Hydrodynamic performance of double rows of piles suspending horizontal c shaped bars

The wave transmission, reflection, and energy dissipation of the double rows of vertical piles suspending horizontal steel C shaped bars are experimentally and theoretically studied under normal regular waves. Different wave and structural parameters are investigated e.g. the wave length, the C shaped bars draft and spacing, the supporting piles diameter and spacing, and the space between the double rows. Also, the theoretical model based on an eigenfunction expansion method is developed to study the hydrodynamic breakwater performance. In order to examine the validity of the theoretical model, the theoretical results are compared with the experimental and theoretical results obtained by different authors. Comparison between experiments and predictions showed that theoretical model provides a good estimate to the different hydrodynamic coefficients when the friction factors of the upper and the lower parts are f_U = 1.5 and f_L = 0.75. The present breakwater physical model gives efficiency near other similar systems of different shapes.     

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.     

Constrained near-optimal control of a wave energy converter in three oscillation modes

This paper investigates the performance of a small axisymmetric buoy under wave-by-wave near optimal control in surge, heave, and pitch modes in long-crested irregular waves. Wave prediction is obtained using a deterministic propagation model. The paper describes the overall formulation leading up to the derivation of the feedforward control forces in surge and heave, and the control moment in pitch. The radiation coupling between surge and pitch modes is accounted for in the model. Actuation is relative to deeply submerged reaction masses. Heave oscillations are constrained by the swept-volume limit. Oscillation constraints are also applied on the surge and pitch oscillations. The paper discusses time-domain simulations for an irregular wave input with and without the present control. Also discussed are results obtained over a range of irregular wave conditions derived for energy periods from 7 s to 17 s, and a significant wave height of 1 m. It is found that, while the gains in power capture enabled by the present control are significant, the actuation forces are also very large, given the small size of the buoy. Further, due to the small size, heave is found to be the dominant contributor to power capture, with relatively modest contributions from surge and pitch.     

Wave modelling in the vicinity of submerged breakwaters

This paper describes a simple method for modelling wave breaking over submerged structures, with the view of using such modelling approach in a coastal area morphodynamic modelling system.A dominant mechanism for dissipating wave energy over a submerged breakwater is depth-limited wave breaking. Available models for energy dissipation due to wave breaking are developed for beaches (gentle slopes) and require further modifications to model wave breaking over submerged breakwaters.In this paper, wave breaking is split into two parts, namely: 1) depth-limited breaking modelled using Battjes and Janssen's (1978) theory [Battjes, J.A. and Jannsen, J.P.F.M. (1978). Energy loss and setup due to breaking of random waves. Proceedings of the 16th Int. Conf. Coast. Eng., Hamburg, Germany, pp. 569-587.] and 2) steepness limited breaking modelled using an integrated form of the Hasselmann's whitecapping dissipation term, commonly used in fully spectral wind–wave models. The parameter γ₂, governing the maximum wave height at incipient breaking (H_max = γ₂d) is used as calibration factor to tune numerical model results to selected laboratory measurements. It is found that γ₂ varies mainly with the relative submergence depth (ratio of submergence depth at breakwater crest to significant wave height), and a simple relationship is proposed. It is shown that the transmission coefficients obtained using this approach compare favourably with those calculated using published empirical expressions.     

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.     

Impact of long separating distances on the energy production of two interacting wave energy converters

In this paper, wave farms composed of two either surging or heaving wave energy converters are considered. Using a numerical model which takes into account wave interactions, the impact on the absorbed wave power of the separating distance between the two systems and the wave direction is studied. In regular waves, a modified q_mod factor is introduced and it is found to be more relevant than the usual q factor for identifying this impact. Then, it is shown that, asymptotically, the alteration of the energy absorption due to wave interaction effects decreases with the square root of the distance. This is a slow decay, which leads to a still significant modification of the wave energy absorption at long distance (up to 15% at a distance of 2000 m). In irregular waves, it is shown that constructive and destructive effects compensate each other, particularly when considering the mean annual power. It leads to a smaller impact of the wave interactions on the absorbed energy and shorter distances (smaller than 10% for distances greater than 400 m). Finally, conclusions on if wave interactions should be taken into account or not when designing a wave farm are drawn in function of the distance.     

Numerical study of wave-induced soil response in a sloping seabed in the vicinity of a breakwater

In this study, a mathematical integrated model is developed to investigate the wave-induced sloping seabed response in the vicinity of breakwater. In the present model, the wave model is based on the Volume-Averaged/Reynolds Averaged Navier–Stokes (VARANS) equations, while Biot's consolidation equation is used to govern the soil model. The influence of turbulence fluctuations on the mean flow with respect to the complicated interaction between wave, sloping seabed and breakwater are obtained by solving the Volume-Averaged k − ϵ model. Unlike previous investigations, the phase-resolved absolute shear stress is used as the source of accumulation of residual pore pressure, which can link the oscillatory and residual mechanisms simultaneously. Based on the proposed model, parametric studies regarding the effects of wave and soil characteristics as well as bed slopes on the wave-induced soil response in the vicinity of breakwater are investigated. Numerical results indicate that wave-induced seabed instability is more likely to occur in a steep slope in the case of soil with low relative density and low permeability under large wave loadings. It is also found that, the permeability of breakwater significantly affect the potential for liquefaction, especially in the region below the breakwater.     

The influence of sea state on formation speed of alongshore variability in surf zone sand bars

The formation time of alongshore morphological variability in surf zone sand bars has long been known to differ from one beach to the other and from one post-storm period to another. Here we investigate whether the type of sea state, i.e. distant swell waves or locally generated short period wind sea, affects the formation time of the emerging alongshore topographic variability.A numerical modeling approach is used to examine the emergence of alongshore variability under different shore-normal wave forcing. A research version of Delft3D, operating on the time-scale of wave groups, is applied to a schematised bathymetry with a single bar. The model is then used to investigate several wave scenarios, examining the impact of peak period, frequency spread and directional spread on the formation time of alongshore variability.Results show that an increase in wave period has a large effect, changing the formation time up to O (250%) in case the wave period is changed from a representative value for the Dutch coast (T_p ~ 5–6 s) to an Australian South East coast value (T_p ~ 10–12 s). In contrast, modifications in the directional and frequency spread of the wave field result only in a minor change in the formation time.Examination of hydrodynamics and potential sediment transport shows that the variations in formation time are primarily related to changes in the magnitude of the time-averaged flow conditions. Variations in the magnitude of very low frequency (f < 0.004 Hz) or infragravity (0.004 < f < 0.04 Hz) surf zone flow velocities do not affect the mean sediment transport capacity. Consequently the formation speed of patterns is primarily governed by positive feedback between mean flow and morphology, and low frequency flow fluctuations are of minor importance.These findings indicate that the development of alongshore topographic variability may be faster at swell dominated open coasts, primarily due to the occurrence of longer period swell. Also, at a given site, the arrival of a long wave period swell after a storm can accelerate the emergence of variability.     

Large capacity multi-float configurations for the wave energy converter M4 using a time-domain linear diffraction model

The moored three-float line absorber WEC M4 has been developed to optimise power capture through experiments and linear diffraction modelling. With the progression down wave from small to medium to large floats, the device heads naturally into the wave direction. The bow and mid floats are rigidly connected by a beam and a beam from the stern float is connected to the hinge point above the mid float for power take off (PTO). Increasing the bow to mid float spacing to be more than 50% greater than the mid to stern float spacing has been found to improve power capture. To increase power capture further and potentially reduce electricity generation cost the number of mid floats and stern floats is increased while maintaining a single bow float for mooring connection. The bow and mid floats still form a rigid body while the stern floats may respond independently. A time domain linear diffraction model based on Cummins method has been applied to configurations of 121, 123, 132, 133, and 134 floats where the numbers indicate the number of floats: bow, mid, stern. This shows how power capture is increased while response remains similar. We only consider uni-directional (long-crested) waves with narrow band width typical of swell. By considering scatter diagrams for various offshore sites capacities may range from 3.7 MW to 17.3 MW for the eight float system with a capacity factor of 1/3 while the cost of electricity assuming capital cost to be a fixed multiple of steel cost is reduced from that for the three-float system.     

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.     

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.     

Numerical and experimental study of a flapping foil generator

The energy extraction performance of a flapping foil generator is studied through experiment and numerical simulation. A practical flapping foil generator has been proposed. The heave motion and the pitch motion of the foil are adjusted through a crankshaft-like structure. The heave and pitch motions of the foil are transferred to the rotational motion of the main shaft. A pair of gears is adopted to increase the pitch angle. A prototype with pitch amplitude θ₀ = 60^∘ has been built and the experiment is carried out in a tunnel. The overall performance of the mechanism has been analysed. Good agreement of numerical results and experiment data has been found. Further simulations with larger pitch amplitudes are carried out. It is found that higher efficiency can be achieved with larger pitch amplitude at medium frequency.     

集成波能转换功能的方箱—挡浪板式浮式防波堤水动力特性研究

浮式防波堤与振荡浮子式波浪能转换装置集成是一种较为合理的波浪能开发利用方式,基于方箱式浮式防波堤—波浪能转换集成系统和幕帘式防波堤的研究成果,提出了一种新型方箱—垂直挡浪板式浮式防波堤—波浪能转换集成系统,建立数学模型对该集成系统的水动力特性和能量输出特性进行研究。模型基于N-S方程,采用紧致插值曲线(CIP)方法结合浸没边界法(IBM)求解。运用数值模型探究在一定波浪条件下,动力输出系统(PTO)阻尼力的大小以及挡浪板对集成系统的水动力特性和能量转换特性的影响,得到如下结论:集成系统的俘获宽度比随PTO阻尼力的增大呈现先增大后减小的趋势,在阻尼力F_(PTO)=150 N时达到最大;相对于方箱型集成系统,增设0.1 m挡浪板后可使其最大俘获宽度比η_e提高33%左右;此外,集成系统的俘获宽度比随挡浪板长度增加而增大,增长趋势逐渐变缓,在挡浪板长度S_p=0.5 m时达到最大,此时俘获宽度比η_e=0.563 1。     

Respiration,mineralization, and biochemical properties of the particulate matter in the southern Nansen Basin water column in April 1981

Determinations of the activity of the respiratory electron transport system (ETS), during the FRAM III expedition permit us to estimate oxygen utilization rates (R_O2) from the surface to 2000 m under the polar pack ice in the Nansen Basin just north of Svalbard (83°N, 7°E) during April 1981. We found R_O2 at in situ temperatures ranging from 20 pM O₂ min⁻¹ just below the ice to 0.2 pM O₂ min⁻¹ at 2000 m. These rates are low compared to most other ocean regions, but they could decrease particulate organic carbon and nitrogen by 76% and 74%, respectively, over a period of ∼6 months. The R_O2 calculations based on measurements made at 0 °C yielded a power function of R_O2 vs. depth (Z) of R_O2=67Z^−0.5534. When this R_O2 profile was superimposed on a more recent oxygen utilization rate profile made using the ³He–³H–AOU method (OUR), in the same vicinity of the Nansen Basin during 1987 (OUR=52Z^–0.4058, [Zheng, Y., Schlosser, P., Swift, J.W., Jones, E.P., 1997. Oxygen utilization rates in the Nansen Basin, Arctic Ocean: implications for new production. Deep Sea Research I 44, 1923–1943]), the agreement of the two profiles was close. On one hand, this was to be expected because R_O2 is the biological basis of OUR, on the other hand, it was a surprise because the methodologies are so different. Nitrate mineralization obtained from ETS activities also compared favorably with calculations based on the data of Zheng et al. [1997. Oxygen utilization rates in the Nansen Basin, Arctic Ocean: implications for new production. Deep Sea Research I 44, 1923–1943]. Chlorophyll ranged from 6 ng L⁻¹ at 5 m to 0.06 ng L⁻¹ at 2000 m. Particulate organic carbon (POC) decreased from 0.93 μM C just below the ice to less than 0.4 μM C at 500 m. Particulate organic nitrogen (PON) was not detectable below 70 m, however in the upper 70 m it ranged from 0.16 to 0.04 μM N. The C/N mass ratio over these depths ranged from 5.8 to 11.3. Annual carbon productivity as calculated to balance the total water column respiration was 27 g C m⁻² y⁻¹. The integrated respiration rate between 50 and 4000 m suggests that exported production and carbon flux from the 50 m level was 24 g C m⁻² y⁻¹. These are minimal estimates for the southern Nansen Basin because they are based on measurements made at the end of the Arctic winter.     

Geometry and migration characteristics of bedforms under waves and currents: Part 2: Ripples superimposed on sandwaves

This paper presents results of a series of detailed measurements of geometric and migrating characteristics of ripples superimposed upon sandwaves under the action of combined waves and currents. Velocity measurements within the fluid, surface wave characteristics and 3D mapping of the bottom were recorded with an Acoustic Doppler Velocimeter (ADV), an acoustic water level sensor and a 32 composite element array of sub-aquatic acoustic sensors, respectively. Bottom records were statistically analyzed to obtain height, length and migration rates of ripples. Experiments examined ripple heights and wavelengths for the mobility factors (as defined in Eq. (4)) and the Reynolds wave number within the ranges 10 < ψ < 88 and 16 × 10³ < Re_w < 5 × 10⁵, respectively. Measured values were compared with laboratory and field data together with semi-empirical and analytical formulae from the literature. Good correlation was obtained when plotting measured ripple length and length in dimensionless form as a function of the Reynolds wave number Re_w. Under a given hydraulic condition, it was observed that ripples with different geometric characteristics may coexist at different locations over the sandwave. Ripple steepness is presented as a function of the Shields parameter although characterized with rather large scatter. Finally, average ripple migration speed is presented as a function of the Shields parameter and the mobility number.     

Microbial biomass and viral infections of heterotrophic prokaryotes in the sub-surface layer of the central Arctic Ocean

Seawater samples were collected for microbial analyses between 55 and 235 m depth across the Arctic Ocean during the SCICEX 97 expedition (03 September–02 October 1997) using a nuclear submarine as a research platform. Abundances of prokaryotes (range 0.043–0.47×10⁹ dm⁻³) and viruses (range 0.68–11×10⁹ dm⁻³) were correlated (r=0.66, n=150) with an average virus:prokaryote ratio of 26 (range 5–70). Biomass of prokaryotes integrated from 55 to 235 m ranged from 0.27 to 0.85 g C m⁻² exceeding that of phytoplankton (0.005–0.2 g C m⁻²) or viruses (0.02–0.05 g C m⁻²) over the same depth range by an order of magnitude on average. Using transmission electron microscopy (TEM), we estimated that 0.5% of the prokaryote community on average (range 0–1.4%) was visibly infected with viruses, which suggests that very little of prokaryotic secondary production was lost due to viral lysis. Intracellular viruses ranged from 5 to >200/cell, with an average apparent burst size of 45±38 (mean±s.d.; n=45). TEM also revealed the presence of putative metal-precipitating bacteria in 8 of 13 samples, which averaged 0.3% of the total prokaryote community (range 0–1%). If these prokaryotes are accessible to protistan grazers, the Fe and Mn associated with their capsules might be an important source of trace metals to the planktonic food web. After combining our abundance and mortality data with data from the literature, we conclude that the biomass of prokaryoplankton exceeds that of phytoplankton when averaged over the upper 250 m of the central Arctic Ocean and that the fate of this biomass is poorly understood.     

Biological versus physical processes as drivers of large oscillations of the air–sea CO2 flux in the Antarctic marginal ice zone during summer

The fugacity of CO₂ and abundance of chlorophyll a (Chla) were determined in two long transects from the Polar Front to the Antarctic Continent in austral summer, December 1995–January 1996. Large undersaturations of CO₂ in the surface water were observed coinciding with high Chla content. In the major hydrographic regions the mean air–sea fluxes were found to range from −3 to +7 mmol m⁻² d⁻¹ making these regions act as a sink as well as a source for CO₂. In the total 40-d period, the summation of the several strong source and sink regions revealed an overall modest net source of 0.3 mmol m⁻² d⁻¹, this based on the Wanninkhof (J. Geophys. Res. 97 (1992) 7373) quadratic relationship at in situ windspeed. A simple budget approach was used to quantify the role of phytoplankton blooms in the inorganic carbonate system of the Antarctic seas in a time frame spanning several weeks. The major controlling physical factors such as air–sea flux, Ekman pumping and upwelling are included. Net community production varies between −9 and +7 mmol m⁻² d⁻¹, because of the large oscillations in the dominance of autotrophic (CO₂ fixation) versus heterotrophic (CO₂ respiration) activity. Here the mixed layer depth is the major controlling factor. When integrated over time the gross influx and efflux of CO₂ from air to sea is large, but the net residual air/sea exchange is a modest efflux from sea to atmosphere.