Evolution Of Wave Field Research Articles

Dynamic behavior of solitons in nonlinear Schrödinger equations

The primary objective of this study is to derive analytical solutions for a significant system that models the evolution of complex wave fields in nonlinear media. This system extends the framework of nonlinear Schrödinger equations and is pivotal in various physical applications, including optical fibers and Bose-Einstein condensates. By employing advanced analytical techniques such as the Khater II, III (Khat II, Khat III) and Unified (UF) methods, we successfully obtain exact analytical solutions that enhance our understanding of the system’s dynamic behavior. The findings reveal a variety of soliton-like solutions, demonstrating the robustness and effectiveness of the methodologies employed. This research underscores the importance of the system in modeling intricate physical phenomena and offers a novel perspective on its solution space. The originality of this study lies in the innovative application of Khat II, Khat III, and UF methods to this system, providing valuable insights and methodologies for future research endeavors. This work represents a significant contribution to applied mathematics and nonlinear dynamics, emphasizing the physical relevance of the system in representing nonlinear wave interactions. The analytical solutions obtained can facilitate precise control and prediction of wave behaviors in practical applications, thereby advancing our capability to manipulate and harness nonlinear wave phenomena in diverse scientific and engineering contexts.

Wavefield Evolution and Arrival Behavior of Elastic Wave Propagation in Two-Dimensional Fractional Brownian Fields

Wavefield Evolution and Arrival Behavior of Elastic Wave Propagation in Two-Dimensional Fractional Brownian Fields

A p-Multigrid Hybrid-Spectral Model for Nonlinear Water Waves

To improve both scale and fidelity of numerical water wave simulations to study the evolution of wave fields within offshore engineering, it is of key practical interest to achieve high numerical efficiency. We propose a p-multigrid accelerated time-domain scheme for efficient and O(nlogn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {O}}(n \\log n)$$\\end{document}-scalable solution of a hybrid-spectral model for the simulation of highly nonlinear and highly dispersive water waves, the accurate calculation of wave kinematics and taking into account varying water depth. To achieve low numerical dispersive and dissipate errors, a high-order hybrid-spectral collocation scheme is implemented to solve the fully nonlinear potential flow (FNPF) equations, and utilizing a p-multigrid iterative solver scheme for solving the Laplace problem. Hereby, the numerical scheme combines the high accuracy of spectral methods, high efficiency of the fast Fourier transform (FFT) algorithm, and multigrid methods. Numerical analysis is performed to evaluate the performance and confirm the spectral accuracy of the scheme. Numerical experiments are considered for steady nonlinear wave propagation. A Fourier-continuation technique is used to extend the scheme from a periodic domain setup to perform benchmarks in a finite domain setup for numerical wave tanks utilizing conventional techniques for wave generation and absorption, and with results in excellent agreement with experimental measurements.

Experimental and numerical study on freak wave using the Peregrine breather

Experimental and numerical study on freak wave using the Peregrine breather

A caustic terminating at an inflection point

A caustic terminating at an inflection point

A Graphic Processing Unit–High-Order Spectral (GPU-HOS) Numerical Wave Tank for the Simulation of Directional Wave Field Evolution over a Long Time

Existing numerical models for direct simulations of stochastically directional waves are limited by their computational burden, and only a few of them can be applied to modeling directional waves on account of nonlinear evolutions on large time scales. In response to these drawbacks, this paper proposes a modified rectangular numerical wave tank based on the high-order spectral (HOS) method. Three main arrangements are responsible for the model improvement. Firstly, the relaxation technique is applied on the four sides of the tank for generating and attenuating waves, with an enhancement in the total computational efforts required of less than 5% being achieved. Secondly, for this paper, the HOS method for solving the nonlinear evolution of waves was modified to a GPU-speedup version for the first time, and the speedup increases dramatically (up to 16-fold) when the grid number is O(106). Thirdly, the higher-order Runge–Kutta method with order 8 is adopted for the purpose of suppressing cumulative temporal errors. Furthermore, several numerical results are presented for the validation of the model. With our modified numerical wave tank, the nonlinear evolutions of random directional waves can be efficiently studied over a large time and space scale.

Evolution and Statistical Analysis of Internal Random Wave Fields within the Benjamin–Ono Equation

This study investigates the numerical evolution of an initially internal random wave field characterized by a Gaussian spectrum shape using the Benjamin–Ono (BO) equation. The research focuses on analyzing various properties associated with the random wave field, including the transition to a steady state of the spectra, statistical moments, and the distribution functions of wave amplitudes. Numerical simulations are conducted across different Ursell parameters, revealing intriguing findings. Notably, it is observed that the spectra of the wave field converge to a stationary state in a statistical sense, while exhibiting statistical characteristics that deviate from a Gaussian distribution. Moreover, as the Ursell parameter increases, the positive skewness of the wave field intensifies, and the kurtosis increases. The investigation also involves the computation of the probability of rogue wave formation, revealing deviations from the Rayleigh distribution. Notably, the study uncovers distinct types of internal rogue waves, specifically referred to as the “two sisters” and “three sisters” phenomena.

Investigating an extreme meteo-oceanographic event in the southern Brazil from in situ observations and modeling results

Investigating an extreme meteo-oceanographic event in the southern Brazil from in situ observations and modeling results

Real-time phase-resolved ocean wave prediction in directional wave fields: Enhanced algorithm and experimental validation

Real-time phase-resolved ocean wave prediction in directional wave fields: Enhanced algorithm and experimental validation

Stiffness tensor estimation of anisotropic crystal using point contact method and unscented Kalman filter

The potential application of Lithium Niobate (LiNbO3) crystal is immense, specifically in the domain of meta-surfaces and nano-resonators. However, the practical application of LiNbO3 is impeded due to unreliable experimental techniques and inaccurate inversion algorithms for material characterization. In the current research, material characterization of anisotropic crystal is proposed by exploring the wavefield evolution in the spatial and temporal domains. The presented framework has three major components: a physics-based mathematical model (Christoffel equation), a novel experimental technique, and an inversion algorithm based on Bayesian filtering. An experimental technique based on Coulomb coupling is devised to visualize the propagation of ultrasonic waves in an anisotropic crystal. The crystal is characterized by measuring the directional-dependent acoustic wave velocity from the spatial-temporal information of the wave propagation. The anisotropic constitutive properties of the crystal are estimated by exploring the wave velocity in the Bayesian filtering algorithm. The proposed algorithm is based on the probabilistic framework that integrates the experimental measurement in a physics-based mathematical model for optimal state prediction of stiffness tensor through the Bayesian filtering algorithm. In particular, we utilize the unscented Kalman filter (UKF) in conjunction with the plane-wave Eigen solution to estimate the constitutive parameters. In the presence of measurement uncertainties, the performance of the optimal prediction algorithm is illustrated by comparing the estimated parameter with the corresponding theoretical value. The comparison demonstrates that the proposed inversion algorithm is efficient and robust and performs satisfactorily even with significant measurement uncertainties.

Numerical investigation on nonlinear evolution behavior and water particle velocity of wave crests for narrow-band wave field with Gaussian spectrum

Numerical investigation on nonlinear evolution behavior and water particle velocity of wave crests for narrow-band wave field with Gaussian spectrum

Numerical Simulation Study on Interactions between the Wave and Newborn Sandbank in the Xisha Islands of the South China Sea

As a unique landform in the island and reef area, the newborn sandbank is not only the initial stage of island development, but also has a rapid evolution and a complex dynamic mechanism. However, the dynamic geomorphology mechanism of the newborn sandbank is still lacking extensive study and direct evidence of the interaction process between the marine dynamics and the newborn sandbank geomorphology. Therefore, in order to reveal the interaction mechanisms between marine dynamics and newborn sandbanks, a newborn sandbank in the sea area of the Xisha Islands, in the South China Sea, has been selected as the focus of this research. The method of numerical simulation was used to discuss and analyze the wave field characteristics around the newborn sandbank and their impacts on the sandbank’s migration and development. The results show that: (1) The islands and reefs have significant refraction, diffraction, and energy dissipation effects on waves, and the newborn sandbank has the same effect, but with a weaker function. The wave height around the reef islands reduced by approximately 60–67% in dominated and strong wave directions. At the same time, the wave height attenuation in the wave shadow zone, behind the newborn sandbank, can reach approximately 27–33%. (2) Wind is important for the evolution of wave fields; in particular, when the wind speed exceeds grades four and five, the effect of the wind on the waves is particularly significant, causing the winds to control the wave characteristics around the islands and newborn sandbanks. This results in significant seasonal differences in wave fields within the sea area. (3) The wave direction primarily controls the migration direction of the newborn sandbank, and the wave height primarily controls the migration speed and distance. After one month of wave action in the strong wave direction, the maximum eastward deposition length was approximately 50 m. After one month of wave action in the dominated wave direction, the maximum eastward deposition length was approximately 60 m. Therefore, the topography of the newborn sandbank affects the wave propagation, meanwhile, the wave conversely determines migration and development of the newborn sandbank in a short term. The dynamic geomorphology action between the wave and newborn sandbank is a fast two-way process, and occurs not only during storms or the winter monsoon, but also during other, more common, weather events.

Effects of finite non-Gaussianity on evolution of a random wind wave field.

We examine the long-term evolution of a random wind wave field generated by constant forcing, by comparing numerical simulations of the kinetic equationand direct numerical simulations (DNS) of the dynamical equations. While the integral characteristics of the spectra are in reasonably good agreement, the spectral shapes differ considerably at large times, the DNS spectral shape being in much better agreement with field observations. Varying the number of resonant and approximately resonant wave interactions in the DNS numerical scheme, we show that when the ratio of nonlinear and linear parts of the Hamiltonian tends to zero, the DNS spectral shape approaches the shape predicted by the kinetic equation. We attribute the discrepancies between the kinetic equationmodeling, on one side, and the DNS and observations, on the other, to the neglect of non-Gaussianity in the derivation of the kinetic equation.

Real-time digital twin for ship operation in waves

This paper introduces a real-time digital twin for ship operations in seaways. The concept of the digital twin is becoming popular, and it is adopted for ship operation systems in this study. In particular, this paper introduces a new and innovative concept of the digital twin to predict ocean waves and hydrodynamic performances, such as seakeeping and maneuvering, which enables the risk and optimum route to be forecast in real time. An essential element in the realization of such a real-time digital twin is the real-time prediction of ocean waves. Hence, a sophisticated algorithm for wave reconstruction using measured wave-radar images is developed, which is extended to predicting the future evolution of a three-dimensional wave field in front of a ship within a time window of the order of 10 min. As another essential element, an analysis program to solve the coupled seakeeping-maneuvering problem is developed. This analysis can also be used in real time. By combining this with wave prediction software, the future occurrence of ocean waves and ship responses can be predicted. By extending this approach, the risk and performance of ships in various ocean environments can be predicted. In this paper, concepts, approaches, and examples are introduced. • This paper introduces an innovative concept of a real-time digital twin for ship operations in seaways. • Modules for wave prediction, ship hydrodynamics, and navigation control are integrated. • The reconstruction and prediction of wave field are investigated considering ship operations. • Real-time predictions for ship operation and future risk within a few tens of minutes are validated. • The operation guidance is established based on the predicted resistances and significant motions.

Impact of fracture normal and shear stiffnesses on the scattering attenuation of P and S waves in a naturally fractured rock

In this paper, numerical simulations are conducted to study elastic wave transport, scattering, and attenuation in a naturally fractured rock associated with length-correlated fracture normal and shear stiffnesses. The model represents the pattern of a real fracture outcrop in an explicit fashion based on the discrete fracture network approach and computes the dynamical interaction between waves and fractures based on the displacement discontinuity method. A broad spectrum of geologically relevant fracture stiffness values are explored to analyse the impact of fracture normal and shear stiffness components on the wavefield evolution. It is observed that when the fracture normal and shear stiffnesses are both high, the wavefield is a propagative mode dominated by a forward ballistic transport. With the reduction of fracture normal and/or shear stiffnesses, the wavefield becomes diffusive characterised by the emergence and dominance of coda waves. If the fracture stiffnesses are very low, waves become trapped entering the so-called localisation regime associated with an absence of effective transport as well as a profound attenuation. Our results show that the scattering attenuation of S waves tends to be greater than that of P waves in the propagation and diffusion regimes, but becomes similar in the localisation regime. The research findings of this paper have important implications for understanding and predicting the seismic wave attenuation behaviour in naturally fractured rocks for various geophysical applications. • Elastic wave transport in a naturally fractured rock is numerically simulated. • Fracture stiffnesses exert a significant impact on wave scattering and attenuation. • S waves are more attenuated than P waves in the propagative and diffusive regimes. • Anderson localisation of elastic waves emerges when fracture stiffnesses are very low.

Non-homogeneous analysis of rogue wave probability evolution over a shoal

Non-equilibrium evolution of wave fields, as occurring over sudden bathymetry variations, can produce rogue seas with anomalous wave statistics. We handle this process by modifying the Rayleigh distribution through the energetics of second-order theory and a non-homogeneous reformulation of the Khintchine theorem. The resulting probability model reproduces the enhanced tail of the probability distribution of unidirectional wave tank experiments. It also describes why the peak of rogue wave probability appears atop the shoal, and explains the influence of depth on variations in peak intensity. Furthermore, we interpret rogue wave likelihoods in finite depth through the $H$ – $\sigma$ diagram, allowing a quick prediction for the effects of rapid depth change apart from the probability distribution.

Experimental Implementation of Wave Propagation in Disordered Time-Varying Media.

Here, we study and implement the temporal analog in time disordered sytems. A spatially homogeneous medium is endowed with a time structure composed of randomly distributed temporal interfaces. This is achieved through electrostriction between water surface and an electrode. The wave field observed is the result of the interferences between reflected and refracted waves on the interfaces. Although no eigenmode can be associated with the wave field, several common features between space and time emerge. The waves grow exponentially depending on the disorder level in agreement with a 2D matrix evolution model such as in the spatial case. The relative position of the momentum gap appearing in the time modulated systems plays a central role in the wave field evolution. When tuning the excitation to compensate for the damping, transient waves, localized in time, appear on the liquid surface. They result from a particular history of the multiple interferences produced by a specific sequence of time boundaries.

Multipole-phase division multiplexing.

The control of structured waves has recently opened innovative scenarios in the perspective of radiation propagation, advanced imaging, and light-matter interaction. In information and communication technology, the spatial degrees of freedom offer a wider state space to carry many channels on the same frequency or increase the dimensionality of quantum protocols. However, spatial decomposition is much more arduous than polarization or frequency multiplexing, and very few practical examples exist. Among all, beams carrying orbital angular momentum gained a preeminent role, igniting a variety of methods and techniques to generate, tailor, and measure that property. In a more general insight into structured-phase beams, we introduce here a new family of wave fields having a multipole phase. These beams are devoid of phase singularities and described by two continuous spatial parameters which can be controlled in a practical and compact way via conformal optics. The outlined framework encompasses multiplexing, propagation, and demultiplexing as a whole for the first time, describing the evolution and transformation of wave fields in terms of conformal mappings. With its potentialities, versatility, and ease of implementation, this new paradigm introduces a novel playground for space division multiplexing, suggesting unconventional solutions for light processing and free-space communications.

Controls on the architectural evolution of deep-water channel overbank sediment wave fields: insights from the Hikurangi Channel, offshore New Zealand

ABSTRACT Deep-water channels can be bound by overbank deposits, resulting from overspilling flows, which are often ornamented with sediment waves. Here, high-resolution bathymetry, backscatter, and 2D and 3D seismic data are integrated to discern the controls on flow processes on the overbank areas of the Hikurangi Channel. Qualitative seismic interpretation and quantitative analyses of sediment wave morphologies and distributions are conducted through the shallowest 600 m of stratigraphy up to the seafloor. Four outer-bend wave fields are present throughout the studied stratigraphy on the landward margin (left margin looking down-channel) only. Originally closely spaced or combined, these fields evolved to become spatially separated; two of the separate wave fields became further subdivided into distinct outer- and inner-bend fields, whose constituent waves developed distinct differences in morphology and distribution. Sediment wave character is used to interpret the direction and strength of overbank flow. Nine controls on such flow and associated deposition are identified: flow versus conduit size, overbank gradient, flow tuning, Coriolis forcing, contour current activity, flow reflection, centrifugal forcing, interaction with externally derived flows, and interaction of overspill from different locations. Their relative importance may vary across parts of overbank areas, both spatially and temporally, controlling wave field development such that: (1) outer-bend wave fields only develop on the landward margin; (2) the influence of centrifugal force on outer-bend overbanks has increased through time, accompanying a general increase in channel sinuosity; (3) inner-bend wave fields on the landward margin form by the interaction of Coriolis-enhanced inner-bend overbank flow, and outer-bank flow from up-channel bends; (4) inner-bend fields on the oceanward margin form by the interaction of axial flow through wave troughs, and a transverse, toward-channel flow component. This work has implications for interpreting overbank flow from seafloor and seismic data, and for palaeogeographic reconstructions from outcrop data.

Effect of the wind acceleration magnitude during the first stages of the wind-wave generation process

A comprehensive analysis of the wavefield evolution under accelerated wind conditions provides an essential contribution to understanding the wind-wave generation process. A set of experiments was carried out in a large wind-wave facility where it is possible to reproduce high wind speed conditions to study the wind acceleration effect in the wind-wave development. The facility was equipped with high-frequency sampling devices that provide accurate air turbulence and water surface displacement measurements. From this deployment, it was possible to describe the evolution of the wave characteristics under different magnitudes of constant wind acceleration in detail. This study analyzes the wind acceleration effect in the early stages of wind-wave generation and evolution. The increase of spectrum energy saturation level and the downshift of the peak frequency are processes associated with the spectral shape evolution under low acceleration wind conditions. Under high wind acceleration conditions, the spectral shape did not vary with wind speed and fetch. Despite under low acceleration wind conditions, the wavefield is more developed than under high acceleration wind conditions; there was no direct relation between wind acceleration and the wavefield efficiency to grow. Besides, during these early instants, it was observed that a more developed wave field, associated with low acceleration wind conditions, could slow down the increase of drag coefficient with wind speed.