Linear Wave Theory Research Articles

Motion of a Load on an Ice Cover in the Presence of a Current 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 is studied. Fluid flow is not potential. The ice cover is modeled by a thin elastic plate with account for uniform compression. The motion of the load can occur at an arbitrary angle to the direction of current. 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 and the deflection of ice cover are studied depending on the current velocity gradient, the direction of motion, and the compression ratio.

Spin wave spectra of single crystal CoPS3

The spin waves in single crystals of the layered van der Waals antiferromagnet CoPS$_3$ have been measured using inelastic neutron scattering. The data show four distinct spin wave branches with large ($\gtrsim 14$ meV) energy gaps at the Brillouin zone center indicating significant anisotropy. The data were modelled using linear spin wave theory derived from a Heisenberg Hamiltonian. Exchange interactions up to the third nearest-neighbour in the layered planes were required to fit the data with ferromagnetic $J_1 = -1.37$ meV between first neighbours, antiferromagnetic $J_3 = 3.0$ meV between third neighbours, and a very small $J_2 = 0.09$ meV between second neighbours. A biaxial single-ion anisotropy was required, with a collinear term $D^x = -0.77$ meV for the axis parallel to the aligned moment direction and a coplanar term $D^z=6.07$ meV for an axis approximately normal to the layered crystal planes.

Hydroelastic Response to the Effect of Current Loads on Floating Flexible Offshore Platform

An analytical model of a current load’s interaction with a moored floating flexible structure based on the Timoshenko–Mindlin beam theory is developed under the assumption of small-amplitude wave theory and the structural response. Theoretical solutions on the displacement of the structure, reflection, and transmission coefficients are obtained by applying the matching technique along with the orthogonal model coupling relation. The results of the transmission coefficient and displacement amplitude are compared with the other calculations and experimental datasets available in the literature. The structural deflection and transmission coefficients are investigated via the hydroelastic response for wave–current loads along with design parameters. The comparison results showed that the present model result is supported by the numerical model’s results. This present analysis can provide further information for marine engineers to design floating flexible platforms in the marine environment.

Offshore Measurements and Numerical Validation of the Mooring Forces on a 1:5 Scale Buoy

Wave energy conversion is a renewable energy technology with a promising potential. Although it has been developed for more than 200 years, the technology is still far from mature. The survivability in extreme weather conditions is a key parameter halting its development. We present here results from two weeks of measurement with a force measurement buoy deployed at Uppsala University’s test site for wave energy research at the west coast of Sweden. The collected data have been used to investigate the reliability for two typical numerical wave energy converter models: one low fidelity model based on linear wave theory and one high fidelity Reynolds-Averaged Navier–Stokes model. The line force data is also analysed by extreme value theory using the peak-over-threshold method to study the statistical distribution of extreme forces and to predict the return period. The high fidelity model shows rather good agreement for the smaller waves, but overestimates the forces for larger waves, which can be attributed to uncertainties related to field measurements and numerical modelling uncertainties. The peak-over-threshold method gives a rather satisfying result for this data set. A significant deviation is observed in the measured force for sea states with the same significant wave height. This indicates that it will be difficult to calculate the force based on the significant wave height only, which points out the importance of more offshore experiments.

Observation of Ultrabroadband Striped Space-Time Surface Plasmon Polaritons

Because surface plasmon polaritons (SPPs) are surface waves characterized by one free transverse dimension, the only monochromatic diffraction-free spatial profiles for SPPs are cosine and Airy waves. Pulsed SPP wave packets have been recently formulated that are propagation-invariant and localized in the in-plane dimensions by virtue of a tight spectral association between their spatial and temporal frequencies, which have thus been dubbed “space-time” (ST) SPPs. Because of the spatiotemporal spectral structure unique to ST-SPPs, the optimal launching strategy of such novel plasmonic field configurations remains an open question. We present here a critical step toward realizing ST-SPPs by reporting observations of ultrabroadband striped ST-SPPs. These are SPPs in which each wavelength travels at a prescribed angle with respect to the propagation axis to produce a periodic (striped) transverse spatial profile that is diffraction-free. We start with a free-space ST wave packet that is coupled to a ST-SPP at a gold-dielectric interface, and unambiguously identify the ST-SPP via an axial beating detected in two-photon fluorescence produced by the superposition of incident ST wave packet and the excited surface-bound ST-SPP. These results highlight a viable approach for efficient and reliable coupling to ST-SPPs and, thus, represent the first crucial step toward realization of the full potential of ST-SPPs for plasmonic sensing and imaging.

Ship waves in rivers: Environmental criteria and analysis methods for measurements

AbstractA literature review shows that the most important physical quantities determining environmental impact of ship waves in a waterway are the fluid velocities, maximum and minimum water levels, and size of drawdown events. Fluid velocity can vary strongly in the vertical so that the usual measurements at a single point are not enough unless made near where the effects are most important, often the bed. Customary use of wave height as a measure of impact has been misleading, because the all‐important fluid velocity is of a scale given by wave height divided by wave period. A good and simple estimate of the surface velocity as a disturbance scale is shown to be given by the time derivative of the free surface height. The most important role of linear wave theory is to explain and understand the physics and measurement procedures, such as done here in several places. Its use for obtaining numerical results is criticised. Instead, three integral measures of impact are proposed, all of which use surface elevation measurements and which require no essential mathematical approximations or wave‐by‐wave analysis. The methods are applied to a study of ship waves on the Danube River. A number of results are presented, including examination of the effects of measurement frequency. After a ship passage, due to repeated shoreline reflections of the wake waves, the river is brought into a long‐lasting state of short‐crested disturbances, with finite fluid velocities. The environmental consequences of this might be important. After the primary and secondary ship waves it could be called the tertiary wave system.

Wave radiation by a horizontal circular cylinder in a three-layer fluid

To construct cylindrical structures like circular pipe bridges or tunnels submerged in the almost still density-stratified ocean or seawater, the study of waves radiated by the cylinder is essential. This research solves the wave radiation problem by calculating non-dimensionalized added mass and damping coefficients to the mass of the fluid displaced by the submerged horizontal cylinder in either layer of a three-layer fluid, which is still otherwise. Under the linear theory of water waves, we investigate the circular cylinder's hydrodynamic forces by its swaying and heaving motion. The time-harmonic wave propagates with three distinct wavenumbers for a given frequency. The method of multipoles has been employed due to its rapid converging solutions by increasing the truncation limit. Potential functions are expressed into systems of linear algebraic equations, which are solved numerically for two sets of unknowns in each case by truncation. Then, the added mass and damping coefficients are obtained from the non-dimensionalized hydrodynamic forces when the horizontal circular cylinder is submerged in the lower, middle and upper layers, respectively. The obtained results are depicted graphically against wavenumber in numerous figures and analysed.

Inversion of Wave Parameters From Time-Doppler Spectrum Using Shore-Based Coherent S-Band Radar

For coherent microwave radar, the Bragg scattering from the broken-short waves generated after wave breaking usually introduces extra low-frequency components in the estimated wave height spectrum and, thus, leads to inaccurate retrievals of wave parameters, especially the overestimation of wave period. In order to eliminate the impacts of wave breaking, some methods based on the removal of “group line” in the spatial–temporal domain are proposed to estimate wave parameters. However, these methods are not suitable for the case that the spatial–temporal data are not available. To address this problem, a method is proposed to invert wave parameters only from the time-Doppler spectrum. Temporal velocity series are derived from the time-Doppler spectrum in which breaking components are removed. Then, the wave height spectrum from which wave parameters can be obtained is estimated from the velocity series by the direct transform relationship based on the linear wave theory. Without spatial–temporal data, the “group line” can be removed using the proposed method, and the method is validated by simulation. In addition, an approximately 11-day dataset collected with a shore-based coherent S-band radar deployed along the coast of Zhejiang province in China is reanalyzed and used to retrieve significant wave height and mean wave period. Compared with the buoy-measured data, the significant wave heights and mean wave periods retrieved by the proposed method have the root-mean-square differences (RMSDs) of 0.25 m and 0.60 s, respectively, and also have the correlation coefficients (CCs) of 0.94 and 0.81, respectively. The results indicate that the proposed method can invert wave parameters from the time-Doppler spectrum with a reasonable performance.

Trajectory analysis of phase effects associated with truncated Airy beams

Airy wave packets constitute a very peculiar type of structured light: during their propagation, their transverse profile undergoes a self-accelerating displacement while it remains shape invariant. They are thus the only non-dispersive beam-type solution to the Helmholtz paraxial equation in free space. Such properties are possible by virtue of their infinite power content. However, experimentally, Airy beams can only be reproduced in an approximate manner, with a limited extension and hence a finite power content. To this end, differentcutoffprocedures have been reported in the literature, based on a convenient tuning of the transmission properties of aperture functions. In this Communication, we present and discuss our latest advances in the analysis of the effects that convolving an Airy beam with different aperture functions have on their propagation properties. More specifically, we make use of a trajectory-based methodology, which allows us to analyze and explain the beam propagation in terms of trajectories directly connected with the beam local phase variations.

Ocean-Wave Gradiometry: Visualizing and Extracting Propagation Features of the 15 January 2022 Tsunami Wavefield with Dense Ocean-Bottom Pressure Gauge Arrays

Abstract Dense geophysical observation networks have recently enabled monitoring the wavefield of sea-bottom pressure changes. Significant sea-bottom pressure disturbances were recorded by ocean-bottom pressure gauge (OBPG) arrays around Japan on 15 January 2022, the day of the massive eruption of Hunga Tonga–Hunga Ha’apai volcano in the Tonga Islands. At the same time, sea-surface height disturbances and atmospheric pressure disturbances were recorded by tide gauges around the Pacific Ocean and barometers around the world. Because the atmospheric disturbances may have affected the propagation of the sea-surface height changes, we investigated the propagation properties of the sea-bottom pressure disturbances recorded by the OBPG arrays around Japan using wave gradiometry. We found that the leading pressure disturbances propagated from southeast to northwest with a velocity expected from linear long-wave theory for ocean waves, that is, tsunamis. We also detected several later coherent sea-bottom pressure disturbances that propagated at the velocity of tsunamis. In addition, we detected anomalous short-period later phases of pressure disturbances with propagation directions more nearly north–south than those of the leading disturbances at the coast of southwestern Japan. These results indicate that the pressure disturbances recorded at the OBPG arrays propagated as tsunamis rather than sea-surface disturbances excited by atmospheric Lamb waves, although atmospheric pressure disturbances might have affected the amplitude of sea-surface height changes. This study demonstrates that wave gradiometry can be successfully applied to data from a dense OBPG array and may be suitable for real-time monitoring of sea-bottom pressure wavefields.

Holes and magnetic polarons in a triangular lattice antiferromagnet

The intricate interplay between charge motion and magnetic order in geometrically frustrated lattices is central for the properties of many two-dimensional quantum materials. The triangular lattice antiferromagnet is a canonical example of a frustrated system, and here we analyze the dynamics of a hole in such a lattice focusing on observables that have become accessible in a new generation of experiments. Using the $t\ensuremath{-}J$ model, we solve the problem exactly within linear spin wave theory in the limit of strong magnetic interactions, showing that the ground state is described by a coherent state of spin waves. The derivation highlights the crucial role played by the interaction between a static hole and the neighboring spins, which originates in the geometric frustration and has often been omitted in earlier works. Furthermore, we show that the nonequilibrium dynamics after a hole has abruptly been inserted at a lattice site is given by a coherent state with time-dependent oscillatory coefficients. Physically, this describes a burst of magnetic frustration propagating through only two-thirds of the lattice sites, since a destructive interference of spin waves leaves spins parallel to that removed by the hole unperturbed. After the wave has propagated through the lattice, the magnetization relaxes to that of the ground state. We then use our analytical solution to benchmark the widely used self-consistent Born approximation (SCBA) in the limit of strong magnetic interactions, showing that it is very accurate also for a triangular lattice. The magnetic polaron spectrum is analyzed for general magnetic interactions using the SCBA, and we compare our results with those for a square lattice.

Second-order Stokes wave-induced dynamic response and instantaneous liquefaction in a transversely isotropic and multilayered poroelastic seabed

The ocean waves exhibit obvious non-linearity with asymmetric distribution of wave crests and troughs, which could induce significantly different effect on the seabed compared to the commonly used linear wave theory. In this paper, a semi-analytical solution for a transversely isotropic and multilayered poroelastic seabed under non-linear ocean wave is proposed by virtue of the dual variable and position (DVP) method. The ocean wave and seabed are, respectively, modelled using second-order Stokes theory and Biot’s complete poroelastodynamic theory. Then the established governing equations are decoupled and solved via the powerful scalar potential functions. Making use of the DVP scheme, the layered solutions are finally gained by combining the boundary conditions of the seabed. The developed solutions are verified by comparing with existing solutions. The selected numerical examples are presented to investigate the effect of main parameters on the dynamic response of the seabed and evaluate the corresponding liquefaction potential. The results show that the anisotropic stiffness and permeability, degree of saturation and stratification have remarkable influence on the dynamic response and liquefaction behavior of the seabed. The present solution is a useful tool to estimate the stability of transversely isotropic and layered seabed sediment in the range of non-linear ocean wave.

Free Vibration Analysis of Stiffened Lock Gate Coupled with Reservoir Fluid considering Linearised Free Surface Condition

The effect of surrounding reservoir fluid on the stiffened lock gate structure is investigated using the finite element method. A single stiffener is used to stiffen the plate, which is placed edge to edge along the height on the plate's center nodal line. Mindlin’s plate bending and Euler’s beam theories are used to formulate plate and stiffener, respectively. The stiffened lock gate material is assumed to be isotropic, homogeneous, uniformly thick and elastic in nature. The fluid is assumed to be incompressible and inviscid, resulting in an irrotational flow field. The fluid domain's top free surface is assumed to be linear based on Airy’s linear wave theory. The far boundary of the fluid domain is truncated numerically close to the lock gate to control the size of computation without influencing the results, very much. It is truncated by solving the Laplace equation using Fourier half range cosine series expansion in the finite element formulation. Pressure and displacement are considered as nodal variables for the fluid domain and the lock gate, respectively. The interaction between the fluid domain and the lock gate is established by finite element formulation and transformed into a computer code, written in FORTRAN. The natural frequencies of clamped and simply supported stiffened lock gates are evaluated by the varying extent of the fluid. Both stiffened and unstiffened gates are compared. The results are beneficial to the engineers/designers when the gate structure is subjected to cataclysmic events.

Comparative study on response of jacket platforms under regular waves using Airy’s and Stokes’ fifth-order wave theories

Despite the random nature of ocean waves, to provide engineering solutions, regular wave theories are commonly used to estimate wave forces from the Morison equation in offshore structural analysis. These wave theories can be defined by three basic parameters, namely water depth, wave height and wave period. The applicability of a particular wave theory to a given set of wave characteristics and water depth is governed chiefly by the ratios of water depth and wave height to the wavelength. Airy’s linear wave theory, on account of its simplicity, is a popular choice, especially for preliminary calculations and for providing insight into the basic characteristics of wave-induced water motion. It is, however, applicable to small wave heights and in many conditions the linear theory is incapable of providing a satisfactory assessment of the water particle kinematics. A nonlinear theory is then required, and Stokes’ fifth order wave theory, based on the expansion of the wave solution in series form, provides a more accurate representation of the free-surface and is generally used for high waves in deep water. In this paper, a comparative study is conducted between the wave forces obtained from Morison equation utilising Airy’s wave theory and Stokes’ fifth order wave theory, acting at different levels of a jacket platform. Two sets of water depth, wave height and wave period are selected so that they satisfy the region of applicability of Airy’s wave theory and Stokes’ fifth order wave theory respectively. Two example four-legged jacket platforms are considered. It is found that for design purposes, in most cases the wave forces and structural responses from Airy’s wave theory are more conservative as compared to those from Stokes’ fifth order wave theory, though the converse is obtained in case of deep water conditions near the seabed. Overall, in deep water, high wave conditions, apart from Stokes’ fifth order wave theory, Airy’s wave theory may be used for preliminary estimations of wave forces and deck displacements, but in shallow water conditions, Stokes’ fifth order wave theory is entirely invalid.

Dynamical modeling and parametric analysis of an electret-based wave energy converter

Carbon neutrality and the Internet of Underwater Things have injected new impetus into the development of wave energy converters (WECs) albeit most of WEC projects have ended in failure due to low cost-effectiveness. Hereupon we present the dynamical modeling and parametric analysis of a novel electret-based WEC that has a distinct power take-off system compared to the conventional ones and has exhibited high power density in our previous study. Linear wave theory and Morison equation are applied for wave field and forces, respectively. WEC motions parallel with incident waves are modeled, and the electrical subsystem of the generator is treated as a current source and a capacitor. With these simplifications, the governing equations of the nonlinear and non-smooth electromechanical system are obtained and then numerically solved using an event-driven algorithm. The new power take-off system is experimentally validated. We find that the power output varies nonlinearly with wave parameters under regular wave excitation but linearly under irregular ones, and that superharmonic resonance can significantly enhance energy conversion performance at relatively low frequencies, based on which the optimum parameters are obtained. A peak average power of around 2 mW (at a matched load resistance) is generated from each generator encapsulated in the WEC of a diameter of 15 cm. The findings shed light on the characteristics of electret-based WECs and provide support for the development of wave energy farm; moreover, the methodologies of modeling and analysis can be extended to the design and optimization of the scaleups of the proposed electret-based WEC.

Two-dimensional quantum universality in the spin-1/2 triangular-lattice quantum antiferromagnet Na2BaCo(PO4)2.

An interplay of geometrical frustration and strong quantum fluctuations in a spin-1/2 triangular-lattice antiferromagnet (TAF) can lead to exotic quantum states. Here, we report the neutron-scattering, magnetization, specific heat, and magnetocaloric studies of the recently discovered spin-1/2 TAF Na2BaCo(PO4)2, which can be described by a spin-1/2 easy axis XXZ model. The zero-field neutron diffraction experiment reveals an incommensurate antiferromagnetic ground state with a significantly reduced ordered moment of about 0.54(2) μB/Co. Different magnetic phase diagrams with magnetic fields in the ab plane and along the easy c-axis were extracted based on the magnetic susceptibility, specific heat, and elastic neutron-scattering results. In addition, two-dimensional (2D) spin dispersion in the triangular plane was observed in the high-field polarized state, and microscopic exchange parameters of the spin Hamiltonian have been determined through the linear spin wave theory. Consistently, quantum critical behaviors with the universality class of d = 2 and νz = 1 were established in the vicinity of the saturation field, where a Bose-Einstein condensation (BEC) of diluted magnons occurs. The newly discovered quantum criticality and fractional magnetization phase in this ideal spin-1/2 TAF present exciting opportunities for exploring exotic quantum phenomena.

Analytical solution of dynamic responses of offshore wind turbine supported by monopile under combined earthquake, wave and wind

Offshore wind turbine system (OWTs) in areas of earthquake activity are potentially threatened by a combination of earthquake, wave, and wind loads. Thus, an analytical solution of OWTs supported by monopile on viscoelastic half-space is developed to investigate the dynamic responses of OWTs subjected to the earthquake, wave, and wind loads. Firstly, the OWTs supported by monopile considering a series of coupled interactions is established, in which monopile end soil-soil viscoelastic half-space interaction is solved by static spring-damping system, monopile-soil and water interaction are solved by analytical horizontal impedance, monopile-wave interaction is solved by linear wave theory, and tower drum-wind interaction is solved by wind loads applied on the turbine blades. Then, the displacement response of OWTs supported by monopile is further obtained based on the continuity conditions between the monopile and tower drum. Finally, the present solution degenerated into a rigid foundation and verified the rationality with existing analytical and substructure methods. In addition, some critical parameters are further conducted by using the present solution. The results indicate that it is necessary to consider the couple influence of earthquake, wave, and wind loads in the design of OWTs supported by monopile.

Low-cost investigation of wave dynamics across low energy reef environments in Indonesia

The interaction between offshore waves and complex reef bottom profiles determines the hydrodynamic processes within the reef beaches, for instance, Sea-Swell (SS) wave dissipation, Infragravity (IG) wave generation as well as wave-induced currents and setups. These hydrodynamics phenomena are important to several ecological processes and control the associated shoreline erosion and flooding. Hence, a good understanding of the dynamics is needed that wave observations are challenging and expensive otherwise. Here we present a short term (12 hours) investigation of non-directional spectral waves using a series of HOBO pressure sensors. Six pressure sensors were deployed at 3 locations along the fringing reefs of Tunda Island, Banten Province - Indonesia. The wave spectra were estimated from the surface water fluctuations using linear wave theory for each hourly burst data. During observation, the Tunda waters were calm with significant wave heights were less than 10 cm with peak wave periods of ∼12 s at all sites. Despite the short period measurement due to memory issue, the result demonstrated the ability of HOBO pressure sensors to measure non-directional wave spectra at shallow water.

Ab initio study of spin fluctuations in the itinerant kagome magnet FeSn

Kagome antiferromagnetic metal FeSn has become an attracting platform for the exploration of novel electronic states, such as topological Dirac states and the formation of flat bands by localized electrons. Apart from the electronic properties, Dirac magnons and flat magnon bands have also been proposed by applying simplified Heisenberg models to kagome magnetic systems.Inelastic neutron scattering studies on FeSn found well defined magnon dispersions at low energies,but magnons at high energies are strongly dampled, which can not be explained by localized spin models. In this paper, we utilize both linear spin wave theory and time-dependent density functional perturbation theory to investigate spin fluctuations of FeSn. Through the comparison of calculated spin wave spectra and Stoner continuum, we explicitly show that the damping of magnons at high energies are due to the Landau damping, and the appearance of high energy optical-magnon like branches at the M and K point are resulted by relatively low Stoner excitation intensity at those regions.

Dissipation of Gravity Waves Due to Submerged Porous Plate Coupled With Porous Structures

Abstract The present study focuses on wave trapping due to the submerged horizontal porous plate combined with the bottom-standing porous structure and surface-piercing porous structure. The submerged plate thickness is considered to be negligible as compared to the incident wavelength and water depth, and the porous structure is considered to be of finite width. The study is performed based on the eigenfunction expansion method, and the wave interaction with the combined structure is investigated using the small amplitude wave theory. The orthogonal mode-coupling relation is used to analyze the wave interaction with the combined structure. The reflection, transmission, and dissipation coefficients along with wave force on the porous structure are investigated to analyze the hydrodynamic performance of the composite porous breakwater system. Further, the effect of porosity of submerged plate and structure, submergence depth of plate and structure, angle of incidence, and the submerged plate length are investigated to analyze the effective wave dissipation by the composite breakwater. In addition, the comparative study of the numerical method is performed with the results available in the literature. The study noted that the wave damping due to the submerged porous plate backed by surface-piercing porous structure is more as compared to the submerged porous plate backed by the bottom-standing porous structure. The study performed will be helpful to scientists and engineers in the design of suitable composite breakwater systems and also assists in selecting the best structural configuration for attenuation of wave height and to protect the offshore facility from high waves in the coastal region.