Linear Wave Theory Research Articles

Rainfall Enhancement Downwind of Hills Due to Stationary Waves on the Melting Level and the Extreme Rainfall of December 2015 in the Lake District of Northwest England

This paper investigates how stationary gravity waves generated by flow over orography enhance rainfall, with particular attention to the role of induced waves in the melting level. The findings reveal a new mechanism by which gravity wave flow focuses precipitation, amplifying rainfall intensity downwind of hills. This mechanism, which depends on the differential velocities of rain and snow, offers fresh insights into how orographic effects can intensify rainfall. A two-dimensional diagnostic model based on linear gravity wave theory is used to investigate the record-breaking rainfall of December 2015 in the Lake District of northwest England. The pattern of ascent is shown to have a qualitatively good fit to that of the Met Office’s operational high-resolution UKV model averaged over 24 h, suggesting that orographically excited stationary waves were the principal cause of the rain. Precipitation trajectories imply that a persistent downstream elevated wave caused by the Isle of Man supported a spray of seeding ice particles directed towards the Lake District, and that these grew whilst suspended in strong upslope flow before being focused by the undulating melting-level into intense shafts of rain.

An adaptive internal mass source wave-maker for short wave generation

The mass source wave-maker is commonly employed for generating water waves in numerical simulations, during which a correct amount of mass is introduced or subtracted from the internal flow region to produce target waves. The method has proven to be effective in producing waves in shallow and intermediate water depths, while its efficiency is declined for short wave generation. The main reason for this efficiency declination is that the internal mass source in deeper water region is not effective to generate short waves with their motions primarily on water surface. In order to overcome this shortcoming, many of the previous numerical treatments have introduced various enhancement factors into the source functions, which are empirically obtained and also violate the law of mass conservation. In this study, we develop a new adaptive internal wave-maker model that can be self-adjusted to suit different wave conditions. The line source starts from the bottom and extends to the computational cell right beneath free surface at each time step. The depth dependent weighting coefficient is introduced to the source function based on the linear wave theory for each wave component. No empirical coefficients are necessary, and the mass conservation is strictly and explicitly enforced. In principle, the method can be applied to all types of linear waves in the entire range of kh. The numerical experiments show that the present method can produce very good results for linear waves with kh up to 16.11, adequate for most of wave conditions in coastal engineering. For generation of fifth-order Stokes waves, the method can be extended straightforwardly for each of five wave components. For irregular waves composed of many linear wave components, different weighting coefficients can be readily calculated for each of them, respectively. As a result, the new model can generate irregular waves with overall better performance of reproducing wave spectrum, whose high-frequency part has been underestimated by previous methods. The numerical experiments also show that the new model can produce better results for focused waves where many linear waves of different frequencies start from the same point with specific phase angles, due to its capability of generating shorter wave components.

Physical Modeling of Tsunamis Generated by Submarine Volcanic Eruptions

AbstractSubmarine volcanic eruptions can induce major local and regional tsunami hazards through varied source mechanisms. Large‐scale experiments of tsunamis generated by submarine volcanic eruptions are conducted to study the cylindrical wave generation and propagation in a three‐dimensional wave basin. A unique volcanic tsunami generator (VTG) was deployed at the bottom of the wave basin to generate volcanic tsunamis with repeatable and controlled source parameters. The physical modeling is based on the generalized Froude number defined with the VTG velocity and the near source water depth. The pneumatically driven vertical stroke motion generates leading elevation waves in the wave basin. The tsunami waves generated by the VTG are measured with a wave gauge array. The wave maker performance is characterized by the dimensionless leading wave amplitudes and periods. The experimental data show the variations of the leading wave amplitude, period, and celerity along the radial propagation distance. The generated cylindrical waves belong to the weakly nonlinear wave regime in the near field with decaying wave amplitude along radial propagation. The attenuation rate of the leading wave exceeds the range from the linear wave theory in runs with higher Froude numbers. The dimensionless leading wave period increases with the dimensionless propagation distance due to the dispersion relation. Empirical equations for the characteristic wave parameters such as amplitudes and periods are derived. The experimental results contribute to the understanding of volcanic tsunami generation processes and may serve rapid volcanic tsunami hazard assessments as well as the advancement and validation of numerical models.

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.

Damage analysis of OC4 jacket subjected to cyclic loading by peridynamic approach

Catastrophic structural failure caused by fatigue damage under cyclic loads can be avoided by identifying critical locations of the damage initiation and the fatigue life during the design stage. Peridynamic (PD) theory defines structure as a collection of material points with non-local bond interactions where the structural discontinuity due to fatigue represented by instantaneous bond breakage is estimated through cumulative decrement of the bond’s life at each load cycle. In this work, we model a reference jacket presented under the Offshore Code Comparison Collaboration Continuation project (OC4) through peridynamic beam formulation. Initially, the static deformations of the beam and deformations of the OC4 jacket under static, harmonic, and irregular point loads are validated with ABAQUS results in all six degrees of freedom. Thereby, the PD fatigue parameters of the jacket’s steel material are calibrated from the experimental data of the corresponding material with a trial simulation for fatigue damage analysis. Later, different load cases from regular waves interacting with the jacket are generated in the PD framework by adopting linear wave theory. Based on the PD cyclic energy release rate model, a comparative study of all load cases to identify critical damage locations with the failure load cycles for damage initiation and fracture is performed for the considered OC4 jacket.

Current Loads on a Horizontal Floating Flexible Membrane in a 3D Channel

A 3D analytical model is formulated based on linearised small-amplitude wave theory to analyse the behaviour of a horizontal, flexible membrane subject to wave–current interaction. The membrane is connected to spring moorings for stability. Green’s function approach is used to obtain the dispersion relation and is utilised in the solution by applying the velocity decomposition method. On the other hand, a brief description of the experiment is presented. The accuracy level of the analytical results is checked by comparing the results of reflection and the transmission coefficients against experimental data sets. Several numerical results on the displacements of the membrane and the vertical forces are studied thoroughly to examine the impact of current loads, spring stiffness, membrane tension, modes of oscillations, and water depths. It is observed that as the value of the current speed (CS) rises, the deflection also increases, whereas it declines in deeper water. On the other hand, the spring stiffness has minimal effect on the vibrations of the flexible membrane. When vertical force is considered, higher oscillation modes increase the vertical loads on the membrane, and for a mid-range wavelength, the vertical wave loads on the membrane grow as the CS increases. Further, the influence of the phase and group velocities are presented. The influences of CS and comparisons between them in terms of water depth are presented and analysed. This analysis will inform the design of membrane-based wave energy converters and breakwaters by clarifying how current loads affect the dynamics of floating membranes at various water depths.

A new paradigm for scattering theory of linear and nonlinear waves: review and open problems

I present a review of the recent advancements in scattering theory, which provides a unified approach to studying dispersive and hyperbolic equations with general interaction terms and data. These equations encompass time-dependent potentials, as well as NLS, NLKG, and NLW equations. Additionally, I discuss a series of open problems along with their significance and potential future applications in scattering and inverse scattering.

Wave excited motion of a body floating on water confined between a semi-infinite ice sheet and a side wall

In this paper, we investigate the diffraction and radiation coupling problem of a floating body confined between a fixed wall and a semi-infinite ice sheet under the action of incident waves. Based on the linear water wave theory and Kirchhoff Love elastic thin plate assumption, the ice sheet is considered as an elastic beam, and the boundary conditions of fluid boundaries covered by the ice sheet are obtained. Dividing flow domains with different upper surfaces, the eigenfunction expansion method was used to obtain the velocity potential expansion equations for each sub-domain. Then, through the matching conditions at the interface of sub-domains, a system of equations was constructed to solve the unknown coefficients of the expansion equations. The influence of the existence of the ice sheet on the diffraction and radiation motion of the floating body is analyzed. The effects of changes in the draft and open water width of the floating body on the wave excitation force and hydrodynamic coefficient of the floating body are discussed. The influence of the reflection effect of the ice sheet on the added mass and damping coefficient of the floating body has been discovered, especially the changes and oscillation rules of their extreme points. This research achievement provides theoretical support for the safety design of floating structures in frozen harbors.

Dynamical response of a floating ice sheet due to a forced oscillation in a running stream

This paper explores the response of a floating ice sheet to a forced, time-harmonic oscillatory pressure applied to the ice-covered surface of a uniform, finite depth fluid. The floating ice sheet is modeled as a thin elastic plate following the Euler–Bernoulli beam equation, with the additional consideration of in-plane compressive forces acting on the ice. Employing linear wave theory, the problem is presented as an initial boundary value problem and is solved using Laplace and Fourier transforms to obtain a mathematical expression for the ice sheet's deflection in terms of infinite integrals. These integrals are thereafter solved asymptotically for large time and distance using the stationary phase method. The asymptotic analysis indicates a growing response over time when the poles and stationary points of the phase functions coalesce. The deflection of the floating ice sheet is graphically presented, highlighting the effects of various non-dimensional parameters, such as flexural rigidity, compressive force, uniform current speed, and the angular frequency of the oscillatory pressure. Additionally, the group velocity and phase velocity of flexural gravity waves are derived from the dispersion relation and elucidated using diagrams. The results show that compressive force and current speed significantly influence wave amplitude, enhancing the oscillatory nature, while the flexural rigidity of the elastic plate and the angular frequency of the applied pressure have a substantial impact on the plate's deflection.

Load motion on an ice cover in the presence of a liquid layer with velocity shear

The behavior of an ice cover on the surface of an ideal incompressible fluid of finite depth under the action of a pressure domain that moves rectilinearly at a constant velocity in the presence of a current with velocity shift in the upper layer is studied. It is assumed that the ice deflection is steady in the coordinate system moving with the load. The Fourier transform method is used within the framework of the linear wave theory. The critical velocities, the deflection of ice cover, and the wave forces are studied depending on the current velocity gradient, the shear layer thickness, the direction of motion, and the compression ratio.

Scattering of Oblique Water Waves by Two Vertical Barriers Over Trench-Type Bottom

The problem of scattering of oblique water waves by two surface-piercing vertical thin rigid barriers over a trench-like bottom is investigated within the framework of linear water wave theory. The eigenfunction expansion technique is used to obtain a system of algebraic equations, which is further solved using the algebraic Least squares method. The reflection and transmission coefficients are computed and contrasted with the prior results. Physical characteristics such as surface elevation and horizontal force on both barriers are also determined and depicted graphically against various parameters to see their behavior. It is possible to strategically construct barriers and trench-like bottoms to regulate how waves reflect and propagate. This might mitigate the wave impact on ships, improving the safety, effectiveness and longevity of ships navigating through the channels. The highlights of the given problem include comparing the impacts of different depth ratios and barrier placements, followed by a study of the modulation parameter to evaluate standing wave patterns in the trench region. The specific circumstances for the formation of the standing wave are identified. Hence, understanding this study is critical for safe navigation because standing waves may produce hazardous conditions for boats, making navigation difficult and causing substantial damage.

Hybrid spin-orbit exciton-magnon excitations in FePS3

FePS3 is a layered van der Waals (vdW) Ising antiferromagnet that has recently been studied in the context of true 2D magnetism and emerged as an ideal material platform for investigating strong spin-phonon coupling, and non-linear magneto-optical phenomena. In this work, we demonstrate an important unresolved role of spin-orbit coupling (SOC) in the ground state and excitations of this compound. Combining first-principles calculations with linear flavor wave theory (LFWT), we find strong mixing and spectral overlap of different spin-orbital single-ion states. Low-lying excitations form hybrid spin-orbit exciton/magnon modes. Complete parameterization of the low-energy model requires nearly half a million coupling constants. Despite this complexity, such a model can be inexpensively derived using local many-body-based approaches, which yield quantitative agreement with recent experiments. The results highlight the importance of SOC even in first-row transition metals and provide essential insight into the properties of 2D magnets with unquenched orbital moments.

Highly efficient Airy beam generator with high polarization purity by a receiving-transmitting metasurface

This paper presents a highly efficient Airy beam generator at microwave frequency using a transparent metasurface with a receiving-transmitting scheme. The amplitude and phase of the transmitted orthogonal polarization wave can be flexibly controlled by orientation angles of receiving and transmitting patches of the proposed meta-atom. Utilizing this property to reshape the field of transmitted waves following the desired phase and amplitude profile of the Airy wave packet, an Airy beam generator is designed and experimentally demonstrated. Simulation and measurement results both show a self-healing Airy beam with an efficiency of 23.5% and polarization purity above 20 dB, which approaches the theoretical limitation of the designed Airy beam. Due to the well-performed beam efficiency and polarization purity resulting from the receiving-transmitting metasurface, our design holds great promise for efficient wavefront shaping and facilitates the use of high-purity Airy beams for practical applications.

Modulation of the wake of a horizontal cylinder by pycnocline thickness in stratified flow

This study investigates the modulating effect of the pycnocline thickness in two-dimensional stratified flow on a cylinder. It encompasses three typical flow regimes identified by Boyer in experiments conducted within the Reynolds number range of Re = 260–2000. Quantitative control of the modulation effect of internal interface waves on the cylinder wake is achieved by varying the thickness of the pycnocline. Under appropriate thickness of the pycnocline, a multiple-centerline-structure can transition to isolated-mixed-structure flow regimes and Double-Eddy-Wavy-Wake flow regimes. Similar modulation patterns are also observed in isolated-mixed flow regimes. Normalized pressure distribution and velocity fields indicate that in low Reynolds number flow regimes (Re < 600), downstream isolated mixed regions generate dynamic pressure that periodically cascades upstream. This periodic reverse energy transfer provides favorable adverse pressure gradients, cyclically reducing the drag force on the cylinder. The cyclic period is, for the first time, classified into four stages: dynamic pressure storage stage, dynamic pressure transfer stage, dynamic pressure consumption stage, and dynamic pressure exhaustion stage. Despite the highly nonlinear modulation effect of internal interface waves in low Reynolds number conditions, the linear predictive theory of lee waves based on streamline equations remains instructive in predicting the trend of lee waves wavelength variation with pycnocline thickness. Drawing upon the modulation study results concerning the pycnocline thickness on lee waves, a regime map is constructed, illustrating the directional evolution of lee waves flow patterns based on variations in pycnocline thickness.

Interaction of short-crested waves with cylinder and concentric segmented arc breakwaters

Using the outer breakwater of Palm Jumeirah in Dubai as a physical geometric model, the diffraction problem of short-crested waves interacting with concentric segmented arc structures was theoretically investigated using linear water wave theory. In this study, the watershed was partitioned into two regions, and a unique coordinate system was established to describe the velocity potential function within each region. The interface between the two regions connects the velocity potentials across them using the matching eigenfunction expansion technique. By accounting for the boundary conditions, the integral equation was streamlined into a series of algebraic equations, which were subsequently resolved to determine an unidentified function. The precision of the model was validated through a comparison with findings from the literature. Numerical investigations have elucidated the correlation between changes in wave force, cylinder run-up, and parameters such as the spacing between adjacent arcs, opening angle, and porous coefficient. The numerical results indicated that the impermeable segmented arcs structure provides better protection against short-crested and plane waves, whereas the permeable segmented arc structure provides better protection against standing waves. Interestingly, for a segmented three-arc structure, when the segments are moderately spaced, the protection of the interior region is superior to that of an unsegmented arc structure.

Elastic jump propagation across a blood vessel junction.

The theory of small-amplitude waves propagating across a blood vessel junction has been well established with linear analysis. In this study, we consider the propagation of large-amplitude, nonlinear waves (i.e. shocks and rarefactions) through a junction from a parent vessel into two (identical) daughter vessels using a combination of three approaches: numerical computations using a Godunov method with patching across the junction, analysis of a nonlinear Riemann problem in the neighbourhood of the junction and an analytical theory which extends the linear analysis to the following order in amplitude. A unified picture emerges: an abrupt (prescribed) increase in pressure at the inlet to the parent vessel generates a propagating shock wave along the parent vessel which interacts with the junction. For modest driving, this shock wave divides into propagating shock waves along the two daughter vessels and reflects a rarefaction wave back towards the inlet. However, for larger driving the reflected rarefaction wave becomes transcritical, generating an additional shock wave. Just beyond criticality this new shock wave has zero speed, pinned to the junction, but for further increases in driving this additional shock divides into two new propagating shock waves in the daughter vessels.

Task-Driven Learning Downsampling Network Based Phase-Resolved Wave Fields Reconstruction with Remote Optical Observations

We develop a phase-resolved wave field reconstruction method by the learning-based downsampling network for processing large amounts of inhomogeneous data from non-contact wave optical observations. The Waves Acquisition Stereo System (WASS) extracts dense point clouds from ocean wave snapshots. We couple learning-based downsampling networks with the phase-resolved wave reconstruction algorithm, and the training task is to improve the wave reconstruction completeness ratio CR. The algorithm first achieves initial convergence and task-optimized performance on numerical ocean waves built by the linear wave theory model. Results show that the trained sampling network can lead to a more uniform spatial distribution of sampling points and improve CR at the observed edge regions far from the optical camera. Finally, we apply our algorithm to a natural ocean wave dataset. The average completeness ratio is improved over 30% at low sampling ratios (SR∈[2−9,2−7]) compared to the traditional FPS method and Random sampling method. Moreover, the relative residual between the final reconstructed wave and the natural wave is less than 15%, which provides an efficient tool for wave reconstruction in ocean engineering.

Two-dimensional diffraction and radiation problems of a floating body in varying bathymetry

In this study, a coupling method of the higher order boundary element method and the eigenfunction expansion method is applied to investigate the diffraction and radiation problems of a floating body over an uneven seabed under the assumption of linear small-amplitude wave theory. The wave exciting forces and hydrodynamic coefficients are calculated for a floating rectangular box. It is found that the curves of the wave exciting forces and hydrodynamic coefficients versus frequency become fluctuating as the horizontal length L and vertical height D of the sloping seabed gradually increase. The period of the fluctuations decreases with the increase of L, and the magnitude of the fluctuations increases with the increase of D. The mechanism of the fluctuation phenomenon is then examined, and found that it is associated with the wave reflection from the slope seabed. With increasing horizontal scale L and vertical scale D of the sloping seabed, the amplitude and phase of the reflection wave change, which leads to the combined action of the incident, scattering and reflection waves fluctuating with the wave frequency.

Model predictive control of a wave-to-wire wave energy converter system with non-linear dynamics and non-linear constraints using a tailored pseudo-spectral method

A novel pseudo-spectral method is proposed to tackle the non-linear control problem of a wave energy converter (WEC) integrated with an all-electrical power-take-off (PTO). The WEC hydrodynamic model is constructed using linear wave theory together with a non-linear viscous damping term. The PTO model encompasses a permanent magnet synchronous generator (PMSG) whose local field weakening mechanism imposes non-linear operational constraints on the WEC’s motion and PTO torque. The energy-maximizing control problem of this wave-to-wire model is non-linear and has not been investigated before. In comparison to pseudo-spectral methods previously studied, the proposed pseudo-spectral method is exempt from the assumption of ideal incoming wave prediction. This is made possible by the introduction of a novel mapping function to convert the finite control horizon onto the Gaussian quadrature interval. This mapping function increases more slowly with time at the beginning of the control horizon where wave prediction attains greater precision. As a result, the collocation points are utilized to the advantage of the better approximation of the objective function, thus better overall control performance.

Oblique wave interaction with dual submerged oscillating buoy as WEC near a partially reflecting wall

The hydrodynamic performance of a submerged dual cylindrical wave energy converter (WEC) in front of a partially reflecting vertical wall is investigated within the framework of linear wave theory. The double cylinders are fully submerged and are constrained only in heave motion. The conversion of wave action into usable power occurs by the coordinated motion of two buoy systems viz. a power take-off mechanism (PTO). The numerical solution for the boundary value problem comprising of wave diffraction and radiation by submerged dual cylinders is obtained using the Boundary Element Method (BEM). The study is devoted to investigating the influence of various factors, the effect of cylinder dimensions, cylinder-cylinder spacing, partially reflecting wall-cylinder distance, angle of wave attack, and its submergence. The compelling results are presented by examining the heave force, surge force, response amplitude operator (RAO), damping factor, and particular interest in the WEC energy capture efficiency under distinct seawall reflections. The study reveals that there is an increase in the WEC efficiency by ≈12% in the case of a dual cylinder compared to a single cylinder. Besides, the amplification of the WEC efficiency is ≈78% for the case of a fully reflecting wall compared to the WEC in the open fluid domain. The present study will further help to understand the dynamics of WECs integrated into protecting shore structures such as breakwaters, groins, and seawalls.