Multidirectional Wave Field Research Articles

Statistical properties of extreme waves in multidirectional wave fields over complex bathymetry

Statistical properties of extreme waves in multidirectional wave fields over complex bathymetry

Diffraction Separation and Least-Squares Imaging Based on Multiscale and Multidirectional Wavefield and Image Decomposition

Diffraction Separation and Least-Squares Imaging Based on Multiscale and Multidirectional Wavefield and Image Decomposition

Wave-by-wave prediction in weakly nonlinear and narrowly spread seas using fixed-point surface-elevation time histories

The development of accurate, real-time predictive models for weakly nonlinear multidirectional wave fields would enable a significant reduction in the cost of wave energy, when combined with control strategies which use the prediction to increase power absorbed. An existing phase-resolved model for predicting weakly nonlinear long-crested wave fields is extended to sea-states with small spreading. When numerically advancing long-crested waves for prediction in spread seas, optimum prediction with the model is obtained when the waves are propagated at an offset angle (shown to be equal to the standard deviation of the component headings in the underlying sea) to the true mean wave direction. The model further exploits concurrent surface-elevation records from multiple adjacent fixed-point locations to obtain a prediction which is shown to be significantly more accurate than using individual input records. Furthermore, the prediction is unaffected by changes in mean wave direction up to a range of 30°, for a prediction using measurements from three points. The model is tested on both synthetic linear and second-order nonlinear wave fields where the directional and bulk wave statistics are assumed to be known. In the nonlinear case, bound harmonics are first estimated using narrow-band approximations and removed. The resulting linear records are then padded at both ends with half a NewWave-type extension to eliminate the step discontinuity in the records before advancing them in both space and time. The bound harmonics are re-calculated and re-inserted into the prediction signal as a final step, if required. The overall computational cost is very small.

CHANNEL CONCENTRATION AND REFLECTIONS FROM DREDGE CHANNELS

Wave reflections from dredge channels are an important consideration for coastal infrastructure. A physical model study of a proposed development for the Port of Townsville demonstrated that channel reflection, and the relatively poorly understood channel concentration are significant processes that need to be considered in coastal developments. The study showed that channel reflection and channel concentration can significantly transform the local waves, resulting in complex multidirectional wave fields and higher design wave conditions.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/XsKsofNZzvQ

Numerical re-creation of multi-directional waves in a circular basin using a particle based method

Numerical wave basins are a powerful tool for the study of fluid-structure interaction (FSI) problems in coastal and ocean engineering fields. Once well validated, numerical wave basins can offer significant advantages over experimental testing in terms of the number and type of available data-streams, and the associated cost. However, conventional numerical wave tanks tend to be limited to the generation of long-crested conditions, and struggle to properly model large fluid deformations along with wave-induced floating body motions and pressure distribution on structures. Here, for the first time we create, and validate, the short-crested wave fields in a circular wave basin, using a particle-based method to solve the full 3D Navier-Stokes equation. The model is based on the FloWave facility at the University of Edinburgh: the geometry enables the generation of multi-directional waves, and the particle-based-approach enables large fluid deformations to be automatically modelled. Multi-directional waves are generated with differing values of steepness and directional spreading, and simulated surface elevations are compared to experimentally-obtained data.Acceptable agreement is found between measured and modelled surface elevation values. Better performance is confirmed for lower-steepness wave cases; where r2 values of greater than 0.7 are found for all cases, and errors in significant wave height range between −8% and +1%. Greater under-production is found for higher-steepness conditions with a −10% to −16% error in significant wave height. It is concluded that a greater number of particles with smaller radius is required to accurately capture the smaller higher frequency disturbances. It is suggested, however, that as the lower-frequency components are well produced for all cases that the model is already suitable for the majority of FSI problems in both uni- and multi-directional wave fields.

Reverse-time migration using multidirectional wavefield decomposition method

Reverse-time migration has attracted more and more attention owing to the advantages of high imaging accuracy, no dip restriction, and adaptation to complex velocity models. Cross-correlation imaging method is typically used in conventional reverse-time migration that produces images with strong low-frequency noise. Wavefield decomposition imaging can suppress such noise; however, some residual noise persists in the imaging results. We propose a 2D multidirectional wavefield decomposition method based on the traditional wavefield decomposition method. First, source wavefields and receiver wavefields are separated into eight subwavefields, respectively. Second, cross-correlation imaging is applied to selected subwavefields to produce subimages. Finally, the subimages are stacked to generate the final image. Numerical examples suggest that the proposed method can eliminate the low-frequency noise effectively and produce high-quality imaging profiles.

Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf , submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.

Simulation of breaking waves using the high-order spectral method with laboratory experiments: Wave-breaking onset

This study investigates a wave-breaking onset criteria to be implemented in the non-linear potential flow solver HOS-NWT. The model is a computationally efficient, open source code, which solves for the free surface in a numerical wave tank using the High-Order Spectral (HOS) method. The goal of this study is to determine the best method to identify the onset of random single and multiple breaking waves over a large domain at the exact time they occur. To identify breaking waves, a breaking onset criteria based on the ratio of local energy flux velocity to the local crest velocity, introduced by Barthelemy et al. (2017) is selected. The breaking parameter is uniquely applied in the numerical model in that calculations of the breaking onset criteria ratio are not made only at the location of the wave crest, but at every point in the domain and at every time step. This allows the model to calculate the onset of a breaking wave the moment it happens, and without knowing anything about the wave a priori. The application of the breaking criteria at every point in the domain and at every time step requires the phase velocity to be calculated instantaneously everywhere in the domain and at every time step. This is achieved by calculating the instantaneous phase velocity using the Hilbert transform and dispersion relation. A comparison between more traditional crest-tracking techniques shows the calculation of phase velocity using Hilbert transform at the location of the breaking wave crest provides a good approximation of crest velocity.The ability of the selected wave breaking criteria to predict single and multiple breaking events in two dimensions is validated by a series of large-scale experiments. Breaking waves are generated by energy focusing and modulational instability methods, with a wide range of primary frequencies. Steep irregular waves which lead to breaking waves, and irregular waves with an energy focusing wave superimposed are also generated. This set of waves provides a wide range of breaking-wave strengths, types and scales for validation of the model. A comparison of calculations made using HOS-NWT with experimental measurements show that the model is successful at predicting the occurrence of wave breaking, as well as accurately calculating breaking onset time and location.Although the current study is limited to a unidirectional wave field, the success of the wave-breaking model presented provides the basis for application of the model in a multidirectional wave field. By including wave breaking onset with the addition of an appropriate energy dissipation model into HOS-NWT, we can increase the application range of the model, as well as decrease the occurrence of numerical instabilities that are associated with breaking waves in a potential flow solver. An accurate description of the wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures and the general physics of ocean waves, for example.

Role of the basin boundary conditions in gravity wave turbulence

Gravity wave turbulence is investigated experimentally in a large wave basin in which irregular waves are generated unidirectionally. The roles of the basin boundary conditions (absorbing or reflecting) and of the forcing properties are investigated. To that purpose, an absorbing sloping beach opposite the wavemaker can be replaced by a reflecting vertical wall. We observe that the wave field properties depend strongly on these boundary conditions. A quasi-one-dimensional field of nonlinear waves propagates towards the beach, where they are damped whereas a more multidirectional wave field is observed with the wall. In both cases, the wave spectrum scales as a frequency power law with an exponent that increases continuously with the forcing amplitude up to a value close to $-4$. The physical mechanisms involved most likely differ with the boundary condition used, but cannot be easily discriminated with only temporal measurements. We also studied freely decaying gravity wave turbulence in the closed basin. No self-similar decay of the spectrum is observed, whereas its Fourier modes decay first as a time power law due to nonlinear mechanisms, and then exponentially due to linear viscous damping. We estimate the linear, nonlinear and dissipative time scales to test the time scale separation that highlights the important role of a large-scale Fourier mode. By estimation of the mean energy flux from the initial decay of wave energy, the Kolmogorov–Zakharov constant of the weak turbulence theory is evaluated and found to be compatible with a recently obtained theoretical value.

Conservation of energy for non-dissipative water waves

In this paper Reynolds transport theory is applied to obtain energy conservation equation (ECE). Depth integrated ECE is derived considering a control volume extended over water depth. It is demonstrated that mild slope equation (MSE) is derivable from depth integrated ECE for linear waves. Two equations are derived by separating real and imaginary parts of depth integrated ECE for multidirectional wave fields that can properly deal with reflecting waves. Geometrical optics equations, derived for non-reflecting waves, can be obtained from aforementioned equations as well. Depth integrated ECE is averaged over a wave period for monochromatic waves. The result is similar in form to energy transport equation (ETE) governing spectral wave models. The terms of energy density and energy flux, obtained here, are more accurate expressions, comparing to those of ETE. It should be mentioned that ETE is also obtained from ECE, the general form derived here. The strength of newly derived equations in dealing with reflective wave fields has been illustrated by simple numerical computations. In this research MSE has been derived by the new presented method. Besides, coupled equations for multidirectional waves as well as time averaged depth integrated ECE have also been obtained through mentioned new approach.

Effect of Asymmetric Directional Spreading on the Total Radiation Stress

AbstractThe process of wave refraction in nearshore zones can result in an asymmetric directional distribution of spectral energy when oblique, multi-directional wave fields propagate into shallow water areas. Here the effect of this directional asymmetry on the net wave-induced radiation stresses is analyzed. The net radiation stresses are calculated for a shoaled JONSWAP frequency spectrum with both symmetric and asymmetric directional distributions and then compared with those calculated from the commonly-used monochromatic formulation (appropriate for spectra that are narrow-banded in frequency and directions). Past studies have demonstrated that the use of the monochromatic approximation in radiation stress calculations results in a significant overestimation of the radiation stress components Sxx and Sxy in broad-banded seas. The present results show that the inclusion of directional asymmetry in radiation stress calculations reduces this overestimation for Sxx but increases the overestimation for S...

Instability of nonlinear standing waves in front of a vertical wall

The standing waves formed in front of a vertical breakwater in Gdansk North Port Harbour are examined. To simplify the wave-structure interaction problem, a laboratory experiment and mathematical model were designed. Standing waves in a limited space were generated under resonance conditions between a vertical wall and wave generator. Such slowly growing standing waves eventually become unstable and, consequently, create an impact impulse on the vertical wall. The dynamics of the vertical wall and hydrodynamics of the standing wave were measured and compared with a numerical model derived by variational calculus. The phenomenon of standing wave instability observed in nature was reproduced by laboratory experimentation and numerical simulation. The presented mechanism of breaking standing waves is more complicated in reality due to wave randomness and the multidirectional wave field.

Diffraction–radiation of multiple floating structures in directional waves

The dynamics of multiple floating structures have been studied using the finite element method. The emphasis is on the hydrodynamic behaviour of multiple bodies under a multi-directional wave field. A two-dimensional numerical model has been adopted to evaluate hydrodynamic coefficients and forces in an oblique wave field. The responses in sway, heave and roll modes are reported. The linear filter technique is then used to extrapolate the responses under directional waves. The effect of mean wave direction and directional homogeneity on the hydrodynamic behaviour of the structure is studied. Based on the present study, it is found that the two-dimensional model is applicable to investigate the wave-structure interaction problems of the type herein considered.

A locally nonlinear interpretation of PUV measurements

A time domain method is presented for analyzing simultaneous measurements of pressure and the horizontal components of velocity obtained beneath irregular multidirectional wave fields. This new method differs from the usual linear directional analyses applied to PUV data in two important aspects. First, the essential nonlinearity of the measured waves is not sacrificed to achieve a solution. Therefore, predictions of sea surface elevation and directional kinematics throughout the water column accurately portray the actual nonlinear character of the waves. Second, the analysis method is `local' in that it can be applied to segments of PUV time series much shorter than an individual wave. The viability of the locally nonlinear methodology developed in this paper is proven by demonstrating agreement with higher-order theoretical steady waves. Predictions of sea surface elevation and wave kinematics are also made using actual measurements from PUV instruments at two ocean sites off the west coast of the United States.

The hydrodynamic behaviour of long floating structures in directional seas

The diffraction/radiation boundary value problem arising from the interaction of oblique waves with freely floating long structures is studied using finite-element techniques. Further, the hydrodynamic behaviour of two-dimensional horizontal floating structures under the action of multi-directional waves has been studied. The linear transfer function approach is used to determine the wave exciting forces and motion responses of a structure of finite length in short-crested seas. The directional spectrum is obtained from a unidirectional spectrum with an associated frequency-dependent or frequency-independent cosine power-type energy spreading function. Based on the numerical predictions, the motions and forces on a rectangular floating structure experiencing unidirectional and multi-directional wave fields are computed.