Random Wave Field Research Articles

Reference-less complex wavefields characterization with a high-resolution wavefront sensor

Wavefront sensing is a widely used non-interferometric, single-shot, and quantitative technique providing the spatial-phase of a beam. The phase is obtained by integrating the measured wavefront gradient. Complex and random wavefields intrinsically contain a high density of singular phase structures (optical vortices) associated with non-conservative gradients making this integration step especially delicate. Here, using a high-resolution wavefront sensor, we demonstrate experimentally a systematic approach for achieving the complete and quantitative reconstruction of complex wavefronts. Based on Stokes' theorem, we propose an image segmentation algorithm to provide an accurate determination of the charge and location of optical vortices. This technique is expected to benefit to several fields requiring complex media characterization.

Experimental investigations on wave impact pressures under the deck and global wave forces and moments on offshore jacket platform for partial and full green water conditions

The wave induced dynamic pressures under the deck and the global wave forces and moments on an offshore platform model were measured for three different model orientations and for partial and full green water conditions in random wave fields of different energy levels. It is found that for partial and full green water conditions, the global vertical wave force dominates when compared to horizontal wave forces. The orientation of the structure to wave direction has some effect, only for 22.5° orientation of the deck to wave direction. Shoreward maximum wave force can reach 3 times the maximum seaward wave force. For zero air gap condition, the highest value of normalized peak vertical force can reach a value of 42, which is 5 times higher than the normalized significant uplift force value. The normalized downward peak force value can reach as high as 8 for full green water condition due to the weight of overrunning water staying on the top of deck slab. For zero air gap condition, the normalized peak impact pressure under the deck can reach as high as 13.2 and 21.5 near the leading and trailing bottom side of the deck.

The influence of finite depth on the evolution of extreme wave statistics in numerical wave tanks

Model tests with unidirectional random wave fields are common for coastal engineering purposes. In this paper, we investigate the finite water depth effect on both the probability of extreme events and the averaged shape of them in such experimental conditions. We simulate some typical model test conditions with a numerical tool, which solves the fully non-linear wave equations. We find the analytical solution based on Nonlinear Schrödinger equation (NLS) to be accurate for low steepness and relatively deep water cases. However, the analytical solution underestimates the kurtosis at the steady state for high steepness cases in shallow water, and also gives zero value of kurtosis at critical water depth, whereas a small but non-zero value of kurtosis is observed in the numerical tank. We also investigate the averaged shape of the extreme events, which are modified by nonlinear physics over the distance. The horizontal asymmetry is significant initially but is greatly reduced to a steady state, and the contraction of the wave groups grows monotonically until the steady state is reached along the wave tank. Finite water depth has limited effects on the averaged shape of large events, especially for the extremely steep waves.

Surface Currents and Significant Wave Height Gradients: Matching Numerical Models and High‐Resolution Altimeter Wave Heights in the Agulhas Current Region

AbstractAdvances in the understanding and modeling of surface currents have revealed the importance of internal waves, mesoscale and submesoscale features. Indeed, all these features should have a large influence on wind waves and in particular on wave heights. Still, the quantitative impact of currents on waves is not well known due to the complexity of the random wavefields and currents that are found in the ocean and the lack of observations of both currents and waves at scales shorter than 150 km. Here, we compare novel satellite altimetry data and state of the art phase‐averaged numerical wave models forced both by wind and currents. Currents used are taken from the oceanic model Coastal and Regional Ocean COmmunity, run at high resolution. The influence of current field resolution is investigated by applying Gaussian filters of different width to that same high‐resolution current field. We find that a numerical wave model that uses currents with resolutions of ∼30 km or less and a directional resolution of 7.5° can provide accurate representations of the significant wave height gradients found in the Agulhas current. Using smoother current fields such as derived from altimeters measurements alone, coarse directional spectral resolution or larger directional spread of the wave model generally underestimates gradients and extreme wave heights. Hence, satellite altimetry provides high‐resolution wave height with a gradient magnitude that is highly sensitive to underlying surface current gradients, at resolutions that may not be resolved by today's altimeters measurements. This is demonstrated here for relatively steady currents averaged over 3 years.

NONLINEAR METHOD FOR REAL-TIME WAVE FORCE RECONSTRUCTION ON A CYLINDER BY USING MEASURED WAVE ELEVATION

For a constructed offshore structure, wave force evaluation on its foundation in an intricate wave field will benefit the load data collection and structural safety monitoring. Then, the collected data can provide valuable references for similar structures constructed in the same ocean region in the future. A real-time wave force prediction can further contribute to the active control of the structural dynamic responses. According to the incident waves known or unknown, the wave force reconstruction issue can be divided into two categories. When the incident waves are known, the wave forces on the cylinder can be achieved by the theoretical methods or numerical methods. When the incident waves are unknown, researchers try to reconstruct the wave force indirectly. For a small-scale cylinder, researchers predicted the wave forces by using the Morison equation in random wave fields with measured data of wave elevation. These studies indicated a shortcut for determining the wave force on the cylinder by using the data of water surface elevation. However, the wave fields are assumed to be undisturbed by the structure in the mentioned studies. For a vertical larger-scale cylinder, Liu et al. (2018) established a prediction method to reconstruct wave force by using the recorded data of wave elevation around the cylinder. A linear method for the circular cylinder is provided that shows an excellent reconstruction of wave force for its dominant frequent components. However, reconstruction results showed that high frequency wave forces are underestimated and low frequency wave forces are overestimated, which means the linear method is incapable to predict the nonlinear wave forces on the structure. An improved method is built for reconstructing wave forces on a circular cylinder in the real-time. Two different algorithms, Fast Fourier Translation (FFT) and Recursive Least Squares (RLS), for real-time reconstruction are conducted. The present method can be applied for the data collection of wave loads on a constructed offshore structure.Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/PYOuCNP8pgQ

Experimental investigations on wave induced dynamic pressures over slotted vertical barriers in random wave fields

Experimental investigations were carried out to assess the wave induced pressures on slotted vertical barriers. Thirty six different wave barrier configurations (10%, 20%, 30%, 40%, 50% and 60% porosities and 1 to 6 numbers of slotted walls) were tested in random wave fields of JONSWAP spectra for different combinations of significant wave heights and peak periods. It is found that on the dynamic pressure on vertical slotted wave barrier reduces progressively from the seaside to the rear side. In general, the dynamic pressure coefficient Ps/(ρgHis/2) reduces with an increase in relative water depth, d/Lp. where Ps is the significant dynamic pressure, ρg is the weight density of water, His is the significant incident wave height, d is the water depth and Lp is the wave length corresponds to peak wave period. It is also found that the highest value of measured Ps/(ρgHis/2) is about 1.5. The barrier with 3 walls and 10% porosity and for d/Lp of 0.3, the seaside wall panel experience dynamic pressure coefficient of 1.44, the first rear wall with 0.82 and the lee side porous wall with 0.58. The results can be used for the optimal design of the panels of multiple slotted vertical wave barriers.

Experimental study of breathers and rogue waves generated by random waves over non-uniform bathymetry

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were recorded with gauges in a wave tank. Statistical analysis was applied to the experimental data, including the space and time distribution of kurtosis, skewness, Benjamin–Feir index, moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random wave field and traveling over shoals, valleys, and slopes were compared with exact solutions of the nonlinear Schrödinger equation with a good match, demonstrating that these localized waves have the same structure as deep-water breathers. We identify the formation of rogue waves at moments and over regions where the kurtosis and skewness have local maxima. These results provide insights for understanding of the robustness of Peregrine and higher-order Akhmediev breathers, Kuznetsov–Ma solitons, and rogue waves, and their occurrence in realistic oceanic conditions, and may motivate analogous studies in other fields of physics to identify limitations of exact weakly nonlinear models in non-homogeneous media.

Singularities of Partially Polarized Vortex Beams

Singularities in the polarization state of nonuniform electromagnetic beams have been a topic of both theoretical and practical interest for many years, as have singularities in the correlation functions of random scalar wavefields. However, there has been relatively little work done to explore the intersection of these phenomena, namely singularities in the polarization state of partially coherent wavefields. In this paper, we use a simple model of a partially coherent electromagnetic vortex beam to highlight three different ways that one can define polarization singularities in scalar wavefields, one of which has been previously undiscussed.

Using a Time‐Based Subarray Method to Extract and Invert Noise‐Derived Body Waves at Long Beach, California

AbstractThe reconstruction of body waves from the cross‐correlation of random wavefields has recently emerged as a promising approach to probe the fine‐scale structure of the Earth. However, because of the nature of the ambient noise field, the retrieval of body waves from seismic noise recordings is highly challenging and has only been successful in a few cases. Here, we use seismic noise data from a 5,200‐node oil‐company survey to reconstruct body waves and determine the velocity structure beneath Long Beach, California. To isolate the body wave energy from the ambient noise field, we divide the entire survey into small‐aperture subarrays and apply a modified double‐beamforming scheme to enhance coherent arrivals within the cross‐correlated waveforms. The resulting beamed traces allow us to identify clear refracted P waves traveling between different subarray pairs, which we then use to construct a high‐resolution 3D velocity model of the region. The inverted velocity model reveals velocity variations of the order of 3% and strong lateral discontinuities caused by the presence of sharp geologic structures such as the Newport‐Inglewood fault (NIF). Additionally, we show that the resolution that is achieved through the use of high‐frequency body waves allows us to illuminate small geometric variations of the NIF that were previously unresolved with traditional passive imaging methods.

Analytical formula for estimation of surface wave power with application in the coastal ocean of Thailand

Two common techniques in determining surface wave power include a full wave spectrum integration and a representative wave approach. Under the concept of spectral wave parameterization, a new estimation formula is introduced in this study to capitalize the advantages of both the numerical method and the closed-form solution. The formula was verified using synthetic wave data and its applicable condition is recommended to be in the upper-intermediate to deep water environment. Validation against reliable field wave data showed that the new solution can outperform the representative wave approach by allowing higher estimation performance around 5%–15% on average. The new formula was applied for a practical estimation of wave power in Thailand. While the resulting wave power was found to be relatively low around 0.3 to 1.5 kW/m, the utility of the new solution can be warranted according to its consistency with the full numerical technique. This encouraging outcome is achievable as the deviation of the resulting estimates is limited and symmetric about a neutral mean. In summary, the superiority of the new analytical formula can be attributed to its dependable replication of typical random wave field and its adaptability to irregular wave energy distribution in the nature.

Reconstruction and Analysis of Freak Waves Generated From Unidirectional Random Waves

Abstract The generation of two freak waves in a broadband and a narrowband random series registered in the experiments of Li, J. X., Li, P. F., and Liu, S. X. (2013, “Observations of Freak Waves in Random Wave Field in 2D Experimental Wave Flume,” China Ocean Eng., 27(5), pp. 659–670) is precisely reconstructed using a fully non-hydrostatic water wave model. The simulation results indicate that even when the background spectral bandwidths are different, the evolution processes of the two freak waves are similar. Both freak waves emerge quickly during the transition from normal states to extreme events. The freak waves can persist over a long distance, i.e., approximately 5 peak wavelengths. The reconstructed time series in both the backward and forward locations at which the freak waves were recorded reveal that the largest freak wave crests were not captured in the experiment. The freak waves gradually emerged from an intense wave group. The waves developed quickly during the transition from a normal state to an extreme event. Very deep troughs were also formed in the evolution process. The two freak waves were actually generated via different spectral bandwidth processes, but the generation mechanisms of the rogue waves were similar. By analyzing the time series of the freak wave groups, the formation of the freak waves is found to result from the combined effect of the dispersive focusing, the third-order resonant wave interactions, and the higher harmonics.

A New Approach for Modeling Dissipation due to Breaking in Wind Wave Spectra

AbstractA robust spectral dissipation term for wind waves has long been a goal of detailed-balance spectral modeling and is represented by many different approximations in spectral models of random wave fields. A Monte Carlo approach is employed here to create a random-phase sea surface that is used to simulate the distribution of horizontal surface velocities at the sea surface and to relate these velocities to deep-water wind wave breaking. Results are consistent with many recent studies that show a kinematic-based breaking criterion can provide a consistent depiction of the onset of wave breaking. This criterion is combined with the calculated nonlinear flux rates to estimate a transition point within a spectrum at which a spectrum changes from an f−4 equilibrium-range form to an f−5 region dominated by dissipation, potentially an important factor within several air–sea interaction mechanisms, turbulence at the sea surface, and remote sensing applications. It also has the potential to improve operational modeling capabilities.

Efficient Acoustic Reverse Time Migration With an Attenuated and Reversible Random Boundary

Pre-stack reverse time migration (RTM) based on the two-way wave equation has been proved to be the most accurate seismic migration method theoretically. However, it requires reverse-order access to the wavefield calculated in forward time. In recursion computing, such out-of-order access requires that most of the recursion history should be stored on the hard disk. For massive amounts of seismic data, loading the saved wavefield data from the disk during imaging has been the bottleneck of RTM, restricting its wide application. To solve this problem, the wavefield in forward time must be reconstructed in reverse order. Although the random boundary can avoid the disk requirement by creating random velocity around the computational domain when propagate the source function. However, the random wavefield reflected from the boundary can generate unwanted artifacts in the final images. In this paper, we develop an attenuated and reversible random boundary condition which is implemented by mixing the reversible attenuation and random boundary conditions. Similar to the random boundary scheme, the proposed method just needs to save the last one or two wavefield snapshots into the memory in forward process. It then reconstructs the source wavefield in reverse order, while greatly reduces the disk input and output (I/O) requirements. Taking the attenuated property into consideration, the artificial events reflected from the boundary can be eliminated. Thus, our method can improve the imaging quality largely compared with the random boundary scheme. Numerical results demonstrate that the RTM images with our proposed attenuated and reversible random boundary condition can not only eliminate the unwanted artifacts, but also improve the computational efficiency greatly.

Effects of random winds and waves on a long-span cross-sea bridge using Bayesian regularized back propagation neural network

Uncertainties from random multiple factors bring great challenges for assessing response of long-span bridges. This study proposes a dynamic analysis framework by integrating the wind–wave–bridge system with Bayesian regularized back propagation neural network, and then investigates stochastic response of a cross-sea cable-stayed bridge under extreme wind and wave parameters. The wind–wave–bridge system involving wind–bridge and wave–bridge interactions is constructed to calculate dynamic response of the bridge by Newmark-β method, considering stationary fluctuating wind fields and multidirectional random wave fields. To reduce the calculation cost, a Bayesian regularized back propagation neural network model is introduced, and the model evaluation is carried out to illustrate its accuracy and efficiency. After performing small-scale finite element analyses, the response statistics are obtained and later used as the known samples for training the neural network. The power spectrum analyses of the deterministic results are performed to investigate the contribution mechanism of the wind and wave. Finally, the correlation between the bridge response and the single wind–wave parameter is given by uncertainty analysis of the Bayesian regularized back propagation neural network model. The results show that the proposed framework is capable of capturing the nonlinear bridge response resulting from nonlinear wind and wave loads, which, however, is significant different from that under wind alone. The bridge response receives significant contribution from wind and waves relative to the vibration characteristic of the bridge at smaller wind and wave loads. The contribution from vibration characteristic of the bridge becomes significant at larger wind and wave loads. The uncertainty analyses illustrate the significant effects of four wind and wave parameters on girder, tower, and submerged structure.

Early stage of integrable turbulence in the one-dimensional nonlinear Schrödinger equation: A semiclassical approach to statistics.

We examine statistical properties of integrable turbulence in the defocusing and focusing regimes of one-dimensional small-dispersion nonlinear Schrödinger equation (1D-NLSE). Specifically, we study the 1D-NLSE evolution of partially coherent waves having Gaussian statistics at time t=0. Using short time asymptotic expansions and taking advantage of the scale separation in the semiclassical regime we obtain a simple explicit formula describing an early stage of the evolution of the fourth moment of the random wave field amplitude, a quantitative measure of the "tailedness" of the probability density function. Our results show excellent agreement with numerical simulations of the full 1D-NLSE random field dynamics and provide insight into the emergence of the well-known phenomenon of heavy (respectively, low) tails of the statistical distribution occurring in the focusing (respectively, defocusing) regime of 1D-NLSE.

Wave transmission, reflection, and dissipation of scrap tire floating breakwater in random waves

ABSTRACT Floating breakwaters are used for wave damping applications. Scrap tires can be used as floating breakwaters, since they are available in plenty around the world. However, the question is ‘How to configure them for effective wave damping?’. A detailed experimental research has been carried out for this question and the results were presented in this paper. Physical models of nine different scrap tire floating breakwater configurations were studied in a range of random wave fields. It was found that wave transmission coefficients (ratio of transmitted wave height to incident wave height) of 0.036 to 0.2 can be obtained for relatively shorter wave lengths. For relatively longer waves, wave transmission coefficients in the range of 0.13 to 0.35 were observed. By increasing the number of rows of scrap tires from 4 to 8 or increasing the layers from 1 to 2, improved wave damping was achieved for longer waves. Multiple regression analysis was carried out and empirical equations were proposed for predicting the wave transmission coefficients for all the models studied. Case studies for coastal erosion protection of two specific sites (the beaches of Kennedy Space Center in the U.S. and Qaru Island in Kuwait) were also reported in this paper.

Combination-Focusing Model of Freak Wave Based on Boussinesq Equation

Freak wave is a kind of instantaneous disastrous wave with large wave height, which has great destructive effect on the navigation of ships at sea. Based on the layered Boussinesq equation, a wave model for focusing simulation of freak wave is established, and the numerical generation of freak wave is realized. Through the calculation results, the evolution process and the non-linear characteristic parameters of the freak wave are analyzed and discussed. The following conclusions are drawn: The influence of different energy distribution modes on the simulation of the freak wave is analyzed. Focusing model of simulated freak wave based on layered Boussinesq equation can reproduce freak wave events on random wave field when energy input of freak wave train reaches 10%. The simulation efficiency is high, the influence on skewness is small, and the influence on kurtosis is large.

Branched flow and caustics in nonlinear waves

Rogue waves, i.e. high amplitude fluctuations in random wave fields, have been studied in several contexts, ranging from optics via acoustics to the propagation of ocean waves. Scattering by disorder, like current fields and wind fluctuations in the ocean, as well as nonlinearities in the wave equations provide widely studied mechanisms for their creation. However, the interaction of these mechanisms is largely unexplored. Hence, we study wave propagation under the concurrent influence of geometrical (disorder) and nonlinear focusing in the (current-modified) nonlinear Schrödinger equation. We show how nonlinearity shifts the onset distance of geometrical (disorder) focusing and alters the peak intensities of the fluctuations. We find an intricate interplay of both mechanisms that is reflected in the observation of optimal ratios of nonlinearity and disorder strength for the generation of rogue waves.

Fast random wave generation in numerical tanks

Generating and absorbing random waves in numerical models is a challenging problem, in particular when meaningful wave statistics should be generated to meet design sea-state requirements. The methodology presented herein allows for the generation of random wave fields (free surface elevation and velocities) to be reconstructed in time and in space by using window processing from a reference time series. It is demonstrated that the methodology is efficient in reproducing long non-repeating wave sequences by using only O(101)–O(102) wave components, rather than O(103)–O(104) required by a direct reconstruction from a single spectrum. This reduces the computational times required for the development of wave-train time-series elements by 40 times. Errors in instantaneous surface elevation and particle velocity between windowed and non-windowed reconstruction techniques were less than 0·4 and 0·2%, respectively, in the cases considered. The technique was combined with the relaxation zone method typically used in numerical wave tanks for generating waves. The simulations were performed using Proteus, a rapidly developing CFD−FEM toolkit for modelling fluid−structure interaction cases. The use of windowed reconstruction reduced the overall computational time associated with the simulation of waves in a numerical wave tank by ∼40 and ∼70% for serial and parallel execution. Results of the study show windowed reconstruction to be suitable for the representation of long-duration wave trains. Wave height and peak period are conserved within 2 and 1%, respectively.

Parametric subharmonic instability in a narrow-band wave spectrum

Parametric subharmonic instability arising in a narrow-band wave spectrum is investigated. Using a statistical equation that describes weakly nonlinear interactions in a random wave field, we perform analytical and numerical stability analyses for a modulating wave train. The analytically obtained growth rate $\unicode[STIX]{x1D706}=(-\unicode[STIX]{x1D707}+\sqrt{\unicode[STIX]{x1D707}^{2}+4CE_{B}})/2$ agrees favourably with the results from direct numerical experiments, where $\unicode[STIX]{x1D707}$ is the half-value width of the background wave frequency spectrum, $E_{B}$ is the background wave energy density, and $C$ is a constant. This expression has two asymptotic limits: $\unicode[STIX]{x1D706}\sim \sqrt{CE_{B}}$ for $\unicode[STIX]{x1D707}\ll \sqrt{CE_{B}}$ and $\unicode[STIX]{x1D706}\sim CE_{B}/\unicode[STIX]{x1D707}$ for $\unicode[STIX]{x1D707}\gg \sqrt{CE_{B}}$. In the terms of weak turbulence, these two growth rates correspond to the ones occurring in the dynamic and kinetic time scales. In this way, our formulation successfully unifies the two conventional types of parametric subharmonic instability and offers a new criterion to determine the applicability of the classical kinetic equation in three-wave systems.