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.     

Long-term distribution of seabed shear stresses beneath random waves

The long-term distribution of seabed shear stresses under random waves is presented. The approach combines short-term distribution of maximum bottom shear stresses with a joint frequency table of significant wave height and peak period. An example of application is given where the long-term probability of exceeding a given level of the maximum bottom shear stress in the central North Sea is presented. The example includes estimation of the return period of the critical shear stress for sheet flow conditions, as well as the bottom shear stresses associated with the 1, 10 and 100 years return periods.     

Seabed shear stress and bedload transport due to asymmetric and skewed waves

A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature.     

Seabed geotechnical parameters from electrical conductivity measurements

Electrical conductivity measurements provide useful geotechnical information, particularly porosity data, and are well suited for use in conjunction with acoustic profiling techniques. A proposed conductivity measurement system for surveying the seabed is characterized by a towed inductive multifrequency probe operating underwater. It is integrated with a shipboard data acquisition and processing system.     

Pressure-induced forces and shear stresses on rubble mound breakwater armour layers in regular waves

This paper presents the results from an experimental investigation of the pressure-induced forces in the core material below the main armour layer and shear stresses on the armour layer for a porous breakwater structure. Two parallel experiments were performed which both involved pore pressure measurements in the core material: (1) core material with an idealized armour layer made out of spherical objects that also allowed for detailed velocity measurements between and above the armour, and (2) core material with real rock armour stones. The same core material was applied through the entire structure i.e. no additional filter layers were applied. For both experiments, high-speed video recordings were synchronised with the pressure measurements for a detailed investigation of the coupling between the run-up and run-down flow processes and the measured pressure variations. Outward directed pressure gradients were found which exerted a lift force up to ≈ 60% of the submerged weight of the core material. These maximum outward directed pressure gradients were linked to the maximum run-down event and were in general situated at, or slightly below, the maximum run-down level. Detailed velocity and turbulence measurements showed that the large outward directed pressure gradients in general coincide, both in time and space, with the maximum bed-shear stresses on the armour layer based on the Reynolds-stresses. The bed-shear stresses were found to result in a Shields parameter in the same order of magnitude as the critical value for movement of the armour stones.     

High-resolution field measurements and numerical modelling of intra-wave sediment suspension on plane beds under shoaling waves

Intra-wave sediment suspension is examined using high-resolution field measurements and numerical hydrodynamic and sediment models within 120 mm of a plane seabed under natural asymmetric waves. The detailed measurements of suspended sediment concentration (at 5 mm vertical resolution and at 4 Hz) showed two or three entrainment bursts around peak flow under the wave crest and another at flow reversal during the decelerating phase. At flow reversal, the mixing length was found to be approximately double the value attained at peak flow under the crest. To examine the cause of multiple suspension peaks and increased diffusion at flow reversal, a numerical “side-view” hydrodynamic model was developed to reproduce near-bed wave-induced orbital currents. Predicted currents at the bed and above the wave boundary layer were oppositely directed around flow reversal and this effect became more pronounced with increasing wave asymmetry. When the predicted orbital currents and an enhanced eddy diffusivity during periods of oppositely directed flows were applied in a Lagrangian numerical sediment transport model, unprecedented and extremely close predictions of the measured instantaneous concentrations were obtained. The numerical models were simplified to incorporate only the essential parameters and, by simulating at short time scales, empirical time-averaged parameterisations were not required. Key factors in the sediment model were fall velocities of the full grain size distribution, diffusion, separation of entrainment from settlement, and non-constant, but vertically uniform, eddy diffusivity. Over the plane bed, sediment convection by wave orbital vertical currents was found to have no significant influence on the results.     

Wave-induced drag force on vegetation under shoaling random waves

This paper provides a practical method for estimating the drag force on a vegetation field in shoaling conditions beneath non-breaking and breaking random waves. This is achieved by using a simple drag formula based on two empirical drag coefficients given by Méndez et al. (1999) and Méndez and Losada (2004), respectively, in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process and propagating in shallow waters. The effects of shoaling and breaking waves are included by adopting the Méndez et al. (2004) wave height distribution. Results are presented and discussed for different slopes, and an example of calculation is also provided to demonstrate the application of the method.     

Measurement and modeling of bed shear stress under solitary waves

Direct measurements of bed shear stresses (using a shear cell apparatus) generated by non-breaking solitary waves are presented. The measurements were carried out over a smooth bed in laminar and transitional flow regimes (~ 10⁴ < R_e < ~ 10⁵). Measurements were carried out where the wave height to water depth (h/d) ratio varied between 0.12 and 0.68; maximum near bed velocity varied between 0.16 m/s and 0.51 m/s and the maximum total shear stress (sum of skin shear stress and Froude–Krylov force) varied between 0.386 Pa and 2.06 Pa. The total stress is important in determining the stability of submarine sediment and in sheet flow regimes. Analytical modeling was carried out to predict total and skin shear stresses using convolution integration methods forced with the free stream velocity and incorporating a range of eddy viscosity models. Wave friction factors were estimated from skin shear stress at different instances over the wave (viz., time of maximum positive total shear stress, maximum skin shear stress and at the time of maximum velocity) using both the maximum velocity and the instantaneous velocity at that phase of the wave cycle. Similarly, force coefficients obtained from total stress were estimated at time of maximum positive and negative total stress and at maximum velocity. Maximum positive total shear stress was approximately 1.5 times larger than minimum negative total stress. Modeled and measured positive bed shear stresses are well correlated using the best convolution model, but the model underestimates the data by about 4%. Friction factors are dependent on the choice of normalizing using the maximum velocity, as is conventional, or the instantaneous velocity. These differ because the stress is not in phase with the velocity in general. Friction factors are consistent with previous data for monochromatic waves, and vary inversely with the square-root of the Reynolds number. The total shear stress leads the free stream fluid velocity by approximately 50°, whereas the skin friction shear stress leads by about 30°, which is similar to that reported by earlier researchers.     

Field measurements of time-averaged suspended sediment concentrations under waves

A suction sediment sampler has been developed for sampling suspended sand in the field. It works by the pressure difference between seabed and water surface, and thus no pump is required. The fact that the sampler has no mechanical moving parts and no electronics makes it very dependable. Seven samples are taken simultaneously at different elevations starting at about 1 cm above the bed. The sampling time is about 3 min for water depths of about 1.5 m. Sixty-five concentration profiles, complete with hydraulic data and sediment characteristics are given in the appendix.     

Dynamics of a moored barge under regular and random waves

Developments in the study of wave forces and construction techniques in deep water by the offshore oil industry have increased the use of marine terminals at deep water locations. A thorough understanding of moored ship dynamics when subjected to waves, wind and current combined with the use of flexible mooring lines would help to design berthing terminals for exposed areas. In this paper, the three dimensional problem of wave interactions with a barge moored to a single point is dealt with, based on the finite element method. The effect of flexibility of the mooring line and the point of mooring on the response of the barge as well as the mooring line tension is investigated. The paper compares the numerical results with model tests carried out on a barge moored to a fixed support under regular and random waves in head sea. The effect of stiffness of the mooring line on the barge response for different mooring points is discussed, which would be useful for the designers. The effect of viscous damping is also considered. The analytical results are in good agreement with the experimental results in both regular and random waves.     

Acoustic measurements of the velocity field beneath shoaling and breaking waves

An acoustic current meter attached to a servo-hydraulic surface-following device was used to obtain near-surface velocity measurements beneath breaking and near breaking surface gravity waves shoaling on a 1:40 beach. The data are compared to velocities predicted by two adaptations of linear theory: superposition and stretching. For unbroken and near breaking waves, the predictions are in close agreement with the measurements. For breaking and broken waves, near surface crest velocity measurements are influenced by air entrainment; trough velocities are relatively well predicted. The problems associated with the acoustic measurement of near-surface velocities are highlighted.     

Performance of an example jack-up platform under directional random ocean waves

This article presents the results of nonlinear dynamic analyses that explore the effects of directionality and the random nature of ocean waves on the overall structural performance of a sample jack-up platform. A finite-element model is developed which rigorously includes the effects of the material and geometrical nonlinearities in the structure and the nonlinear soil-structure interaction. Two wave theories, NewWave and Constrained NewWave, are adopted to simulate the water surface and water particle kinematics, which are implemented in the numerical model developed. Analyses are performed for both two and three-dimensional wave models, and the results are compared in terms of the deck and spudcan foundation displacements. The results obtained from the analyses indicate that the inclusion of wave spreading can result in reductions in the deck displacements of the sample jack-up platform. The level of reduction is greater when considerable plasticity occurs in the foundation. Furthermore, the probability of failure can be significantly decreased when the wave-spreading effects are included. In addition, it is shown that the effects of wave-spreading on the response and failure of the sample jack-up is increased when wave period is decreased.     

Drag force on a vegetation field due to long-crested and short-crested nonlinear random waves

This paper provides a practical method for estimating the drag force on a vegetation field exposed to long-crested (2D) and short-crested (3D) nonlinear random waves. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (1999), in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process. Effects of nonlinear waves are included by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D random waves.     

Observations of freak waves in random wave field in 2D experimental wave flume

Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index （BFI） are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.     

植被对波浪作用下床面切应力影响的数值模拟分析

本文基于OpenFOAM建立三维波浪数值水槽,模拟计算植被水域波浪作用下的床面切应力,分析了入射波高、植被密度、植被淹没高度、水流对植被水域波浪作用下床面切应力的影响。结果表明：纯波时,由于植被的阻水作用,植被水域床面切应力沿程衰减,其衰减程度与入射波高、植被密度及植被淹没高度呈现正相关;与纯波时相比,在波浪和同向流共同作用下正向床面切应力幅值增大,负向床面切应力幅值减小;弱水流对植被水域床面切应力的大小及分布无明显影响;强水流时,床面切应力在植被水域先增大后逐渐减小并在植被水域后显著降低。     

Laboratory measurements of large-scale near-bed turbulent flow structures under spilling regular waves

The instantaneous turbulent velocity field created by the breaking of spilling regular waves on a plane slope was measured in a plane running parallel to the slope using particle image velocimetry. The measurement plane was located at a height of about 1 mm above the bed. The measurement area encompassed the region where the large eddies generated at incipient wave breaking impinged on the bottom inside the surf zone. A total of 30 trials were conducted under identical experimental conditions. In each trial, six consecutive wave cycles were recorded. The measured velocity fields were separated into a mean flow and a turbulence component by ensemble averaging. The instantaneous turbulent velocity fields were analyzed to determine the occurrence frequency, location, geometry and evolution of the large eddies, and their contributions to instantaneous shear stresses, turbulent kinetic energy and turbulence energy fluxes. The motion of single glass spheres along the bed was also investigated. The two-phase flow measurements showed that the velocity and displacement of large solid particles on a smooth bed were significantly affected by the magnitude and direction of turbulence velocities. Overall, this study has examined the kinematic and dynamic properties of large eddies impinging on the bed and the interaction of these large-scale turbulent flow structures with the mean flow. The study has also highlighted the important role of large eddies in sediment transport.     

Shallow water reverberation: normal-mode model predictions comparedwith bistatic towed-array measurements

A normal-mode model for calculating reverberation in shallow water is presented. Some illustrative calculations are given for the bistatic case and for vertical and horizontal line-array receivers. Emphasis is on comparison with measurements of bistatic reverberation obtained at a shallow-water area in the Mediterranean. The data are from explosive sources received by a towed array, analyzed in one-tenth-decade frequency bands at subkilohertz frequencies. Model calculations for a flat-bottomed environment indicate a strong dependence on propagation conditions and a weak dependence on beam steering direction. Preliminary comparisons give quite good agreement between measured reverberation and model predictions, but point to the need for extending modeling efforts to handle range-dependent environments     

Verification of linear theory for particle velocities in wind waves based on field measurements

Analyses are presented of field measurements of spectral transfer functions between surface elevation and subsurface three-dimensional particle velocity in wind-generated waves, in conditions ranging from young seas to old swells. The results are in agreement with the linear theory predictions to within the measurement error margin, which is estimated to be ± 5% for the gain functions and ± 4° in phase as far as the possible systemic errors are concerned. No correlation is found of the degree of agreement between measurements and linear theory with wave age or wave sleepness.