding connection between the tank and the ground in the SPH model. It should be emphasized that this study is one of the first studies on three-dimensional tracing of a tsunami-drifted body during a real event, and the tracing can be more accurate in further simulations by applying higher-resolution topography data and faster computation systems that help include more details in the nearshore model.