Wave Surface Research Articles

Biaxial Gaussian Beams, Hermite–Gaussian Beams, and Laguerre–Gaussian Vortex Beams in Isotropy-Broken Materials

We have developed the paraxial approximation for electromagnetic fields in arbitrary isotropy-broken media in terms of the ray–wave tilt and the curvature of materials’ Fresnel wave surfaces. We have obtained solutions of the paraxial equation in the form of biaxial Gaussian beams, which is a novel class of electromagnetic field distributions in generic isotropy-broken materials. Such beams have been previously observed experimentally and numerically in hyperbolic metamaterials but have evaded theoretical analysis in the literature up to now. Biaxial Gaussian beams have two axes: one in the direction of the Abraham momentum, corresponding to the ray propagation, and another in the direction of the Minkowski momentum, corresponding to the wave propagation, in agreement with the recent theory of refraction, ray–wave tilt, and hidden momentum [Durach, 2024]. We show that the curvature of the wavefronts in the biaxial Gaussian beams correspond to the curvature of the Fresnel wave surface at the central wave vector of the beam. We obtain the higher-order modes of the biaxial beams, including the biaxial Hermite–Gaussian and Laguerre–Gaussian vortex beams, which opens avenues toward studies of the optical angular momentum (OAM) in isotropy-broken media, including generic anisotropic and bianisotropic materials.

Simulation of time-invariant three-dimensional Freak waves and their scattering identification based on the JONSWAP spectrum and Donelan direction function

Abstract The results of recent maritime accident investigations show that many maritime accidents are related to the attack of freak waves, which can sink ships instantaneously with colossal energy. To identify and forecast freak waves accurately and avoid the danger of freak waves to marine structures and people, we have conducted further research on freak waves. In this paper, we propose an efficient time-invariant three-dimensional (3-D) freak wave computational model to study the scattering characteristics of time-invarian 3-D freak waves and obtain a more explicit identification of their scattering differences. First, this paper adopts linear superposition method to simulate a 3-D random rough sea surface based on the JONSWAP wave spectrum and Donelan directional distribution function. Moreover, we analyze the effect of different angular frequencies on the simulated sea surface. At the same time, the Monte Carlo method is used to further simulate the capillary waves based on the random sea surface, and this method vastly improves the computational accuracy of the random sea surface. Then, based on the two-wave train superposition wave energy focusing mode, a numerical calculation method of time-invariant 3-D freak waves is proposed, and the time-series evolution process of 3-D freak waves is simulated. Finally, the backscattering coefficients of the 3-D freak wave surface are calculated using the two-scale method, and the electromagnetic scattering characteristics of the freak wave surface under different evolution stages, wind speeds, and radar incidence angles are analyzed. By this method, we conclude that the recognition of freak waves is more accurate under medium-high wind speed and significant incidence angle conditions. The experiments show that the research in this paper can identify and predict freak waves more effectively, further improve the forecast accuracy of future freak waves, and also have some application value for freak wave risk warnings.

An Improved Direct Forcing Immersed Boundary Method With Integrated Mooring Algorithm for Floating Offshore Wind Turbines

Abstract An upgraded direct forcing immersed boundary method is implemented in the open-source hydrodynamic framework REEF3D::CFD for simulating the six-degrees-of-freedom (6DOF) motions of a floating offshore wind turbine (FOWT) based on the OC5 semi-submersible design. The direct forcing method is enhanced with a new density interpolation method across the fluid-structure interface that removes unphysical spurious phenomena and ensures stable and accurate wave load calculations on floating objects. A quasi-static algorithm is used for modeling the mooring system of the OC5 platform and restraining its motions in waves. The Navier-Stokes equations are solved on a staggered structured rectilinear grid for the hydrodynamic simulations. The level-set method is used to capture the free surface of the ocean waves. A ray-casting algorithm is employed to get inside-outside information near the fluid-solid interface while maintaining the underlying Cartesian grid in the hydrodynamic domain. The performance and accuracy of the mooring algorithm are compared to the widely-used mooring model MoorDyn, which is coupled to the hydrodynamic solver in REEF3D::CFD. The study demonstrates that the enhanced direct forcing method with the integrated quasi-static mooring algorithm in REEF3D::CFD provides a robust and accurate tool, suitable for the numerical analysis of the state-of-the-art FOWT in ocean waves.

Influence of the stratification parameters on the wake field of an underwater vehicle in a two-layer stratified flow

Because the ocean exhibits different stratification states in different seasons and regions, the effect of different stratification parameters on a submarine wake must be studied. In particular, to investigate such effect in a two-layer stratified flow, this study established a computational fluid dynamics (CFD) model based on the URANS equations, shear-stress transport (SST) k-ω turbulence model, and Eulerian multiphase flow model. The volume of fluid (VOF) method was adopted to implement the free-surface capture method. The working conditions of the SUBOFF model under an infinite diving depth and near the free surface were compared with those of the experiments, and the convergence of the time step and grid number under stratified flow conditions was verified. These validation steps proved the feasibility of the CFD method. Finally, the effects of the stratification parameters on the free surface waves, internal waves, and turbulent kinetic energy behind the vehicle were observed by varying the stratification parameters to achieve different working conditions. The results show that when an underwater vehicle sails in a two-layer stratified flow, the interstratified density ratio and depth of the internal wave surface affect its wake field. When the underwater vehicle sails in the water layer, with an increase in the interstratified density ratio, the free-surface roughness increases and the turbulent kinetic energy decreases. When the underwater vehicle sails in the salt water layer, the result is just the opposite.

Influence of density variations of ionosphere plasma on the conditions of electromagnetic whistler waves propagation in the ionosphere

Background. Plasma density variations caused by infrasonic wave can significantly affect conditions of propagation and reflection of whistler electromagnetic wave incident on the ionosphere from above. Aim. In that work, relationship between the coefficient of wave energy reflection from ionosphere, electromagnetic wave field near the ground surface and parameters of infrasonic wave are studied. Methods. The collocation method for solving the boundary problem for a plane-layered ionosphere and the perturbation theory method are used to find the electromagnetic wave field. Results. The greatest modulation of the reflection coefficient is associated with density perturbations at altitudes 80–110 km where whistler decay increases by an order of magnitude at the local altitude region (less than 15–20 km). In that case, the reflection coefficient variation can achieve 40 %. Conclusion. The results obtained are important for understanding the interconnection of magnetosphere radiation processes of different nature. The study of the modulation of coefficient of whistler reflection from the ionosphere is relevant for explaining the operation modes of a plasma magnetospheric maser.

Study on Depth Estimation and Characteristic Analysis of Underwater Source Based on Deep-Sea Broadband Signal Modeling

Studies on estimating the underwater sound source localization using acoustic signal characteristics have mainly been conducted in shallow waters. Recently, technologies for stably and efficiently estimating the underwater sound sources localization using the underwater sound propagation characteristics of the Reliable Acoustic Path(RAP) in deep water areas are being studied. Underwater surveillance technology in deep sea areas is known to have the advantage of having low detection performance variability due to time-varying underwater environments and having a small shadow zone, making it easy to stably detect underwater sound sources and estimate location even from relatively long distance. In this study, we analyzed the sound propagation characteristics based on the actual marine environment in the deep sea of the Korean Peninsula and conducted a study to analyze the estimation performance of sound source depth using the broadband interference pattern of direct wave and sea surface reflected waves radiating from underwater sound sources.

Numerical investigation on the slamming loads of a truncated trimaran hull entering regular waves

For ship slamming, waves can disturb the water entry progress and thus affect the slamming load characteristics. This paper studied the slamming loads of a trimaran entering regular waves based on the CFD method. The results of a trimaran model impacting calm water and wedge impacting waves are used to verify the present method. The free surface evolution and load characteristics of the trimaran model considering wave effects are discussed. The results showed that the position at which the structure touches the wave surface depends on the formation, deformation and escape of bubble flows, which cause obvious asymmetrical flow. The enclosure of the air cavity induces a step increase in pressure, and the pressure peak appears when the bubble fully escapes. Three typical positions, wave crest, wave cross and wave through, are chosen to explore the influence of waves on slamming loads. The impact load shows a 98% difference at different wave locations. In ship load forecasting, the position of the waves relative to the hull is noteworthy. The influence of the water entry velocity on the slamming load is further discussed. Bubble retention related to the water entry velocity is the key factor affecting the peak load.

Investigation of Aerodynamic Performance of Multi-element Airfoil in Free Surface Effect

Abstract This study examines the aerodynamic performance of the 30P30N multi-element airfoil flying on a free surface, a numerical computational model is established, the governing equations are addressed through the application of the finite volume method, while the volume of fluid method is utilized for the simulation of two-phase flow. Different mesh strategies and turbulence models are compared, with the numerical methods validated against experimental data. The aerodynamic properties of the 30P30N multi-element airfoil on the free surface at different wavelengths and wave heights are given by numerical computations, which show that the ground effect of the 30P30N multi-element airfoil differ from those on a clean airfoil, the aerodynamic coefficients of the 30P30N multi-element airfoil decrease as flight altitude lowers, with the pitching and drag moment of the slat is opposite to that of the main airfoil and the flap. Additionally, when the 30P30N multi-element airfoil flies over a regular wave surface, the aerodynamic coefficients of each component exhibit periodic behavior.

Mechanically forced meniscus water waves in a square container with functionalized wetting conditions

Capillary–gravity surface waves, called meniscus waves, are excited at the air–water interface near the lateral boundary of a mechanically forced square container. Experiments are conducted in two working containers: one is overall hydrophilic at four boundaries and the other is functionalized to have a hydrophobic boundary. The static meniscus structures and instantaneous wave topography are reconstructed at high resolution from the side-view and top-view high-speed camera recordings. Wave resonances arise from the interaction of four inward-traveling waves, with the frequency-response characteristics indicating the effect of wetting conditions on the selection of standing wave patterns. The most-resonant modes are identified as a superposition of dominant modes and higher-order components. An analytical model of the rest-state meniscus and resonant-state wave surface decomposes the wave responses into two groups of resonances along two transverse directions linked by a frequency-dependent parameter γ. Theoretical selection of the dominant wave components and the second-order harmonics is in close agreement with the spatiotemporal surface-fitting experimental results. Additionally, the wetting boundary conditions can be functionalized to excite specific standing wave patterns, which could provide a novel approach to precise pattern control in bioprinting technology for tissue engineering applications.

Experimental Study of the Random Wave-Induced Hydrodynamics and Soil Response in a Porous Seabed Around Double Piles

The evaluation of the wave-induced pore pressures around the offshore piles has attracted great attentions among coastal engineers, because they have been commonly used as foundations of numerous marine infrastructures. This paper presents comparative studies of the random wave-induced transient seabed response around single and double piles in a sandy seabed through a series of wave flume experiments. The influences of relative spacing ratios, wave incidence angles, and front pile diameters under different random wave parameters on oscillatory pore pressures in the vicinity of double piles are examined. In addition, variations in wave profiles and dynamic wave pressures surrounding single and double piles are quantitatively analyzed. Based on the experimental results, the following conclusions can be drawn: (1) under the influence of random waves, the wave profiles around the double piles exhibit obvious irregularity and nonlinearity; (2) the shielding effect existing in the tandem piles results in lower dynamic wave pressures around the rear pile compared to the front pile; (3) the pore pressures on the front surface of the double piles decrease with increasing soil depth, with a decreasing attenuation rate at each layer; (4) when the relative spacing ratio G/D2=3, the group-pile effect weakens, leading to an increase in the pore pressures around the rear pile, approaching the results of a single pile under conditions of lower significant wave heights or periods; (5) the intense disturbance effect caused by large wave incidence angles exacerbates the pore pressure response around the double piles; (6) when the diameter of the front pile in the tandem piles increases, it enhances the shielding effect, thus suppressing the seabed response around the rear pile. In contrast, it causes an increase in the wave surface around the double piles, exacerbating the pore pressure response in the seabed. The latter effect becomes more pronounced when the significant wave height is larger.

GWECS: An indicator to describe the energy absorption characteristics of wave energy converter arrays in real sea states

Grouping wave energy converters (WECs) into an array has become a trend to improve power production and achieve economies of scale. Therefore, the performance of a WEC array in real sea states is of vital importance. To intuitively reflect an array's frequency-based energy absorption characteristics instead of only the total extractable power in given irregular wave conditions, a new indicator of group wave energy capture spectrum (GWECS) is proposed by extending the concept of wave energy capture spectrum (WECS) to an array. A practical method to measure the indicator by estimating the absorbed wave surface from the array's power signal is also given. Simulations in two-dimensional conditions with a 2-cuboid WEC array and in three-dimensional conditions with a 2-cylinder WEC array are conducted to study the concept. The results examine the consistency in capture efficiency between the newly proposed indicator and conventional ones, and present the effect of various parameters, including linear power take-off (PTO) damping, buoy permutation, separation distance, and incident wave angle on the GWECS.

Self-organization of the tribosystem under non-stationary conditions of friction from the standpoint of deformation-wave representations

Mechanisms of structural adaptation of contact surfaces and lubricating materials during friction with the dominance of deformation processes in tribocontact have been analyzed. The purpose of the work was to model the elastic-plastic properties of dissipative structures taking into account the anisotropic properties of the surface layers of the friction pairs and the boundary layers of the lubricating material. The modeling took into account the structural state of the latter formed due to heating and saturation with wear products, along with the physical and mechanical interaction of this layer with the outer surface of the part. An algorithm for determining the distributed tangent force along the length of the boundary layer of the lubricating material adjacent to the part has been developed based on the hypothesis of the wave-like state of the surface layer of the lubricating material on an absolutely flat (non-deformed) rough surface. Herein, under the action of tangent forces, the strip of lubricant is subject to horizontal compression and transverse movement. The distributed tangent stress along the length of the adjacency of the layer of densified lubricant to the part causes micro-slipping of the layer. Amplitude horizontal displacements of the boundary of the lubricant layer are determined when the beam-film is loaded with longitudinal stresses, which leads to partial disorientation of the film and loss of its originally rectilinear structured form, the transition of the lubricant layer to the state of the wave surface of a sinusoid shape. Also, a procedure for calculation of tangent forces causing the loss of elastic stability of the lubricant boundary layers resulting in the direct mechanical destruction of the lubricant boundary layer in the slipping zone of the contact surface is proposed based on the elastic-frictional interaction of this layer with the near-surface layer of the metal

Flow Structure and Periodic Processes in a Disc-Shaped Vortex Chamber of a Hydrodynamic Cavitator

Introduction. The essence of the acoustic – cavitation processes is that the liquid is passed through sound with a pressure at the wave surface of more than 3 bar that causes local breaks of the liquid in the vacuum phase of the wave and the collapse in the manometric phase. The opposite walls of each cavern in the collapse approach at a speed exceeding two speed of sound, due to which a high energy density is achieved at the meeting point, and what is especially valuable is the mutual transitions of energies from one form to another, unattainable under normal conditions, and, moreover, as inside cavitation area and near it. The novelty of the work is confirmed by the results of a periodic information and patent analysis, and by four patents received for inventions on the topic under consideration.Aim of the Study. The study is aimed at improving the acoustic-cavitation qualities of a disk-shaped vortex chamber used as a liquid whistle.Materials and Methods. In the study, there were used numerical modeling of flows in the FlowVision program, experimental determination of flow rates using a pitot tube, film method, removal of frequency response using SpectraPLUS 5.0, and visualization of flows and processes on optically transparent devices by the method of color indicators in stroboscopic lighting high-speed video shooting.Results. The mechanism of sound generation and noise in the flow transiting through the device has been found. The corrective effect of pump pulsations f = 300 Hz on the sound generation mechanism was revealed. The disc-shaped character of the device, which encloses the input flow in cross section from three directions, contributes to creating a more expressive acoustic signal, forming two conjugate torus vortices along the shell that ensures uniformity of the circumferential flow, attenuation of longitudinal high-frequency oscillations f = 200 kHz, and the creation of periodic zones of increased pressure along the shell. The concentrated tangential entrance to the device determines the central asymmetry of the flows in it and a number of processes that create acoustic noise.Discussion and Conclusion. The frequency of the useful acoustic signal in the vortex chamber is proportional to the speed of the transit flow, and the amplitude is proportional to the dimensions of the device. Along with the useful signal created by the interaction of the peripheral and input parts of the transit flow, noise of similar frequencies is created in the device. Other sources of noise generation are due to the presence of a concentrated tangential input. The formation of two conjugate torus vortices along the shell can be used as a means of controlling the process of interaction between parts of the transit flow. The disc-shaped vortex chamber combines the functions of sound generation and the ability to create a centrifugal field, which expands its technological capabilities.

Hetero-Bäcklund Transformation for a (2+1)-Dimensional Generalized Modified Dispersive Water-Wave System

This work is designed for a (2+1)-dimensional generalized modified dispersive water-wave system for the nonlinear and dispersive long gravity waves travelling along two horizontal directions in the shallow water of uniform depth, with our results as a hetero-B acklund transformation, from that system to a known generalized (2+1)-dimensional dispersive long-wave system. As for the height of the water surface and horizontal velocity of the water wave, our hetero-Backlund transformation depends on the shallow-water coefficients in that system.

Vibration Friction Investigation on the NCS of Joints of the CNC Machine Tools Considering Friction Factor

Machine tool vibrations play a significant role in hindering productivity during machining. The growing vibrations accelerate tool wear and chipping, cause a poor wave surface finish, and may damage the spindle bearing. Some research showed that tribological properties such as friction factors can have obvious influences on the topography of rough surfaces and the nonlinear dynamic characteristics of machine tool systems. Therefore, studying the vibration friction dynamic characteristics on the normal contact stiffness (NCS) of joints of CNC machine tools is absolutely necessary for improving the machining accuracy and precision of the whole system. The study results of NCS of joints of the CNC and the friction coefficient are discussed in this paper. The model of NCS based on fractal parameters was obtained. The models of deformations of the rough surfaces and contact surfaces were deduced. The results showed that the NCS based on the calculation method considering the elastic–plastic deformation of the asperity is much higher in precision than the methods considering only elastic or plastic deformation separately. The observations this paper described suggest that in the CNC machine tools system, higher D and G and higher friction coefficients lead to higher normal contact stresses (NCSs).

Structural Design and Horizontal Wave Force Estimation of a Wall-Climbing Robot for the Underwater Cleaning of Jackets

Currently, divers face significant safety risks when cleaning marine organisms from the steel structures of offshore underwater platform jackets. Consequently, utilizing robots instead of divers to carry out underwater biofouling removal operations will be an important development direction for the underwater maintenance of offshore platforms in the future. In this study, a wall-climbing robot was designed to clean marine organisms from the underwater surface of a platform jacket leg. The overall structure of the underwater cleaning wall-climbing robot is introduced, including the cleaning actuator and the variable curvature-adapted connecting rod mechanism. The corresponding relationship between the variable curvature-adapted connecting rod mechanism and the jacket leg is analyzed in detail. The variable curvature-adapted connecting rod mechanism was optimized using a genetic algorithm to ensure that the underwater cleaning wall-climbing robot can adapt to a minimum diameter of 1 m for the jacket leg. By drawing on Airy wave theory and random wave theory, the Airy wave parameters for waves were analyzed under different sea conditions, considering practical application scenarios. By using Fluent software 2022, a 2D numerical wave tank was constructed to simulate waves under various sea conditions, and the wave surface shapes for different sea states were determined. By building on the Morison equation, a method for calculating the horizontal wave forces on the underwater cleaning wall-climbing robot using the equivalent area and equivalent volume is proposed. By using the two aforementioned methods, the horizontal wave forces on the underwater cleaning wall-climbing robot under specific sea states were determined. The horizontal wave forces of the underwater cleaning wall-climbing robot under different sea conditions were analyzed and simulated in a 3D numerical wave tank. By comparing the theoretical analysis results with the numerical simulation results, where the maximum difference at the extreme points is approximately 11%, the feasibility of the proposed horizontal wave force estimation method was verified.

Development of a Wind–Wave Coherence Function Based on Numerical Studies

The synchronization and intensity of fluctuating wind speeds and wave surfaces in wind–wave joint propagation processes are affected by the coherence of the marine ambient factors of fluctuating wind and random waves. This coherence further affects the precise calculations of wind–wave joint actions on marine structures. Therefore, a wind–wave joint propagation numerical flume was established based on the numerical simulation of random waves and fluctuating wind fields. A series of numerical simulations of wind–wave joint propagations were carried out. Based on the numerical results, the influences and influence laws of factors such as wind speed position height, significant wave height and wave spectrum peak frequency on the wind–wave coherence values were studied. According to the influence characteristics of these factors, a function of wind–wave coherence values for random wind–wave joint propagation was calculated. The coherence function takes frequency as the variable, while parameters include significant wave height, wind speed position height and wave spectrum peak frequency. Through a series of numerical simulation results, data fitting was used to calculate the parameter coefficients of the coherence function. The established random wind–wave coherence function can be described using the wind–wave joint fields of marine structures and the computational analyses of structural wind–wave joint actions.

Hydrodynamic analysis of sea-crossing bridge piers subjected to freak waves

Coastal areas are witnessing a surge in critical infrastructure development, such as sea-crossing bridges, to support growing populations and economic activities. However, these structures face ongoing challenges in harsh marine environments. Therefore, understanding the hydrodynamics of bridge structures under extreme freak wave conditions is imperative for designing effective countermeasures. This study investigates pier hydrodynamics using a three-dimensional numerical flume simulated by OpenFOAM, focusing on loading characteristics and wave climb differences under freak and linear waves. Results show that freak waves induce larger surges and forces compared to linear waves, with a notable “bell vibration” effect near the wave surface. Moreover, peak forces and bending moments increase nonlinearly with the wave height-to-significant wave height ratio. For double-column piers, transverse alignment concentrates wave climb on the rear side of the front pier, with forces increasing with spacing, while those on the rear pier decrease. Conversely, longitudinal arrangements show amplified loading effects. These findings provide valuable insights into the hydrodynamic behaviour of bridge piers under freak wave conditions, offering practical implications for the design and protection of sea-crossing bridges.

Theory of Refraction, Ray–Wave Tilt, Hidden Momentum, and Apparent Topological Phases in Isotropy-Broken Materials Based on Electromagnetism of Moving Media

The mysterious nature of electromagnetic momentum in materials is considered one of the most significant challenges in physics, surpassing even Hilbert’s mathematical problems. In this paper, we demonstrate that the difference between the Minkowski and Abraham momenta, which consists of Roentgen and Shockley hidden momenta, is directly related to the phenomenon of refraction and the tilt of rays from the wavefront propagation direction. We show that individual electromagnetic waves with non-unit indices of refraction (n) appear as quasistatic high-k waves to an observer in the proper frames of the waves. When Lorentz transformed into the material rest frames, these high-k waves are Fresnel–Fizeau dragged from rest to their phase velocities, acquiring longitudinal hidden momentum and related refractive properties. On a material level, all electromagnetic waves belong to Fresnel wave surfaces, which are topologically classified according to hyperbolic phases by Durach and determined by the electromagnetic material parameters. For moving observers, material parameters appear modified, leading to alterations in Fresnel wave surfaces and even the topological classes of the materials may appear differently in moving frames. We discuss the phenomenon of electromagnetic momentum tilt, defined as the non-zero angle between Abraham and Minkowski momenta or, equivalently, between the rays and the wavefront propagation direction. This momentum tilt is only possible in isotropy-broken media, where the E and H fields can be longitudinally polarized in the presence of electric and magnetic bound charge waves. The momentum tilt can be understood as a differential aberration of rays and waves when observed in the material rest frame.

Evaluating the accuracy of pressure measurements on the surface of shock waves propagating in an underwater environment of experimental explosion

Evaluating the accuracy of pressure measurements on the surface of shock waves propagating in an underwater environment of experimental explosion