The effect of yaw angle on VIV suppression for an inclined flexible cylinder fitted with helical strakes

Experimental studies were carried out to investigate the response features of an inclined flexible bare cylinder as well as a straked cylinder in a towing tank, with the main purpose of further improving the understanding of the effect of yaw angle on vortex-induced vibration (VIV) suppression. Four yaw angles (a = 0°, 15°, 30°, 45°), which is defined as the angle between the cylinder axis and the plane orthogonal to the oncoming fluid flow, were tested. The cylinder model was towed along the tank to generate a uniform fluid flow. The towing velocity was in the range of 0.05–1.0 m/s with an interval of 0.05 m/s. The corresponding Reynolds number ranged from 800 to 16000. The strakes selected for the experiments had a pitch of 17.5D and a height of 0.25D, which is generally considered as the most effective configuration for VIV suppression of a flexible cylinder in water. The experimental results indicate that VIV suppression effectiveness of the inclined flexible straked cylinder is closely related to the yaw angle. The displacement amplitudes are significantly suppressed in both cross-flow (CF) and in-line (IL) directions at a = 0°. However, with increasing yaw angle, the suppression efficiencies of the CF and IL displacement amplitudes gradually decrease. In addition, the CF dominant frequencies of the straked cylinder obviously deviate from those of the bare cylinder at a = 0° and 15°. This deviation is substantially alleviated with increasing yaw angle. The IL dominant frequencies show less dependency on the yaw angle. Similar trends are also observed on the dominant modes of vibration and the mean drag coefficients.     

The validity of the independence principle applied to the vortex-induced vibration of an inclined cylinder in steady flow

The validity of the independence principle applied to the vortex-induced vibration (VIV) of an inclined cylinder in steady flow is investigated by conducting numerical simulations. In order to create a perfect end-effect-free condition, periodic boundary condition is applied on the two end boundaries that are perpendicular to the cylinder. It is found that the response amplitude and frequency for an inclination angle of α = 45° agree well with their counterparts for α = 0°. The numerical results demonstrated the validity of the independence principle in the case of vortex-induced vibration, which has not been demonstrated by laboratory tests due to the difficulty in avoiding the end effects.     

Cross-flow vortex-induced vibration reduction of a long flexible cylinder using 3 and 4 control rods with different configurations

Control rod is one of the common passive control methods to suppress the vortex-induced vibration (VIV) of cylindrical structures. In this paper, the experimental study is conducted to detailed understand the performance of multiple control rods in suppressing the cross-flow (CF) VIV for a long flexible cylinder. The influence of the spatial arrangement of 3 and 4 control rods on CF VIV response of the main cylinder is investigated in a towing tank. It is observed that the attack angle θ is a very significant parameter to affect the vibration response, dominant frequency and the VIV suppression efficiency of the main cylinder. Based on the suppression efficiencies analysis of VIV response in the present experimental investigation, the spatial arrangement of 3 control rods with θ = 40° and 4 control rods with θ = 30° is the best choice for suppressing the CF VIV response of the main flexible cylinder. Overall, the use of 4 control rods could reduce VIV more effectively than the application of 3 control rods.     

Numerical evaluation of passive control of VIV by small control rods

Flow past a circular cylinder with multiple small control rods is studied by numerical simulation for Re_D ranging from 1161.3 to 6387.1. The Reynolds-Averaged-Navier–Stokes (RANS) equations and shear stress transport (SST) k − ω turbulence model are used to calculate the vortex field, while a fourth-order Runge–Kutta method is employed for evaluating the structure dynamics of the cylinder group. Comparisons with experimental results demonstrate the validation of this method. This study is concerned with the vortex induced vibration (VIV) suppression efficacy of small control rods placed around a main cylinder. The effects of control rod number, diameter ratio, spacing ratio and Reynolds number on the hydrodynamics and vibration responses of the main cylinder are investigated. The reduced percents of in-line and cross-flow amplitudes and the increased percents of the whole cross-sectional area of cylinders and the drag coefficient are used to give a comprehensive evaluation. Results of simulation indicate that placing small rods with appropriate number at appropriate locations can achieve good suppression effectiveness at a wide range of Reynolds number. The numerical result for the case with nine control rods, diameter ratio of 0.15 and spacing ratio of 0.6 shows the best suppression effect among the cases investigated in this study.     

Experiments with flexible shrouds to reduce the vortex-induced vibration of a cylinder with low mass and damping

Experiments employing a low-mass-damping cylinder have been conducted to determine the vortex-induced vibration (VIV) response of four suppressors of the flexible-shroud family. The VIV suppressors were inspired in the concept of the Ventilated Trousers (VT), a flexible shroud composed of a flexible net fitted with three-dimensional bobbins. Reynolds number varied between 5 × 10³ and 25 × 10³, while reduced velocity varied from 2 to 26. The VIV dynamic response showed that the VT suppressed the peak amplitude of vibration down to 40% of that of a bare cylinder. Other flexible shrouds also achieved suppression, but not as efficiently. Drag was reduced during the VIV synchronization range, but remained above the value for a bare static cylinder thereafter. Spectral analysis of displacement and lift revealed that, depending on the geometry and distribution of the bobbins, the flexible shroud can develop an unstable behavior, capturing energy from the wake and sustaining vibrations for higher reduced velocities. PIV measurements of the wake revealed that the entrainment flow through the mesh is necessary to extend the vortex-formation length of the wake; this mechanism only occurs for the VT mesh.     

Flow induced vibrations of a sharp edge square cylinder in the wake of a circular cylinder

The response of an oscillating circular cylinder at the wake of an upstream fixed circular cylinder was classified by different researchers as galloping, wake induced galloping or wake induced vibration. Furthermore it is already known that a sharp edge square cylinder would undergo galloping if it is subjected to uniform flow. In this study the influence of the wake of a fixed circular cylinder on the response of a downstream square cylinder at different spacing ratios (S/D = 4, 8, 11) is experimentally investigated. The subject appears not to have received previous attention. The lateral displacements, lift forces and the pressure data from gauges mounted in the wake of the oscillating cylinder are recorded and analyzed. The single degree of freedom vibrating system has a low mass-damping parameter and the Reynolds number ranges from 7.7 × 10² to 3.7 × 10⁴.In contrast to that for two circular cylinders in tandem arrangement, the freely mounted downstream square cylinder displays a VIV type of response at all spacing ratios tested. There is no sign of galloping or wake induced galloping with the square cylinder. With increase at the spacing ratio the cross-flow oscillations decrease. It is shown that the vortices arriving from the upstream fixed circular cylinder play a major role on the shedding mechanism behind the downstream square cylinder and cause the square cylinder to shed vortices with frequencies above Strouhal frequency of the fixed square cylinder (St = 0.13). The VIV type of oscillations in the downstream square cylinder is most probably caused by the vortices newly generated behind the square cylinder.     

Experimental investigation on the flow induced vibration of an equilateral triangle prism in water

A series of flow induced vibration (FIV) experiments for an equilateral triangle prism elastically mounted in a water channel are performed with different system stiffness at constant damping and mass. An amplitude variation coefficient is proposed to describe FIV stationarity in the present study. The FIV of the prism can be divided into three primary regions based on the amplitude and frequency responses, which are the vortex induced vibration (VIV) branch, the transition branch from VIV to galloping, and the galloping branch. The transition branch occurs at the reduced velocity in the range of 7.8 < U_r = U/(f_n,air·D) < 10.4, accompanied with a relatively rapid increase in amplitude and a precipitous drop in frequency and vibration stationarity. In addition, the reduced velocity where the transition region is initiated is independent of the system stiffness. The maximum amplitude reaches 3.17 D in the galloping branch. The ratio of the response frequency to the natural frequency of the prism in air remains locked to approximately 0.65 throughout the fully developed galloping branch. Large amplitude responses in an infinite range of flow velocities, excellent vibration stationarity and steady vibration frequencies, which are characteristics of the galloping of the prism, have a positive impact on improving energy conversion.     

Force and flow characteristics of a circular cylinder with uniform surface roughness at subcritical Reynolds numbers

The main purpose of this study is to establish a better understanding of the relationship between drag reduction and surface roughness. Experiments were conducted to measure the force and flow characteristics of a circular cylinder with different types of artificial surface roughness over the range 6 × 10³ < Re < 8 × 10⁴ (Re is based on the cylinder diameter D). The roughness cylinder was formed by covering the exterior surface of the cylinder with uniformly distributed (1) sandpaper, (2) netting, and (3) dimples. The roughness coefficient ranged from k/D = 0.0028 to 0.025 (k is the roughness height). A detailed quantitative measurement of the flow field around the cylinder using Particle Imaging Velocimetry (PIV) was carried out. The hydrodynamic force coefficients (drag and lift) of the rough cylinders are compared against those of a smooth cylinder measured under the same flow conditions. It is found that certain configuration of surface roughness significantly reduces the mean drag coefficient of the cylinder, particularly at large Reynolds numbers. In addition, the root-mean-square (r.m.s.) lift coefficient of the rough cylinders is considerably lower than that of a smooth cylinder.     

Passive VIV Reduction of An Inclined Flexible Cylinder by Means of Helical Strakes with Round-Section

A series of experimental tests of passive VIV suppression of an inclined flexible cylinder with round-sectioned helical strakes were carried out in a towing tank. During the tests, the cylinder models fitted with and without helical strakes were towed along the tank. The towing velocity ranged from 0.05 to 1.0 m/s with an interval of 0.05 m/s.Four different yaw angles(a=0°, 15°, 30° and 45°), defined as the angle between the axis of the cylinder and the plane orthogonal of the oncoming flow, were selected in the experiment. The main purpose of present experimental work is to further investigate the VIV suppression effectiveness of round-sectioned helical strakes on the inclined flexible cylinder. The VIV responses of the smooth cylinder and the cylinder with square-sectioned strakes under the same experimental condition were also presented for comparison. The experimental results indicated that the roundsectioned strake basically had a similar effect on VIV suppression compared with the square-sectioned one, and both can significantly reduce the VIV of the vertical cylinder which corresponded to the case of a=0°. But with the increase of yaw angle, the VIV suppression effectiveness of both round-and square-section strakes deteriorated dramatically, the staked cylinder even had a much stronger vibration than the smooth one did in the in-line(IL)direction.     

Benchmark computations for flows around a stationary cylinder with high Reynolds numbers by RANS-overset grid approach

The aim of this paper is to evaluate the accuracy, stability and efficiency of the overset grid approach coupled with the RANS (Reynolds Averaged Navier-Stokes) model via the benchmark computations of flows around a stationary smooth circular cylinder. Two dimensional numerical results are presented within a wide range of Reynolds numbers (6.31 × 10⁴ ∼ 7.57 × 10⁵) including the critical flow regime. All the simulations are carried out using the RANS solver pimpleFoam provided by OpenFOAM, an open source CFD (Computational Fluid Dynamics) toolkit. Firstly, a grid convergence study is performed. The results of the time-averaged drag and lift force coefficients, root-mean square value of lift force coefficient and Strouhal number (St number) are then compared with the experimental data. The velocity, vorticity fields and pressure distribution are also given. One main conclusion is that the numerical solutions in regard to a fixed cylinderare not deteriorated due to the implementation of the overset grid. Furthermore, it can be an appealing approach to facilitate simulations of Vortex Induced Vibrations (VIV), which involves grid deformation. The present study is a good start to implement the overset grid to solve VIV problems in the future.     

An octo-generator for energy harvesting based on the piezoelectric effect

A renewable energy harvester using the piezoelectric effect is developed for the ocean tidal and wind flow. The harvester is made of connected driving blades to an octo-generator, which has a rotator with n blades and a stator attached by eight mass-spring-piston-cylinder-piezoelectricity devices. The resonance and force magnification are utilized to increase the power output of the harvester. A corresponding mathematical model is developed to calculate the root mean square of the generated electric power. The simulation results indicate that the generated power is largely enhanced when the near-resonant condition is established. The power increases with increases in the magnetic flux density, the large-to-small diameter ratio of the cylinder, the size of magnetic bar face, and decreases in the gap between two magnetic faces and the size of the piezoelectric bar face. A generated power of 5 kW is realized by the harvester working under an ocean tidal speed, V = 1.75 m/s, and its geometric and material properties of driving length L = 7.5 m, spring constant k_v = 65000 N/m, gap between the two magnets s = 0.0015 m, large to small diameter ratio of the cylinder z = 6, and magnetic flux density Br = 1.45 T.     

Investigation of drag crisis phenomenon using CFD methods

When fluid flow passes a cylinder, the drag crisis phenomenon occurs between the sub-critical and the super-critical Reynolds numbers. The focus of the present studies was on the numerical prediction of the drag crisis based on CFD methods. In this work, block structured meshes with refined grids near the cylinder surface and in the downstream were employed. Both 2D and 3D simulations were performed using various turbulence models, including the SST k − ω model, the k − ϵ model, the SST with LCTM, the DES model, and the LES model. In the convergence studies, the effects of the grid size, the time step, the first grid size and the aspect ratio (for 3D simulations) on the solutions were examined. The errors due to spatial and time discretizations were quantified according to a V&V procedure. Validation studies were carried out for various Reynolds numbers between Re = 6.31 × 10⁴ and 7.57 × 10⁵. The averaged drag force, the RMS of lift force and the Strouhal number were compared with experimental data. The studies indicated that standard 2D and 3D RANS methods were inadequate to capture the drag crisis phenomenon. The LES method however has the potential to address the problem.     

Persian Gulf response to a wintertime shamal wind event

The results from a～1 km resolution HYbrid Coordinate Ocean Model (HYCOM), forced by 1/2° Navy Operational Global Atmospheric Prediction System (NOGAPS) atmospheric data, were used in order to study the dynamic response of the Persian Gulf to wintertime shamal forcing. Shamal winds are strong northwesterly winds that occur in the Persian Gulf area behind southeast moving cold fronts. The period from 20 November to 5 December 2004 included a well defined shamal event that lasted 4–5 days. In addition to strong winds (16 m s^?1) the winter shamal also brought cold dry air (T_a=20 °C, q_a=10 g kg^?1) which led to a net heat loss in excess of 1000 W m^?2 by increasing the latent heat flux. This resulted in SST cooling of up to 10 °C most notably in the northern and shallower shelf regions. A sensitivity experiment with a constant specific humidity of q_a=15 g kg^?1 confirmed that about 38% of net heat loss was due to the air–sea humidity differences. The time integral of SST cooling closely followed the air–sea heat loss, indicating an approximate one-dimensional vertical heat balance. It was found that the shamal induced convective vertical mixing provided a direct mechanism for the erosion of stratification and deepening of the mixed layer by 30 m. The strong wind not only strengthened the circulation in the entire Persian Gulf but also established a northwestward flowing Iranian Coastal Current (ICC, 25–30 cm s^?1) from the Strait of Hormuz to about 52°E, where it veered offshore. The strongest negative sea level of 25–40 cm was generated in the northernmost portion of the Gulf while the wind setup against the coast of the United Arab Emirates established a positive sea level of 15–30 cm. The transport through the Strait of Hormuz at 56.2°E indicated an enhanced outflow of 0.25 Sv (Sv≡10⁶ m³ s^?1) during 24 November followed by an equivalent inflow on the next day.     

Scour depth under pipelines placed on weakly cohesive soils

We here study the scouring processes that evolve around a submarine pipeline placed on a weakly cohesive seabed. We first analyze some laboratory tests carried out by Vijaya Kumar et al. [21], Xu et al. [25] and Zhou et al. [28] that focused on the scouring around a horizontal cylinder lying on a cohesive bed, subject to waves and currents. The specific purpose is that of finding a new formula for the prediction of the equilibrium scour depth under submarine pipelines. After a theoretical analysis of the main parameters, the sought formula has been found to be a function of: (i) the hydrodynamic forces acting on the cylinder (through the Keulegan–Carpenter parameter KC), (ii) the clay content of the soil C_c, and (iii) the burial depth e₀/D. In the presence of small amounts of clay (C_c< 5 %), the scour depth depends directly on KC (as confirmed by many literature works for pipelines lying on sandy soils, e.g. [18]) and inversely on C_c (as already seen for bridge abutments on cohesive soils, e.g. [1]), the best-fit law being characterized by a coefficient of determination R² = 0.62. If some burial depth is accounted for, this being a novelty of the present work, a more general formulation can be used, valid in the presence of weakly-cohesive soils and with burial depths of the pipe smaller than 0.5 (R² = 0.79). For large clay-content ranges (2% < C_c < 75 %), the scour depth depends directly on both KC and C_c, this giving R² = 0.79 (no burial depth) and 0.91 (some burial depth). However, this finding is at odds with the main literature, because, for large amounts of clay, it is fundamental to consider the liquidity index LI, which accounts for some important clay properties, like the plasticity. We argue that the absence of LI is balanced by the direct dependence of the scour depth on C_c. Notwithstanding the small number of available data, a formula for the prediction of the scour depth under pipelines lying on cohesive soils is fundamental for several engineering applications. The present contribution represents the first attempt to build such a formula, when the pipeline is subject to the wave-current forcing and the seabed is characterized by a relatively small clay content.     

Population dynamics and secondary production of the cockle Cerastoderma edule: A comparison between Merja Zerga (Moroccan Atlantic Coast) and Arcachon Bay (French Atlantic Coast)

Cockle (Cerastoderma edule) population dynamics were studied at the southern limit of the distribution of this marine bivalve in Merja Zerga, Morocco. Parameters such as growth, mortality, and production were compared with those of a population at Arcachon Bay (France) a site in the center of the cockle's range. At each sampling period between two and three cohorts were simultaneously observed at each site and the average total abundance was usually higher at Merja Zerga. Recruitment occurred at both sites in spring when temperature rose above 19 °C, independently of the month. In Merja Zerga, winter recruitment was also observed at one occasion, following high sediment disturbance. The first year (2005–06) at Merja Zerga, the mortality rate was close to nil for juveniles and was Z = 1.5 yr^? 1 for adults, providing a high production (64 g dry weight m^? 2 yr^? 1). At Arcachon during the same period, the juvenile mortality rate was Z = 10.9 yr^? 1, the adult mortality rate was 3.4 yr^? 1 and production was 26 gDW m^?2 yr^? 1. The second year (2006–07), mortality after recruitment was much higher (Z = 8.6 yr^? 1, for juveniles) and similar to what was observed at Arcachon (Z = 8.4 yr^? 1). Mortality rate of adults was higher at Merja Zerga (Z = 3.0 yr^? 1) than at Arcachon (Z = 1.5 yr^? 1). Production was lower at Arcachon than at Merja Zerga although growth performances were higher at Arcachon. The higher growth performance at Arcachon (Φ′ = 3.3) was mainly due to high asymptotic length (L_∞ = 38 mm) and was related to low intraspecific competition compared to Merja Zerga where cockle abundance was higher (Φ′ = 3.1, L_∞ = 31 mm). P/B was low in both sites and slightly higher at Arcachon (1.1–1.5 against 1.0–1.1 yr^? 1). At Arcachon, recruitment was correlated with temperature, a peak occurring when temperature rose above 19 °C (June–July). At Merja Zerga, recruitment was already 2–3 months earlier but was not significantly correlated to temperature.This study showed that population dynamics of cockles at the southern limit of this distribution fell in the range of what was observed elsewhere in the North-Eastern Atlantic coast. Most factors that were involved in population regulation (intraspecific competition, predation and sediment dynamics) were not strictly dependent on latitude. The direct role of temperature (latitude dependent factor) was not obvious. Variation in temperature could explain the recruitment delay between Arcachon and Merja Zerga and the low maximum shell length at Merja Zerga.     

Wave climate scatter performance of a cycloidal wave energy converter

A lift based cycloidal wave energy converter (WEC) was investigated using potential flow numerical simulations in combination with viscous loss estimates based on published hydrofoil data. This type of wave energy converter consists of a shaft with one or more hydrofoils attached eccentrically at a radius. The main shaft is aligned parallel to the wave crests and submerged at a fixed depth. The operation of the WEC as a wave-to-shaft energy converter interacting with straight crested waves was estimated for an actual ocean wave climate. The climate chosen was the climate recorded by a buoy off the north-east shore of Oahu/Hawaii, which was a typical moderate wave climate featuring an average annual wave power P_W = 17 kWh/m of wave crest. The impact of the design variables radius, chord, span and maximum generator power on the average annual shaft energy yield, capacity factor and power production time fraction were explored. In the selected wave climate, a radius R = 5 m, chord C = 5 m and span of S = 60 m along with a maximum generator power of P_G = 1.25 MW were found to be optimal in terms of annual shaft energy yield. At the design point, the CycWEC achieved a wave-to-shaft power efficiency of 70%. In the annual average, 40% of the incoming wave energy was converted to shaft energy, and a capacity factor of 42% was achieved. These numbers exceeded the typical performance of competing renewables like wind power, and demonstrated that the WEC was able to convert wave energy to shaft energy efficiently for a range of wave periods and wave heights as encountered in a typical wave climate.     

Kinetic study reveals weak Fe-binding ligand,which affects the solubility of Fe in the Scheldt estuary

The chemistry of dissolved Fe(III) was studied in the Scheldt estuary (The Netherlands). Two discrete size fractions of the dissolved bulk (< 0.2 μm and < 1 kDa) were considered at three salinities (S = 26, 10 and 0.3).Within the upper estuary, where fresh river water meets seawater, the dissolved Fe concentration decreases steeply with increasing salinity, for the fraction < 0.2 μm from 536 nM at S = 0.3 to 104 nM at S = 10 and for the fraction < 1 kDa from 102 nM to 36 nM Fe. Further downstream, in the middle and lower estuary, this decrease in the Fe concentration continues, but is far less pronounced. For all samples, the traditionally recognised dissolved strong organic Fe-binding ligand concentrations are lower than the dissolved Fe concentrations.Characteristics of dissolved Fe-binding ligands were determined by observing kinetic interactions with adsorptive cathodic stripping voltammetry. From these kinetic experiments we concluded that apart from the well-known strong Fe-binding organic ligands (L, logK′ = 19–22) also weak Fe-binding ligands (P) existed with an α value (binding potential = K′ · [P]) varying between 10^11.1 and 10^11.9. The presence of this relatively weak ligand explained the high concentrations of labile Fe present in both size fractions in the estuary. This weak ligand can retard or prevent a direct precipitation after an extra input of Fe.The dissociation rate constants of the weak ligand varied between 0.5 × 10^− 4 and 4.3 × 10^− 4 s^− 1. The rate constants of the strong organic ligand varied between k_d = 1.5 × 10^− 3–17 × 10^− 2 s^− 1 and k_f = 2.2 × 10⁸–2.7 × 10⁹ M^− 1 s^− 1. The dissociation rate constant of freshly amorphous Fe-hydroxide was found to be between 4.3 × 10^− 4 and 3.7 × 10^− 3 s^− 1, more labile or equal to the values found by Rose and Waite [Rose, A.L., Waite, T.D., 2003a. Kinetics of hydrolysis and precipitation of ferric iron in seawater. Environ. Sci. Technol., 37, 3897–3903.] for freshly precipitated Fe in seawater.Kinetic rate constants of Fe with the ligand TAC (2-(2-Thiazolylazo)-p-cresol) were also determined. The formation rate constant of Fe(TAC)₂ varied between 0.1 × 10⁸ and 3.6 × 10⁸ M^− 1 s^− 1, the dissociation rate constant between 0.2 × 10^− 5 and 17 × 10^− 5 s^− 1 for both S = 26 and S = 10. The conditional stability constant of Fe(TAC)₂ (β_Fe(TAC)2′) varied between 22 and 23.4 for S = 10 and S = 26 more or less equal to that known from the literature (logβ_Fe(TAC)2′ = 22.4; [Croot, P.L., Johansson, M., 2000. Determination of iron speciation by cathodic stripping voltammetry in seawater using the competing ligand 2-(2-Thiazolylazo)-p-cresol (TAC). Electroanalysis, 12, 565–576.]). However, at S = 0.3 the logβ_Fe(TAC)2′ was 25.3, three orders of magnitude higher. Apparently the application of TAC to samples of low salinity can only be done when the correct β_Fe(TAC)2′ is known.     

Wave climate variability in the North-East Atlantic Ocean over the last six decades

Ocean surface gravity waves play a major role in many engineering and environmental problems, both in the open ocean and in coastal zones. Therefore, it is essential to improve our knowledge on spatial and temporal variability of wave climate. This study aims at investigating this variability in the North-East Atlantic Ocean (25°W–0°W and 30°N–60° N), using a 57-year hindcast (1953–2009) obtained with a spectral wave model forced with reanalysis wind fields. The hindcast analysis reveals firstly strong seasonal fluctuations of wave climate, with winters characterized by large and long-period waves of mean direction spreading from south-west to north-west, and summers characterized by smaller and shorter-period waves originating from norther directions. From northern (55°N) to southern (35°N) latitudes, the significant wave height (Hs) decreases by roughly 40%, the mean wave direction (Mwd) rotates clockwise by about 25% while the peak period (Tp) only grows by 5%. These three parameters also exhibit a strong inter-annual variability, particularly when winter-means (from 1st of December to 1st of April) are considered. Linear trend analysis over the studied period shows spatially variable long-term trends, with a significant increase of Hs (up to 0.02 m yr^?1) and a counterclockwise shift of Mwd (up to ?0.1° yr^?1) at northern latitude, contrasting with a fairly constant trend for Hs and a clockwise shift of Mwd (up to +0.15° yr^?1) at southern latitudes. Long-term trends of Tp are less significant, with still a slight increase in the north-eastern part of the study area (up to +0.01 s yr^?1). Eventually, a comparison between the inter-annual variability of the winter-means of the three selected wave parameters and the North Atlantic Oscillation (NAO) reveals: (1) a strong positive correlation between Hs and the NAO index at northern latitudes (correlation coefficient up to R = 0.91) and a significant negative correlation at southern latitudes (up to R = ?0.6); (2) no significant correlation for Mwd north of 40°N and a clear positive correlation southward of 40°N (up to R = 0.8) and (3) a northward increasing correlation for Tp (up to R = 0.8). Long-term trends for Hs, Mwd and Tp are finally explained by a significant increase in the NAO index over the studied period.     

Experimental study of interactions between multi-directional focused wave and vertical circular cylinder,part II: Wave force

We describe experiments with multi-directional focused waves interacted with a vertical circular cylinder in a 3D wave basin. The focus of this study is on the run-up of multi-directional focused waves, wave forces, and wave pressures on the cylinder. Part I, the study on wave run-up, has already been presented by Li et al. (2012). In this paper, the analysis of the wave force on the vertical cylinder is presented.In this experiment, a cylinder with 0.25 m in diameter was adopted and different wave parameters, such as focused wave amplitude, peak frequency, frequency bandwidth and directional spreading index, are considered. The model scale k_pa (k_p is the wave number corresponding to peak frequency, a is the radium of the cylinder) varies from 0.32 to 0.65. The maximum forces of multi-directional focused wave on cylinder were measured and investigated. The results showed that the wave parameters have a significant influence on the wave force, and that the spatial profile of the surface of multi-directional focused wave can also affect its force on the cylinder, which is different from two-dimensional wave. In addition, the ‘secondary loading cycle’ phenomenon was also observed and discussed. In our experiments, the ‘secondary loading cycles’ occur when kA > 0.36 for all cases. While in some referred small scale experiments, the secondary load cycles are observed even for kA = 0.2, when the waves are longer enough. To larger model scale, the pronounced secondary load cycle occurs with larger wave steepness waves.     

Transport processes of uniform and mixed sands in oscillatory sheet flow

New experiments were carried out in the Large Oscillating Water Tunnel of WL|Delft Hydraulics (scale 1:1) using asymmetric 2nd-order Stokes waves. The main aim was to gain a better understanding of size-selective sediment transport processes under oscillatory plane-bed/sheet-flow conditions. The new data show that for uniform sand sizes between 0.2 < D < 1.0 mm, measured net transport rates are hardly affected by the grain size and are proportional to the third-order velocity moment. However for finer grains (D = 0.13 mm) net sand transport rates change from the ‘onshore’ direction into the ‘offshore’ direction in the high velocity range. A new measuring technique for sediment concentrations, based on the measurement of electro-resistance (see [McLean, S.R., Ribberink, J.S., Dohmen-Janssen, C.M. and Hassan, W.N.M., 2001. Sediment transport measurements within the sheet flow layer under waves and currents. J. Waterw., Port, Coast., Ocean Eng., ISSN 0733-950X]), was developed further for the improved measurement of sediment dynamics inside the sheet-flow layer. This technique enabled the measurements of particle velocities during the complete wave cycle. It is observed that for long period waves (T = 12.0 s), time-dependent concentrations inside the sheet-flow layer are nearly in phase with the time-dependent flow velocities. As the wave period decreases, the sediment entrainment from the bed as well as the deposition process back to the bed lags behind the wave motion more and more. The new data show that size-gradation has almost no effect on the net total transport rates, provided the grain sizes of the sand mixture are in the range of 0.2 < D < 1.0 mm. However, if very fine grains (D = 0.13 mm) are present in the mixture, net total transport rates of graded sand are generally reduced in comparison with uniform sand with the same D₅₀. The transport rates of individual size fractions of a mixture are strongly influenced by the presence of other fractions in a mixture. Fine particles in sand mixtures are relatively less transported than in that uniform sand case, while the opposite occurs for coarse fractions in a mixture. The relative contribution of the coarse grains to the net total transport is therefore larger than would be expected based on their volume proportion in the original sand mixture. This partial transport behaviour is opposite to what is generally observed in uni-directional (e.g. river) flows. This is caused by vertical sorting of grain sizes in the upper bed layer and in the sheet flow and suspension layers. Kinematic sorting is believed to be responsible for the development of a coarse surface layer on top of a relatively fine sub-layer, providing in this way a relatively large flow exposure for the coarser sizes. Furthermore fine grains are suspended more easily than coarse grains to higher elevations in the flow where they are subject to increasing phase-lag effects (settling lags). The latter also leads to reduced net transport rates of these finer sizes.