Directional Spreading Function Research Articles

A numerical study of added resistance performance and hydrodynamics of KCS hull in oblique regular waves and estimation of resistance in short-crested irregular waves through spectral method

Research on multidirectional waves is increasing as studies on added resistance advance. In this study, the added resistance of the multidirectional regular waves of the KCS hull was estimated by numerical analysis. The direction of the grid was changed according to the heading angle to consider waves in multiple directions. In addition, the method in which the entire domain moved along the movement of the hull was used without using the overset method to minimize the numerical errors. The added resistance and motion RAOs for each angle and the flow characteristics were compared to support the results. For fluid dynamics, time-averaged stern dynamics pressure, boundary layer, and nominal wake for each heading angle were compared, and differences compared to calm water were also reviewed. Based on the bow quartering sea condition analysis results, the added resistance in long-crested and short-crested irregular wave conditions was estimated using the spectral method. The JONSWAP spectrum was used as the target wave spectrum, and the cos-power type was considered the directional spreading function.

Effects of Directional Wave Spectra on the Modeling of Ocean Radar Backscatter at Various Azimuth Angles by a Modified Two-Scale Method

Knowledge of the ocean backscatter at various azimuth angles is critical to the radar detection of the ocean environment. In this study, the modified two-scale model (TSM), which introduces a correction term in the conventional TSM, is improved based on the empirical model, CMOD5.n. Then, the influences of different directional wave spectra on the prediction of azimuthal behavior of ocean radar backscatter are investigated by comparing the simulated results with CMOD5.n and the Advanced Scatterometer (ASCAT) measurements. The results show that the overall performance of the single spectra of D, A, E, and H18 and the composite spectra of AH18 and AEH18 in predicting ocean backscatter are different at different wind speeds and incidence angles. Generally, the AH18 spectrum has better performance at low and moderate wind speeds, while the A spectrum works better at high wind speed. Nevertheless, the wave spectra have little effect on the prediction of the azimuthal fluctuation of scattering, which is highly dependent on the directional spreading function. The relative patterns of azimuthal undulation produced by different spreading functions are rather different at different wind speeds, but similar under different incidence angles. The Gaussian spreading function generally has better performance in predicting the azimuthal fluctuation of scattering.

Representation of 3-h Offshore Short-Crested Wave Field in the Fully Nonlinear Potential Flow Model REEF3D::FNPF

Abstract Stochastic wave properties are crucial for the design of offshore structures. Short-crested seas are commonly seen at the sites of offshore structures, especially during storm events. A long time duration is required in order to obtain the statistical properties, which is challenging for numerical simulations. In this scenario, a potential flow solver is ideal due to its computational efficiency. A procedure of reproducing accurate short-crested sea states using the open-source fully nonlinear potential flow model REEF3D::FNPF is presented in the paper. The procedure examines the sensitivity of the resolutions in space and time as well as the arrangements of wave gauge arrays. A narrow band power spectrum and a mildly spreading directional spreading function are simulated, and an equal energy method is used to generate input waves and avoid phase-locking. REEF3D::FNPF solves the Laplace equation together with the boundary conditions using a finite difference method. A sigma grid is used in the vertical direction and the vertical grid clustering follows the principle of constant truncation error. High-order discretization methods are implemented in space and time. Message passing interface is used for high performance computation using multiple processors. Three-hour simulations are performed in full-scale at a hypothetic offshore site with constant water depth. The significant wave height, peak period, kurtosis, skewness and ergodicity are examined in the numerically generated wave field. The stochastic wave properties in the numerical wave tank (NWT) using REEF3D::FNPF match the input wave conditions with high fidelity.

A spectral description for extreme sea states offshore Denmark Part II: Directional spreading function

Power spectral density and frequency-dependent directional spreading functions are developed for describing extreme sea state spectra in the Danish sector of the North Sea. The input to the spectral models are the significant wave height, the spectral peak period, the spectral second-moment period, and the circular root-mean-square spreading at the spectral peak frequency. The new spectral functions have been developed from measurements of large sea states, made with a Directional Waverider buoy, at two sites in the Danish sector of the North Sea. This paper describes the new directional spreading function; a companion paper describes the new power spectral density function. The new directional spreading function is based on a simple parameterisation of measured frequency-dependent spreading derived from the Directional Waverider buoys. It is defined in terms of the peak period and significant wave height, with different expressions depending on whether the dominant component in the spectrum is a wind-sea or a swell. A form for a combined wind-sea and swell sea state is also defined. The new spreading function is compared against measurements for the location and found to provide an accurate representation of the spreading estimated from the measurements.

Determination of Spatial-Temporal Characteristics of Sea Wind Waves

The nonlinearity of sea surface waves is an important property of them. Despite the fact that the nonlinearity is weak, it must be taken into account when solving many applied and fundamental problems. In this work, we study the effect of nonlinearity on the space-time structure of sea waves. The results of determining the spatial-temporal structure from the data of measurements by an array of wave sensors and from optical images of the sea surface are compared. It is shown that there is a discrepancy between the wave characteristics determined in different ways. Partially, but not completely, these discrepancies are explained by incomplete consideration of the directional spreading function.

A spectral description for extreme sea states offshore Denmark Part I: Power spectrum

A power spectral density function that describes extreme sea states in the Danish sector of the North Sea is developed. The power spectrum is specified in terms of the parameters: significant wave height, spectral peak period, and spectral second-moment period. The power spectral density function is a modified Torsethaugen spectrum, involving an expression for the peak enhancement factor that is dependent on the inverse of the square root of wave steepness and a high-frequency tail that decays at a rate which is dependent on the significant wave height and the ratio of the peak and second-moment periods. The new function was developed from Directional Waverider data measured at two sites in the Danish sector of the North Sea and validated with data from other sites offshore Denmark, primarily recorded with Saab WaveRadars. A companion paper describes a new directional spreading function, which together with the power spectral density function, provides a description of the complete frequency-direction spectrum of extreme sea states in the Danish sector of the North Sea.

Effects of Ocean Wave Directional Spectra on Doppler Retrievals of Ocean Surface Current

The Doppler shift of microwave radar signal is determined by the relative motion between radar and ocean surface, including contributions from the movement of the radar platform and the wind-wave-induced motion (phase velocity of the resonant Bragg waves and orbital motions of ocean waves that are longer than the Bragg waves) in addition to the ocean surface current. One of the main challenges in ocean surface current retrieval is the accurate estimation of the wind-wave-induced Doppler shift, which needs to be accurately removed from the total Doppler shift to determine the surface current. In this study, we investigate the effects of different wave directional spectra on estimates of the wind-wave-induced Doppler shift using a modulation transfer function (MTF)-based and time-independent Doppler model. Our results show that the wind-wave-induced Doppler shift estimates are highly dependent on the selection of wave spectra and the directional spreading function. This study also confirms the importance of ocean wave spectra parameterization on Doppler estimation of the ocean current. We find that Apel’s spectra model is a more consistent fit to the observations, but the optimal spreading function is wind-speed-dependent.

Wind Direction Inversion Using Shore-Based UHF Radar

Shore-based Ultra-high-frequency (UHF) radars have similar characteristics as the High-frequency (HF) ocean radars, for example, the sea waves generating Bragg resonance are gravity waves. Compared to HF radars, UHF radars are more sensitive to the small changes of sea waves, have finer spatial resolution and measure sea areas closer to the coast, hence are expected to complement the nearshore sensing capacity of HF radars. Two wind direction inversion methods for coastal UHF radars are adopted. One is based on the Bragg peak power ratio and the other is based on the modified Doppler spectrum centroid. The latter is proposed to address the problem that it is often difficult to calculate the Bragg peak power ratio at high wind speeds. In both methods, several models describing the relationship between the Doppler spectrum characteristics and wind direction are used respectively in combination with the least square method to estimate the wind direction with the ambiguity removed. Using the buoy wind sensor data as the ground truth, the results of a three-week experiment demonstrate the feasibility of the two methods. It is also shown that the former method has slightly smaller errors and the latter method applies to a wider range of wind speeds. For both methods, the most recommended model is the one based on the cosine-type directional spreading function with variable spreading parameter, because it has small errors and does not require data fitting.

Directional spreading resolution from point measurements for mixed seas and sea states with frequency dependent spreading

Recently (Adcock and Taylor, 2009) devised a method to estimate the underlying directional spreading from a single point measurement. Subsequently, this method has been successfully applied to sea states with frequency independent directional spreading. In contrast, the present work has applied this method to synthetic sea states generated with an underlying frequency dependent spreading. However, in the application of the method, it was assumed that the underlying sea states have a frequency independent spreading. It was found that applying this method in this manner predicts directional spreading that is close to the spectrally averaged spreading. Re–computing the widely used Velocity Reduction Factor (vrf) based on the predictions from the new method showed that it agreed within ±1.5% with the actual value, showing that a reasonable estimate of the directional spreading can be obtained by the new method even under the restrictive assumption of frequency independent spreading. The major implication of these findings is that, a reasonable estimate of the directional spreading function can be obtained for sea states with complex spreading from a single point measurement even with the assumption of frequency dependent spreading.

Определение функции углового распределения энергии гравитационно-капиллярных волн по данным дистанционного зондирования в СВЧ-диапазоне

Определение функции углового распределения энергии гравитационно-капиллярных волн по данным дистанционного зондирования в СВЧ-диапазоне

Dynamic Response Analysis of a Semi-Submersible Floating Wind Turbine in Combined Wave and Current Conditions Using Advanced Hydrodynamic Models

In this study, advanced hydrodynamic models are proposed to predict dynamic response of a floating offshore wind turbine (FOWT) in combined wave and current conditions and validated by laboratory and full-scale semi-submersible platforms. Firstly, hydrodynamic coefficient models are introduced to evaluate the added mass and drag coefficients in a wide range of Reynolds numbers. An advanced hydrodynamic model is then proposed to calculate the drag force of cylinder in combined wave and current conditions. The proposed model is validated by the water tank tests in the current-only, wave-only and current-wave conditions and is used to investigate the effect of current on the dynamic response of FOWT. Finally, the full-scale semi-submersible platform used in the Fukushima demonstration project is investigated. It is found that the predicted dynamic responses of platform by the proposed hydrodynamic models are improved by the directional spreading function of the sea wave spectrum and show favorable agreement with the field measurement.

Bioinspired Unidirectional Liquid Spreading Channel–Principle, Design, and Manufacture

AbstractLiquid unidirectional spreading without energy input has attracted worldwide attentions owing to its potential applications in various fields. The liquid transfer between the adjacent microcavities on the peristome of Nepenthes alata provides great inspiration in that the concave curvature edge structure has the possibility to induce liquid directional spreading. Herein, the effect of concave curvature edge on liquid spreading is found to be different from that of the solid edge described by the Gibbs inequality condition. In this condition, there exist two liquid transfer states, namely conduction and resistance. Taking the advantages of the concave curvature edge, a new unidirectional liquid spreading channel is designed and fabricated by the traditional machining method, and its liquid directional spreading function is validated. This article provides a theoretical and technical support for the design and fabrication of liquid unidirectional spreading channel without an external energy input.

IRREGULAR WAVE MODELLING WITH CFD IN SULAFJORD FOR THE E39 PROJECT

The E39 project aims at building a continuous ferry-free coastal highway along the west coast of Norway. Sulafjord is one of the fjords where ferries are to be replaced with floating bridges or floating tunnels. The floating structures demand accurate and realistic numerical simulations of the wave propagation and transformation in the fjords. The Norwegian coastline is characterized by dramatic water depth changes and deep water conditions. The coastal water also contains both swells and local wind-generated waves. These conditions, along with series of islands outside the fjords and very irregular coastline, make wave modeling more challenging for this region. Thus, the application of CFD models which provide high-resolution and phase-resolved solutions for complicated wave freesurface is explored. First, the spectral wave model SWAN is used to estimate the wave properties at the inlet of the Sulafjord from offshore wave data. Using the estimated wave data at the inlet as input, a large-scale 3D regular wave CFD simulation is performed using the open-source model REEF3D. Then unidirectional and multi-directional irregular wave CFD simulations are performed to represent a more realistic sea state, using a frequency spectra and a directional spreading function. The statistical properties of the simulated irregular ocean waves at three locations inside the fjord are compared among the CFD simulations and with the spectral wave model. The differences in the simulation results are discussed and studied.

A comprehensive study on ship motion and load responses in short-crested irregular waves

Wave-induced ship motion and load responses are usually investigated on the assumption that the incident waves are long-crested. The realistic sea waves are however short-crested irregular waves. Real practice reveals that the ship motion and load responses induced by short-crested waves are different from those induced by long-crested waves. This paper aims to conduct a comprehensive study on ship motions and loads in different wave fields. For this purpose, comparative studies by small-scale model towing tank test and large-scale model sea trial are conducted to experimentally identify the difference between ship motions and loads in long-crested and short-crested irregular waves. Moreover, the influences of directional spreading function of short-crested waves on ship motions and loads are analyzed by numerical seakeeping calculation. The results and conclusions obtained from this study are of great significance for the further extrapolation and estimation of ship motions and loads in short-crested waves based on long-crested wave response results.

Directional Spreading Function of the Gravity-Capillary Wave Spectrum Derived from Radar Observations

Directional spreading function of the gravity-capillary wave spectrum can provide the high-wavenumber wave energy distribution among different directions on the sea surface. The existing directional spreading functions have been mainly developed for the low-wavenumber gravity wave with buoy data. In this paper, we use radar observations to derive the directional spreading function of the gravity-capillary wave spectrum, which is expressed as the second-order Fourier series expansion. So far the standard form of the second-order harmonic coefficient has not been proposed to correctly unify the gravity and gravity-capillary wave. Our strategy is to introduce a correcting term to replace the inaccurate gravity-capillary spectral component in Elfouhaily’s directional spreading function. The second-order harmonic coefficient at L, C and Ku band calculated by the radar observation is used to fit the correcting term to obtain one at the full gravity-capillary wave region. According to our proposed the directional spreading function, there is a spectral region between the gravity and gravity-capillary range where it signifies the negative upwind–crosswind asymmetry at low and moderate speed range. And this is not reflected by the previous models, but has been confirmed by radar observations. The Root Mean Square Difference (RMSD) of the proposed second-order harmonic coefficient versus the radar-observed one at L, C band Ku band is 0.0438, 0.0263 and 0.0382, respectively. The overall bias and RMSD are −0.0029 and 0.0433 for the whole second-order harmonic coefficient range, respectively. The result verifies the accuracy of the proposed directional spreading function at L, C band Ku band.

Efficient computation of cross-spectral densities in the stochastic modelling of waves and wave loads

A new method is presented for efficient calculation of auto- and cross-spectral densities in the stochastic modelling of ocean waves and wave loads. As part of the short-term response analyses, the method may contribute to more efficient long-term response prediction. Specifically the cross-spectral densities of the first order wave excitation forces are considered, but the method is straightforwardly generalized to other cross-spectral densities, e.g. for wave elevation, wave kinematics or second order loads. The method can be used with any choice of directional spreading function, but special attention is given to the commonly used cos-2s type directional distribution. In addition to the development of the new method, the traditional method using the trapezoidal rule for numerical quadrature is improved by developing an adaptive way of choosing the number of integration points. The accuracy of the adaptive method and the new method is investigated, revealing rapid convergence for both methods. However, the new method appears more robust as it avoids so-called spurious hat errors. When applied to two different pontoon type floating bridges the adaptive method and the new method both achieve a great improvement in computational effort compared to the traditional trapezoidal rule method. When the dimensions of the floating bridge increase, i.e. the number of pontoons and their relative distances increase, the new method is superior with respect to computation time.

Development of a bi-modal directional wave spectrum

Addressing sea state in a coastal region of Gulf of Oman by a directional wave spectrum for the very first time is the main focus of this study. The region encounters wind-sea as well as swell. So, proper modeling of the sea state requires in general a double peak spectral model.The research is firstly conducted to calibrate nondirectional Torsethaugen double peak spectrum for the region by entering the separation frequency; a frequency in which wind-sea and swell parts could be divided. This novel calibration procedure is simple while results in much better outcome. Besides, one has to decide about an appropriate Directional Spreading Function (DSF) for the wind-sea and swell components. Then, nine possible combinations of three well-known DSFs have been investigated and calibrated to provide maximum conformity between observed and modeled directional wave spectra.

Development of Multidirectional Nonlinear Numerical Wave Tank by Naoe-FOAM-SJTU Solver

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.

Laboratory research on effective test area of short-crested waves generated by two-sided segmented wavemakers

The size and shape of the effective test area are crucial to consider when short-crested waves are created by segmented wavemakers. The range of the effective test area of short-crested waves simulated by two-sided segmented wavemakers is analyzed in this paper. The experimental investigation on the wave field distribution of short-crested waves generated by two-sided segmented wavemakers is conducted by using an array of wave gauges. Wave spectra and directional spreading function are analyzed and the results show that when the main direction is at a certain angle with the normal line of wave generators, the wave field of 3D short-crested waves generated by two-sided segmented wavemakers has good spatial uniformity within the model test area. The effective test area can provide good wave environments for seakeeping model tests of various ocean engineering structures in the deep ocean engineering basin.

Development of Multidirectional Nonlinear Numerical Wave Tank by Naoe-FOAM-SJTU Solver

A three-dimensional multidirectional nonlinear numerical wave tank (NWT) based on the Navier-Stokes equations and the Finite Volume Method (FVM) is developed by using the two-phase hydrodynamic flow solver naoe-FOAM-SJTU based on the open source toolbox OpenFOAM. The free surface is capturing with the Volume Of Fluids (VOF). The directional wave including Stokes wave, solitary wave and nonlinear wave are simulated and verified. The multi-directional waves are also simulated with particular wave spectral such as JONSWAP and wave directional spreading function. The obtained numerical results show the capability of the solver to generate different type of multidirectional nonlinear waves accurately. Meanwhile, it implies that the presented NWT can easily extend to model the wave-structures interactions, which will be great help to the offshore structures design.