Small Wave Heights Research Articles

Ship Vertical Loads From Using an Adaptive Mesh Pressure Integration Technique for Froude–Krylov Forces Calculation

Dynamic vertical bending moments are determined for a military vessel hull in still water and under head waves, with a weakly nonlinear method. The domain for hydrostatic and undisturbed pressures integration is time-variant and generated with a quad-tree adaptive mesh algorithm, on which exact formulations for pressure on polygonal elements are used. Linear radiation and diffraction pressures, on another mesh superimposed with the aforementioned one, are calculated with a frequency domain code. Results are compared with published experimental ones for small and large wave heights.

Coupled aerodynamic and hydrodynamic response of a long span bridge suspended from floating towers

The present study introduces a fully coupled time-domain analysis of a multi-span suspension bridge supported by two floating towers, considered for crossing the wide and deep fjords along the west coast of Norway. The time-domain analysis is performed with a finite element model considering simultaneously the turbulent wind, irregular inhomogeneous ocean waves and sheared ocean current. The numerical results suggest that under extreme conditions with a return period of 100 years, the bridge horizontal response is dominant and governed by the low-frequency modes. For the vertical and torsional responses, the largest contributions are due to the respective motion components of the low-frequency horizontal motion-dominated modes. The investigation into the significance of the aerodynamic and hydrodynamic load reveals that in the case studied, over 80% of the bridge girder response is due to the aerodynamic excitation. The hydrodynamic loads acting on the floating towers are small due to a relatively small significant wave height in the fjord and the counteracting aerodynamic damping effect. By considering the inhomogeneity of the waves, i.e. different conditions at the two floating supports, the contribution of the aerodynamic action to the lateral, vertical and torsional dynamic responses increases by 6%, 7% and 9% respectively.

Numerical simulation of wave transformation over platform reef using SPH method

Different from the fringing reef along the coastal beach, the reef face of the deep-sea platform reef is very steep and the water depth varies rapidly from a few thousand meters at the reef toe to a few meters at the reef edge. The special geomorphology of the deep-sea platform reef makes its hydrodynamics much different from that of the fringing reef with a gentle reef-face. Besides, the wave-generated flow induced by wave breaking has a great influence on sediment movement, nutrient transport and habitats for marine organisms on the reef flat. Therefore, the knowledge of the hydrodynamics of the deep-sea platform reef is of great importance to guide the subsequent development and protection of the deep-sea platform reefs. An improved smoothed particle hydrodynamic (SPH) model using the periodic boundary conditions and a water circulation technology as well as a non-reflected momentum source wave maker is developed to study wave transformation over the deep-sea platform reef. The Favre average N-S equations along with the sub-particle scale (SPS) turbulence closure model are employed as the governing equations to describe the wave motion. The idealized model of the platform reef is composed of a reef face with a slope of 1:1 and a horizontal reef flat. To verify the SPH model, the corresponding physical model tests are also carried out in the nonlinear wave flume of the state key laboratory of coastal and offshore engineering, Dalian university of technology. A good agreement is obtained between the numerical and experimental results, which indicates the present SPH model can accurately simulate wave transformation over the deep-sea platform reef and that it also can reasonably capture the spatial distributions of wave height and wave set-up on the reef flat. In addition, the unphysical rise and fall of the water level in the lagoon and the ocean due to the overtopping on the reef-flat, which usually occur for the long-time simulation using the vertical 2D numerical model, can be overcome by using the periodic boundary condition and a water flow circuit instead of the solid boundary condition to simulate the left and right boundaries of the flume. The wave height decay tempestuously due to wave energy dissipation by wave breaking. As observed both in the physical and numerical tests, wave breaking occurs on the reef-face or the reef-rim at the low water levels and emerges over the reef-rim or the reef-flat at the high water levels. For the coral reef with a gentle reef-face, the previous studies pointed that the basic type of wave breaking at the reef-rim is collapsing for a small relative wave height ( H / h r) and is plunging for a large relative wave height. While for the coral reef with a very steep reef-face focused in the present study, collapsing wave is the main type of wave breaking at the reef-rim as observed both in the physical and numerical tests.The wave height after breaking decreases dramatically and the broken wave propagates along the reef-flat as a bore-like wave, and the amplitude of wave setup is almost constant along the reef-flat.

Numerical study on overtopping performance of a multi-level breakwater for wave energy conversion

Overtopping wave energy converter (OWEC) is capable of converting the unstable wave energy into the relatively stable potential energy in its reservoir. The small wave height and the large tidal range in China will cause a lower efficiency of the traditional single-level overtopping device especially at the lower tidal level. The design of the multi-level reservoirs may be a solution to improve the overtopping performance, which can be integrated in the sloping-ramp breakwater. In this study, a multi-level breakwater for wave energy conversion, consisting of two reservoirs with sloping walls at different levels, is proposed. A numerical wave tank based on the VOF model is established in ANSYS-Fluent® 12.0 for the OWEC's performance investigation. The numerical model on predicting the overtopping process and time-averaged discharges is validated by corresponding experimental data. Effects of the opening width of the lower reservoir, sloping angles of two reservoirs and the gap height between the reservoirs on the dimensionless overtopping discharges are studied numerically. It is found that a smaller opening width, larger height ratio, and two sloping angles of 30° have positive effects to improve the overtopping performance of the device.

Uncertainty and sensitivity of wave-induced sea surface roughness parameterisations for a coupled numerical weather prediction model

The impact of wave-induced sea surface roughness (SSR) parameterisation methods on tropical cyclone (TC) forecasts in a coupled numerical weather prediction (NWP) model is investigated by comparing the results of sensitivity experiments. A wind-dependent SSR parameterisation as a control experiment and five wave-induced SSRs parameterised by wave age, wave steepness, wave-induced stress, and input wave age, which are the most commonly used to estimate the air–sea exchange coefficients, are used in our comparative sensitivity experiments. In this study, we clearly show the magnitude of uncertainties given by the different choice of roughness parameterisations. Our results show that the choice of SSR parameterisation has a considerable influence on the atmospheric boundary layer and wave conditions, leading to a significant difference in both the forecast of TC intensity and the wave fields. The air-sea momentum and enthalpy transports are modified by the differences in exchange coefficients between the various SSR parameterisation methods, which result in differences in frictional convergence, and variation in the amount of energy input to the TC, thus changing the TC intensity. This process is linked to the alteration of the wind fields and then the wave fields. Comparison of observation data with the results obtained via several SSR parameterisation methods indicates that wind speed, and consequently energy transfer to the waves, is reduced by increased SSR, resulting in smaller wave heights. In addition, the increased SSR produces enhanced turbulent heat flux and rainfall rates by inducing an increase in thermal and moisture exchange coefficients.

Experimental study on multi-level overtopping wave energy convertor under regular wave conditions

A multi-level overtopping wave energy converter was designed according to the large tidal range and small wave heights in China. It consists of two reservoirs with sloping walls at different levels. The reservoirs share a common outflow duct and a low-head axial turbine. The experimental study was carried out in a laboratory wave-flume to investigate the overtopping performance of the device. The depth-gauges were used to measure the variation of the water level in the reservoirs. The data was processed to derive the time-averaged overtopping discharges. It was found that the lower reservoir can store wave waters at the low water level and break the waves which try to climb up to the upper reservoir. The upper sloping angle and the opening width of the lower reservoir both have significant effects on the overtopping discharges, which can provide more information to the design and optimization of this type of device.

Experimental and numerical investigations on the intact and damage survivability of a floating–moored oscillating water column device

This paper investigates the intact and damage survivability of a floating–moored Oscillating Water Column (OWC) device using physical model experiments and Computational Fluid Dynamics (CFD) simulations. Different extreme wave conditions have been tested using irregular and regular wave conditions. The device was moored to the tank floor via four vertical taut lines and the effect of the mooring line pre–tension on the device response was studied. It was found that the instantaneous position of the floating device was a key factor in the survivability analysis such that a certain irregular wave train that might not include the largest wave could induce the maximum response. Reducing the pre–tension minimized the maximum surge, but significantly increased the maximum tension due to mooring slack events causing snatch loads. A design regular wave with a period equal to the peak period and a height of 1.9–2.0 times the significant wave height could reasonably predict the same maximum line tension as the irregular sea state, but a smaller wave height was required to achieve the maximum surge. A single failure in the mooring system increased the maximum tension by 1.55 times the intact tension. For a damaged mooring system, using the same design regular wave condition derived from the survivability analysis with an intact mooring system could result in overestimating the maximum tension by more than 20% in comparison to the tension from the irregular sea state, but a smaller regular wave height or a different regular wave condition representing another sea state could lead to the same maximum tension. This highlighted the importance of investigating survival conditions with a damaged mooring system instead of simply using the same conditions derived for the intact mooring system.

Experimental modeling of horizontal and vertical wave forces on an elevated coastal structure

A large-scale physical model was created in Oregon State University's Large Wave Flume to collect an extensive dataset measuring wave-induced horizontal and vertical forces on an idealized coastal structure. Water depth was held constant while wave conditions included regular, irregular, and transient (tsunami-like) waves with different significant wave heights and peak periods for each test. The elevation of the base of the test specimen with respect to the stillwater depth (air gap) was also varied from at-grade to 0.28 m above the stillwater level to better understand the effects of raising or lowering a nearshore structure on increasing or decreasing the horizontal and vertical wave forces. Results indicate that while both horizontal and vertical forces tend to increase with increasing significant wave height, the maximum and top 0.4% of forces increased disproportionally to other characteristic values such as the mean or top 10%. As expected, the horizontal force increased as the test specimen was more deeply submerged and decreased as the structure was elevated to larger air gaps above the stillwater level. However, this trend was not true for the vertical force, which was maximized when the elevation of the base of the structure was equal to the elevation of the stillwater depth. Small wave heights were characterized by low horizontal to vertical force ratios, highlighting the importance of considering vertical wave forces in addition to horizontal wave forces in the design of coastal structures. The findings and data presented here may be used by city planners, engineers, and numerical modelers, for future analyses, informed coastal design, and numerical benchmarking to work toward enabling more resilient nearcoast structures.

Trapping mechanism for long waves over circular islands with power function profiles

Long waves such as tsunamis can be trapped by islands due to wave refraction, and these trapped waves will cause huge damage even in the sheltered shoreline of the island. That all waves propagating into the topography and finally reaching the coastline are called perfect trapped modes, while any waves escaping from the topography are called leaky modes. Whether these long waves can be trapped is dependent on the depth profile of the island. This paper presents analytic solutions of the ray path for waves propagating into the circular island with power function profiles. Wave height distributions over the island are further investigated based on the principia that crowded rays correspond to large wave height and sparse rays correspond to small wave height. The trapped mechanism for water waves over the island is revealed based on their ray paths. Furthermore, the perfectly trapped criterion is derived, that is, when the slope gradient at the topography toe is greater than twice the ratio of the water depth to the radial distances, all wave rays propagating on the island will finally reach the coastline, and the waves are perfectly trapped.

Linear diffraction analysis of the three-float multi-mode wave energy converter M4 for power capture and structural analysis in irregular waves with experimental validation

A frequency domain dynamic model based on the DIFFRACT code has previously been applied to the moored, three-float, multi-mode wave energy converter M4 in regular waves, modelled as a two-body problem, showing good agreement of relative rotation and power capture with experiments for small wave height (Sun et al., 2016 J Ocean Eng Mar Energy 2(4):429–438). The machine has both a broad-banded and relatively high capture width for the range of wave periods typical of offshore sites. The float sizes increase from bow to stern facilitating alignment with the local wave direction; the bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the relative rotation is damped to absorb power. The floats are approximately half a representative wavelength apart so the float forces and motion in anti-phase generate relative rotation. The mid and stern floats have hemispherical and rounded bases giving negligible drag losses. Here the multi-body model is generalised to enable bending moment prediction in the beams and by including excitation by irregular wave fields with and without directional spreading. Responses are compared with experiments with input wave spectra of JONSWAP type. In uni-directional waves, the measured spectra were a close approximation to the target JONSWAP spectra and were input into the model giving excellent predictions of relative rotation and bending moment in all cases and slight overprediction of power. Predictions of bending moment in regular waves were surprisingly somewhat less accurate. With multi-directional waves the measured wave spectra did not match the target JONSWAP spectra as well, particularly for smaller periods, and the directional spreading was not measured. However with the target spreading function and the measured spectra input to the model the predictions were again excellent. Since the model is validated for uni-directional waves it seems likely that it will also be valid in multi-directional waves and the accurate predictions thus suggest that the actual spreading was indeed close to the target. The model indicates that realistic directional spreading can reduce power capture by up to about 30%. However, optimising the damping coefficient in the linear damper can increase power capture by a similar amount, and optimising the vertical hinge position can increase this further although this cannot be varied in situ. Power optimisation is inevitably less marked than with regular waves. Good agreement with experiment is thus achieved for small to moderate wave heights (about twice average) at typical full scales, indicating that this efficient frequency domain method is valuable for fatigue analysis and energy yield assessment. Accurate prediction based on linear diffraction theory in steep or extreme waves is however not expected.

Low-frequency propagation and noise in the intertidal zone

Measurements of ambient noise and short-range propagation (<2m) were made in the intertidal zone with water depths ranging from 50 to 80 cm using vector sensors. The sites selected for the measurements were known nesting areas for plainfin midshipman (Porichthys notatus). Males of this species produce continuous acoustic advertisement calls with fundamental frequencies in the 70 to 100 Hz range. The temporal and spectral structure of these calls must convey information regarding the source’s range, direction, and/or fitness over the maximum detectable range in a complex environment. Both fundamental and harmonic components appear to be above a rapid low-frequency increase in the noise floor due to local wave motion and below the frequency range of several observed noise transients at times with modest wind speeds (<5 mph) and small wave heights (<20cm). There is little evidence of significant propagation differences between specific frequencies within the band of interest.

Linear diffraction analysis for optimisation of the three-float multi-mode wave energy converter M4 in regular waves including small arrays

A general frequency domain dynamic model based on the DIFFRACT code has been developed to predict the motion and power generation of the three-float multi-mode wave energy converter M4, modelled as a two-body problem. The machine has previously been shown experimentally and numerically to have broad-band high capture widths for the range of wave periods typical of offshore sites. The float sizes increase from bow to stern; the bow and mid float are rigidly connected by a beam and the stern float is connected by a beam to a hinge above the mid float where the rotational relative motion is damped to absorb power. The floats are approximately half a wavelength apart so the float forces and motion in antiphase generate relative rotation. Here regular waves representative of swell are investigated and the model is shown to give accurate predictions of experimental results for motion and power for small wave heights and motion which are representative of operational conditions. A linear damper is used to model the power take-off. Without changing the float geometry or the hinge position, adjusting the linear damping factor for each frequency is shown to increase the power by up to three times the experimental value, with a maximum close to the theoretical value for a single float. Increasing the height of the hinge point above the mid float increases the power for the higher periods but can reduce power at lower periods. Since float motion can be quite large, this result can only be indicative of qualitative trends. The effect of small rows has been investigated, up to five machines, and it is shown in particular how the performance of wave energy devices in a row was affected by the multi-body interactions and wave directions. These results are important since the optimum damping factor is shown to be frequency dependent, and increase power generation by up to three times. Furthermore, hydrodynamic interference between M4 machines in a row may significantly increase the power generation when appropriate spacings are chosen.

Initial spreading of a mega feeder nourishment: Observations of the Sand Engine pilot project

Sand nourishments are a widely applied technique to increase beach width for recreation or coastal safety. As the size of these nourishments increases, new questions arise on the adaptation of the coastal system after such large unnatural shapes have been implemented. This paper presents the initial morphological evolution after implementation of a mega-nourishment project at the Dutch coast intended to feed the surrounding beaches. In total 21.5millionm3 dredged material was used for two shoreface nourishments and a large sandy peninsula. The Sand Engine peninsula, a highly concentrated nourishment of 17millionm3 of sand in the shape of a sandy hook and protruding 1km from shore, was measured intensively on a monthly scale in the first 18months after completion. We examine the rapid bathymetric evolution with concurrent offshore wave forcing to investigate the feeding behaviour of the nourishment to the adjacent coast. Our observations show a large shoreline retreat of O (150m) along the outer perimeter of the peninsula, with locally up to 300m retreat. The majority (72%) of the volumetric losses in sediment on the peninsula (1.8millionm3) were compensated by accretion on adjacent coastal sections and dunes, confirming the feeding property of the mega nourishment. Further analyses show that the morphological changes were most pronounced in the first 6months while the planform curvature reduced and the surf zone slope flattened to pre-nourishment values. In the following 12months the changes were more moderate. Overall, the feeding property was strongly correlated to incident wave forcing, such that months with high incoming waves resulted in more alongshore spreading. Months with small wave heights resulted in minimal change in sediment distribution alongshore and mostly cross-shore movement of sediment.

Amplitude and Dilation Compensation of the SAR Altimeter Backscattered Power

A new method of forming the synthetic aperture radar altimeter multilook backscattered power waveform is proposed for application over water. The method compensates the waveform for both variations in amplitude and dilation in range, which are caused by the geometry of the observation and the signal processing chain of the instrument. Using Cryosat data collected over the Pacific Ocean and over the Black Sea, the method is used to retrack the geophysical parameters of sea surface height and significant wave height, and the noise level of these retracked parameters is compared with the noise levels of conventionally retracked parameters. It is found that applying amplitude compensation and dilation compensation leads to a reduction in the noise level by up to a factor of 4.0 for sea surface height and 2.5 for significant wave height. The reduction in noise is largest for small significant wave heights. In addition, the waveform is accurately modeled by a single argument function, needing only a scaling and offset to fit the multilook waveform, greatly improving the theoretical description of the waveform dependence on the sea state and instrument parameters.

Dynamics of rip currents associated with groynes — field measurements, modelling and implications for beach safety

Rip currents can occur around groynes and other coastal structures (e.g. breakwaters and geological headlands), which provide a boundary to the wave-induced flow field and present a hazard to water users worldwide. Shore-normal groynes are common along drift-aligned coasts. In northern Europe these are often low-energy, fetch-limited environments that are dominated by locally generated wind waves. The presence of boundary-controlled rip currents due to groynes is supported anecdotally in literature, but few field measurements of their presence and dynamics exist. This study provides new quantitative scientific understanding of the dynamics of boundary-controlled rip currents within this setting. A 10-day field experiment at Boscombe beach on the south coast of England measured rip currents and nearshore hydrodynamics around an impermeable groyne field. Observations from both fixed instruments (wave, tide and current metres) and GPS-drifters confirmed the presence and characteristics of hazardous topographic rip currents around a groyne structure during a number of oblique wave events and drift reversals. The strongest offshore-directed rip velocities of up to 1ms−1 (10-min average) and 2ms−1 (instantaneous) were measured on the updrift side of the groyne where the longshore current generated within the embayment was deflected offshore. These strong rip flows were measured under relatively small wave heights (Hs<1m) and presented a significant bathing hazard. A calibrated and validated numerical model (XBeach) was used, in support of measured data, to explore the key environmental controls on rip behaviour across a range of groyne configurations and wave conditions not observed in the field. Key outcomes were that: 1) upstream deflected rip flows were found to be strongly correlated to the alongshore thrust due to wave forcing; 2) the groyne length relative to surf zone width strongly controlled the offshore extent of rip flows, with a significant increase in surf zone exits above a relative groyne length (length/surf width) of 1.25; and 3) rip flows increase up to a relative groyne spacing (spacing/length) of around 4–6, above which alongshore currents are fully developed. These findings have been distilled into some key principals that are relevant to the assessment of boundary-controlled rip hazard on beaches.

Establishment of Motion Model for Wave Capture Buoy and Research on Hydrodynamic Performance of Floating-Type Wave Energy Converter

Abstract Floating-type wave energy converter has the advantages of high wave energy conversion efficiency, strong shock resistance ability in rough sea and stable output power. So it is regarded as a promising energy utilization facility. The research on hydrodynamic performance of wave capture buoys is the precondition and key to the wave energy device design and optimization. A simplified motion model of the buoys in the waves is established. Based on linear wave theory, the equations of motion of buoys are derived according to Newton’s second law. The factors of wave and buoys structural parameters on wave energy absorption efficiency are discussed in the China’s Bohai Sea with short wave period and small wave height. The results show that the main factor which affects the dynamic responses of wave capture buoys is the proximity of the natural frequency of buoys to the wave period. And the incoming wave power takes a backseat role to it at constant wave height. The buoys structural parameters such as length, radius and immersed depth, influence the wave energy absorption efficiency, which play significant factors in device design. The effectiveness of this model is validated by the sea tests with small-sized wave energy devices. The establishment methods of motion model and analysis results are expected to be helpful for designing and manufacturing of floating-type wave energy converter.

Theoretical study on the power take-off estimation of heaving buoy wave energy converter

Heaving buoy wave energy converter is applicable to small wave height and short wave period, which are the main characteristics of the China Sea. The device captures the wave power by buoy's heaving motion, transfers it by hydraulic system, and converts it into the electric power by generator. Power Take-Off (PTO) of the device is related to the resistance of the hydraulic system. However, effects of the hydraulic damping on the motion of buoy are often neglected and the study on the optimal hydraulic system is rare. In this paper, a new theoretical analysis has been developed, which is more applicable to the buoy considering hydraulic system. The paper establishes the governing equation considering buoyancy, wave dynamic force and hydraulic damping. The displacement and the velocity of the buoy are both obtained. The time-averaged power captured is calculated by integrating the square-velocity expression derived, and the existence of the maximum PTO is proved. Theoretical result is compared with the experimental result. The paper demonstrates the displacements and average output power of the buoy with different values of damping and inertia coefficients. The results of the study could be a guidance for the PTO design of the heaving buoy sets.

Mechanical behavior analysis for the determination of riser installation window in offshore drilling

The purpose of this paper is to figure out the safety operation window of riser in installation through taking three kinds of mechanical behavior. In this paper, the sea surface current velocity, surface wind velocity, wave height and wave period are taken as the evaluation factors of marine environment. The fleet angle at riser top section, the Mises equivalent stress on riser critical section, the axial dynamic load on riser bottom section and the riser transverse resonance are considered as the limiting factors which restrains the further complicacy of marine environment. Results show that the wave height and wave period mainly affect the lateral vibration frequency and the dynamic load. The sea surface wind velocity and sea surface current velocity determines the fleet angle and the Mises equivalent stress. However, compared with the fleet angle, the maximum equivalent stress is the main influence factor which limits the installation operation window. In general, under the circumstance of avoiding transverse resonance, smaller wave height and longer wave period are good for marine riser installation. The research has some reference value for safe and effective installation of marine riser.

Surface Wave Measurements from Subsurface Floats

AbstractPressure gradient measurements on a subsurface Lagrangian float are used to measure the spectrum of surface waves for 100 days of measurements at Ocean Weather Station Papa. Along Lagrangian trajectories of surface waves, the pressure is constant and the vertical pressure gradient fluctuations equal the Eulerian fluctuations at the mean float depth to second order in wave height. Measurement of the pressure difference between the top and the bottom of the float can thus be used to measure the waves. Corrections for the wave decay with depth, for the vertical motion of the float, for the finite sampling interval, and for the sampling noise (among others) are necessary to obtain accurate results. With these corrections, scalar spectra accurately match those from a nearby Waverider buoy for significant wave heights greater than about 3 m. For smaller wave heights, noise in the pressure measurements biases the float spectral measurements. Significant wave height is measured with an rms error of 0.37 m over the measured range of 1–9 m. This demonstrates that Lagrangian floats accurately follow the Lagrangian trajectories of surface waves. More detailed and quieter measurements of float motion could likely measure directional wave spectra from below the surface. Similar methods could be used to infer surface wave properties from other subsurface vehicles.

Numerical Modeling of Nearshore Wave Conditions at Al Huwaisat Island, KSA

A wave study was carried out around Al Huwaisat Isalnad, KSA to establish the characteristics of waves there. A wave generation/transformation model that takes into consideration: wave generation/growth by wind and wave transformation due to: wave shoaling, wave refraction, bottom dissipation, wave blocking, wind generation, wave braking, frequency spreading, directional spreading, wave-wave interaction,and wave current interaction. The input data to the model consisted of ships’ observation wave and wind data covering a period of 49 years and seabed levels obtained from a recent bathymetric survey and admiralty chart. The results of the model showed that the wave climate around Al Huwaisat Island is mainly governed by waves generated locally by wind rather than waved approaching from the offshore and transformed across the seabed configuration and other transforming factors. Such waves show the typical characteristics of wind generated waves over shallow seabed, i.e. small wave heights and periods.