Linear Wave Theory Research Articles

Observed Structure of an Internal Tide Beam Over the Mid‐Atlantic Ridge

AbstractInternal tides are key players in ocean dynamics above mid‐ocean ridges. The generation and propagation of internal tides over the Mid‐Atlantic Ridge (MAR) have been studied through theoretical and numerical models, as well as through moored, that is, one‐dimensional, observations. Yet, observations remain sparse and often restricted to the vertical direction. Here we report on the first two‐dimensional in situ observation of an internal tide beam sampled by a shipboard acoustic Doppler current profiler through a vertical section over the MAR. The beam is generated by the interaction of the barotropic tidal current with a supercritical abyssal hill that sits in the rift valley of the MAR. A vertical mode decomposition is carried out to characterize the spatio‐temporal variability of the beam. Although the modal content of the velocity field is dominated by modes 1 to 3, higher modes display localized and not persistent bursts of energy. The use of an analytical theory for linear internal waves allows us to rationalize the observed velocity field and interpret it as the superposition of modal waves generated on the hill and propagating in the same direction. The observed beam is qualitatively reconstructed as the superposition of waves of modes 2 to 6. The velocity field was sampled seven times across the same section and displayed qualitatively different patterns, unveiling the complexity of the dynamics above the MAR. A ray tracing of modal waves shows that the refraction by mesoscale currents could explain the observed variability of the tidal beam.

Time-dependent water wave scattering by a marine structure consisting of an array of compound porous cylinders

Under the assumption of linear wave theory, a semi-analytical model is developed to address the time-dependent water wave scattering problem involving a marine structure consisting of several circular rigid vertical cylinders, each of which is surrounded by a thin cylindrical porous wall with a water region between the inner cylinder and the wall. The problem is tackled by applying the eigenfunction expansion approach. The energy dissipation relation is also derived for the system of compound cylinders. The principal focus of this work lies in locating the optimum geometrical configurations for which the wave forces acting on the structure are minimal along a given wave direction in the frequency domain. Subsequently, the time-dependent response of the structure under the impact of a Gaussian wave pulse is examined. The wavenumber at which the force acting on the inner cylinder is at its maximum is obtained for a given value of the porous-effect parameter. Moreover, the value of that corresponding wavenumber decreases as the magnitude of the porous-effect parameter increases. The model is also carefully validated numerically against results available in the existing literature.

On the Evolution Equations of Nonlinearly Permissible, Coherent Hole Structures Propagating Persistently in Collisionless Plasmas

AbstractA fundamental study describing nonlinear plasma wave propagation is presented. Elementary linear wave theory describes small‐amplitude random waves, but lacks information about coherent structures. This improved wave model arises from the fact that structure formation is inevitably associated with particle trapping, which can only be properly addressed by the pseudo‐potential method instead of Bernstein, Greene, and Kruskal (BGK) ‐ likemethods. Only by using this method can legitimate nonlinear dispersion relations be obtained and reconciled with trapping scenarios. This privilege is used to derive evolution equations for five structures, the derivation being simplified by the acoustic nature of the permitted modes. The focus is on a special structure, the solitary electron hole of negative polarity, with which it can explain a spacecraft observation for the first time. Furthermore, it is shown that an intrinsically nonlinear structure can become macroscopically linear and thus harmonic by suitably adjusting the trapping scenario. An example is the monochromatic ion acoustic wave that propagates at ion sound velocity without dispersion. In this literature research, it also takes a critical look at a recently awarded work.

A mathematical study of a two-layer fluid flow system in the presence of a floating breakwater in front of VLFS

The present study deals with the usefulness of a surface-piercing porous structure of definite width in a two-layer fluid placed at a finite distance from a floating elastic plate to mitigate the hydrodynamic response of the elastic plate. We use linear water wave theory with the eigenfunction expansion approach to develop analytical solutions to the model problem in finite water depth. Here, we identify and explore the complete parameter space associated with the problem by examining the hydrodynamic coefficients for waves in surface and internal modes, plate elevation, shear force, bending moment, wave loads on the elastic plate, flow amplitude in the plate-covered region and wave attenuation. We investigate the effectiveness of structures of various configurations and geometries on wave scattering. This study demonstrates an oscillatory pattern of wave reflection in the confined region between the plate and the breakwater. Moreover, optima in the oscillatory pattern can be observed due to the resonating interaction of waves and the breakwater-plate system. Furthermore, the research shows that an ideal width and distance between the breakwater and floating plate can be calculated while assuming an appropriate configuration of the porous structure to create a breakwater-plate system with a reasonable efficiency that possesses both reflection and dissipation properties. The design of various types of coastal structures employed in the marine environment for the reflection and dissipation of wave energy at continental shelves dominated by stratified fluid, described here as a two-layer fluid, will significantly benefit from the findings of the current study.

Temperature-induced magnonic Chern insulator in collinear antiferromagnets

Thermal fluctuation in magnets causes temperature-dependent self-energy corrections in magnons; however, its effects on the topological orders of magnons is not well explored. Here we demonstrate that such corrections can induce a Chern insulating phase in two-dimensional collinear antiferromagnets with sublattice asymmetries by increasing temperature. We present the phase diagram of the system and show that the trivial magnon bands at zero temperature exhibit Chern insulating phase above a critical temperature before the paramagnetic phase transition. The self-energy corrections close and reopen the band gap at $\mathrm{\ensuremath{\Gamma}}$ or $\mathbf{K}$ points, accompanied by a magnon chirality switch and nontrivial Berry curvature transition. The thermal Hall effect of magnons or detecting the magnon polarization can highlight the experimentally prominent signatures of the topological transitions. We include the numerical results based on the van der Waals magnet ${\mathrm{MnPS}}_{3}$, calling for experimental implementation. Our work presents a paradigm for constructing topological phases that is beyond the linear spin wave theory.

Magnetic quantum and spin-wave behavior of three-layer graphene-like materials

This study examines the spin-wave and magnetic quantum behavior of three-layer graphene-like based on the Heisenberg model. The system is diagonally solved for Hamiltonian quantities using the linear spin wave theory and postponed Green's functions. The effects of exchange coupling, anisotropy, and spin quantum number on the resonance frequency and quantum fluctuation are discussed, providing a basis for regulating resonance frequency and quantum fluctuation.

Theoretical Analysis Method for Roll Motion of Popup Data Communication Beacons

The popup data communication beacon (PDCB) can send data to the shore and ships through the BeiDou navigation satellite system (BDS) when it surfaces. The data can be collected by a deep-sea landing vehicle (DSLV) and transmitted using a magnetic induction coil. PDCBs can reduce the cost of DSLV recovery and redeployment. Whether the data can be successfully sent mainly depends on the outlet height and roll angle of the PDCB. Thus, accurately assessing the effect of the roll angle on data transmission is crucial. In this study, first, the differential equation of roll motion was preliminarily established using the small-amplitude wave theory along with the shape characteristics of the PDCB. Next, the nonlinear term of the recovery moment was processed using the Linz Ted Poincaré method. Then, the wave current force was analyzed using the Morrison theoretical formula along with an additional inertia moment calculation formula that is suitable for slender cylindrical small buoys. Finally, the theoretical calculation results were verified using the computational fluid dynamics (CFD) method and pool test. The roll angle error of the theoretical calculation was within 5%. Thus, the heave and roll response of PDCBs can be evaluated using theoretical calculation methods. The proposed calculation formula of additional inertia moment has guiding significance for the further optimization of the structure.

Compressible Turbulence in the Near-Sun Solar Wind: Parker Solar Probe’s First Eight Perihelia

Many questions remain about the compressibility of solar wind turbulence with respect to its origins and properties. Low plasma beta (ratio of thermal to magnetic pressure) environments allow for the easier generation of compressible turbulence, enabling study of the relationship between density fluctuations and turbulent Mach number. Utilizing Parker Solar Probe plasma data, we examine the normalized proton density fluctuations as a function of turbulent Mach number M t conditioned on plasma beta and cross helicity. With consideration of statistical error in the parameters computed from in situ data, we find a general result that , consistent with both linear-wave theory and nearly incompressible turbulence in an inhomogeneous background field. We compare observational results conditioned on plasma beta and cross helicity with 3D magnetohydrodynamic simulations and observe rather significant similarities with respect to how those parameters affect the proportionality between density fluctuations and turbulent Mach number. This study further investigates the complexity of compressible turbulence as viewed by the density scaling relationship and may help better understand the compressible environment of the near-Sun solar wind.

Evaluation of wave-induced instability of nearly saturated sandy slopes under partially undrained condition: A case study of landslide in Fraser River delta front

A significant amount of Methane gas in soil deposits at Fraser River Delta (FRD), Canada, was identified as it adversely impacted the stability of the sloping seabed in the area under waves and tides. In this study, an integrated FEM model is utilized to investigate the instability of FRD front due to 1985 storm waves. Despite earlier studies that focused only on the role of residual pore pressure reached at late wave cycles in inducing the slide of FRD front (using empirical correlations), the transient response of sediments at early wave cycles is considered herein. The effect of coupled-flow-and-deformation processes within the sediments on the extent of the sliding plane is considered. For wave-seabed interaction modeling, Biot’s poroelasticity and linear wave theory are employed to represent the fluid and seabed domains, respectively. The slide evaluation of the sloping seabed is conducted using Strength Reduction Technique with Mohr-Coulomb failure criterion. The results indicate that the storm waves cause a shallow slide within the slope, and the proximity of the unsaturated layer to mudline exacerbated the instability condition. Moreover, instantaneous liquefaction zones are found to emerge away from the slope; thus, they may not lead to an exacerbated sliding of the slope.

Spin excitation continuum to topological magnon crossover and thermal Hall conductivity in Kitaev magnets

There has been great interest in identifying a Kitaev quantum spin liquid state in frustrated magnets with bond-dependent interactions. In particular, the experimental report of a half-quantized thermal Hall conductivity in $\alpha$-RuCl$_3$ in the presence of a magnetic field has generated excitement as it could be strong evidence for a field-induced chiral spin liquid. More recent experiments, however, provide a conflicting interpretation advocating for topological magnons in the field-polarized state as the origin of the non-quantized thermal Hall conductivity observed in their experiments. An inherent difficulty in distinguishing between the two scenarios is the phase transition between a putative two-dimensional spin liquid and the field-polarized state exists only at zero temperature, while the behaviour at finite temperature is mostly crossover phenomena. In this work, we provide insights into the finite temperature crossover behavior between the spin excitation continuum in a quantum spin liquid and topological magnons in the field-polarized state in three different theoretical models with large Kitaev interactions. These models allow for a field-induced phase transition from a spin liquid (or an intermediate field-induced spin liquid) to the field-polarized state in the quantum model. We obtain the dynamical spin structure factor as a function of magnetic field using molecular dynamics simulations and compute thermal Hall conductivity in the field-polarized regime. We demonstrate the gradual evolution of the dynamical spin structure factor exhibiting crossover behaviour near magnetic fields where zero-temperature phase transitions occur in the quantum model. We also examine nonlinear effects on topological magnons and the validity of thermal Hall conductivity computed using linear spin wave theory. We discuss the implications of our results to existing and future experiments.

Analysis of Wave Parameters on the Uprighting Process of a Grounded and Capsized Ship

It is a complicated task to right a capsized ship on the sea bottom because of wave load. Based on the influence of waves on stability and mechanical action, this paper constructs a wave force calculation model by the airy wave theory, and the stability and righting force models of righting a grounded and capsized ship are obtained. The uprighting process of a grounded and capsized ship is simulated by GHS software. In the process, stability and righting force are solved, and the effect of wave parameters on stability and mechanical action is studied. The result shows that when the wave phase is at its origin, the stability and the righting force can be effectively reduced. The wavelength has a significant effect on the hull stability, righting force and ground force in the range of 25 m–35 m. The change of wave height has significant influence on the stability and ground force, but the maximum ground force does not always change regularly with the wave height. Variation of the angle between the hull and the direction of the wave could significantly affect the stability, righting force, and ground force. When the encounter angle is 90°, the righting force is smaller than in other cases, and the maximum negative-going stability, the maximum righting force, and the maximum ground force values are 7.1%, 7.57%, and 3.83%, respectively, 11.7% smaller than those of still water. It is found by comparing several groups of wave parameters that a transverse wave could significantly reduce the difficulty of righting a grounded and capsized ship.

Reduction of wave load on monopile-supported offshore wind turbine by a gear-type plate

This study investigates the wave diffraction problem of a vertical cylinder with a gear-type plate by using the linear wave theory and the method of eigenfunction expansion. The present model is demonstrated to be accurate, through a comparison with the numerical results of the boundary element method. The horizontal wave force acting on the cylinder can be reduced considerably by the gear-type plate. Meanwhile, the variation in bending moment at the bottom of the cylinder depends on the wave conditions and geometry parameters. A low value of the ratio between water depth and cylinder radius (d/r0) can result in an increase in the bending moment on the cylinder, rather than a decrease, due to the additional loads exerted by the gear-type plate. The bending moment on the cylinder can be reduced significantly by the gear-type plate as d/r0 increases. Within d/r0∈[4,10] of the present monopile-supported wind turbines, the wave loads on the monopile foundation can be reduced significantly by the proposed gear-type plate. Compared with a ring-type plate, a gear-type plate exhibits superior reduction effects over an equal plate area. The loads on the structures are insensitive to the wave exposure angle when the teeth number increases beyond three.

Wave Action Analysis of Multiple Bottom Fixed Semi-Circular Breakwaters in the Presence of a Floating Dock

Abstract The comprehensive usage of an array of natural or artificial semi-circular breakwaters (SCBs) as supporting structures to secure the floating/fixed structures are received increasingly more consideration in recent years. The performance characteristics of bottom-fixed SCB in the presence of a floating dock are investigated under the framework of linear wave theory. The edge conditions such as continuity of velocity and pressure along the SCB and zero-flow condition near rigid surfaces are adopted. The multi-domain boundary element method (MBEM) is used to examine the wave attenuation performance of the whole breakwater system in two dimensions. The correctness of the present study's numerical results is confirmed by performing the comparative study with the readily available experimental and analytical results reported by various researchers. The reflection, transmission, energy loss coefficients, and fluid force experienced by floating dock are examined as a function of incident wave properties and breakwater physical properties. The Bragg resonant reflection and performance comparison with other shapes are also studied. The study results strongly suggest that the damage of floating structures and leeward locales due to incident wave stroke is minimized with the introduction of porosity for SCB located on the seabed by dissipating the wave energy. A pair of bottom-fixed SCBs having 10–20% breakwater porosity placed far away from the dock is identified as the optimal choice to reduce the fluid force experienced by the dock and wave transmission coefficient.

Dynamic Response Analysis of Offshore Flaoting Hose Strings Under Wave Load

A floating hose is key item for offshore oil transportation. In this paper, a mathematical model is derived for the overall dynamic performance of a single point-moored floating hose string under wave and current load. Airy wave theory was selected to calculate the wave force on the floating hose string. The dynamics of buoy, floating hose string and FSO were modelled using elastic foundation beam theory and discretised by using a fixed grid finite difference method. Discontinuities in the bending stiffness due to the flange connections are also considered. To verify the accuracy of the mathematical model, the finite element model of the buoy, floating hose string and FSO as a system was established by use of Orcaflex software tool. Numerical results for the displacement and bending moment at each section of the floating hose under severe sea conditions were obtained.

Effective stress analysis of residual wave-induced liquefaction around caisson-foundations: Bearing capacity degradation and an AI-based framework for predicting settlement

Excessive wave-induced pore pressure buildup around offshore foundations results in liquefaction, settlement and bearing capacity degradation, which may threaten the safety of Offshore Wind Turbines (OWTs). Despite the extensive research efforts on wave-induced seabed residual response in the recent years, there is still a lack of knowledge on mechanisms of wave-induced liquefaction and settlement around caisson foundations. Employing a code-based framework implemented in OpenSees, the cyclic response of wave-seabed-foundation (WSF) system is evaluated. Biot’s consolidation theory, linear wave theory and CycLiqCPSP constitutive soil model are integrated to evaluate the response of soil-foundation system accounting for the hydrodynamic pressure of wave imposed on the seabed surface considering the fully-coupled wave-seabed-foundation interaction (WSFI). Soil model parameters are calibrated against cyclic simple shear (CSS) tests and the numerical model is validated by a well-documented centrifuge experimental model. Various seabed characteristics, and a range of the geometrical properties of foundation with different OWT weights are put into practice for evaluating the geotechnical aspects of wave-induced liquefaction. Stress paths are provided to demonstrate quite different level of reduction in effective stresses and likelihood of liquefaction occurrence upon cyclic shear stresses application for different locations in the vicinity of the foundation area. The present study will also improve understanding of the interplay among the state variables on the wave-induced foundation settlement and bearing capacity degradation allow to feed the output data into development of simplified procedure for assessing the bearing capacity. Finally, results from over 250 analyses with different model configurations are used to provide an estimate of wave-induced caisson settlement with reasonable accuracy on the basis of artificial intelligence (AI) method known as Group Method of Data Handling (GMDH).

Wavenumber-Frequency Spectra of Normal Mode Function Decomposed Atmospheric Data: Departures from the Dry Linear Theory

The study of tropical tropospheric disturbances has led to important challenges from both observational and theoretical points of view. In particular, the observed wavenumber-frequency spectrum of tropical oscillations has helped bridge the gap between observations and the linear theory of equatorial waves. In this study, we obtained a similar wavenumber-frequency spectrum for each equatorial wave type by performing a normal mode function (NMF) decomposition of global Era–Interim reanalysis data. The NMF basis used here is provided by the eigensolutions of the primitive equations in spherical coordinates as linearized around a resting background state. In this methodology, the global multi-level horizontal velocity and geopotential height fields are projected onto the normal mode functions, characterized by a vertical mode, a zonal wavenumber, a meridional quantum index, and a mode type, namely, Rossby, Kelvin, mixed Rossby-gravity, and westward/eastward propagating inertio-gravity modes. The horizontal velocity and geopotential height fields associated with each mode type are then reconstructed in the physical space, as well as their corresponding filtered versions defined according to the vertical mode classes that exhibit barotropic and baroclinic structures within the troposphere. The results reveal expected structures, such as the dominant global-scale Rossby and Kelvin waves constituting the intraseasonal frequency associated with the Madden–Julian Oscillation. On the other hand, a number of unexpected features, such as eastward propagating westward inertio-gravity waves, are revealed by our observed 200 hPa zonal wind spectrum. Among all possible nonlinear processes, we focus on the analysis of the interaction between Kelvin and westward inertio-gravity waves, providing evidence for their coupling. Apart from the nonlinearity, we discuss the potential roles of a vertically/meridionally varying background state as well as the coupling with moist convection in explaining the departures of the observed spectra from the corresponding linear equatorial wave theory.

Characterization and modeling of greenwater overtopping of a sea-level deck

Greenwater overtopping occurs when the deck of a marine structure or ship is submerged by a large non-breaking wave. This overtopping wave develops into a fast-moving mass of water that can damage deck structures. In this work we use laboratory experiments to characterize the kinematics of the greenwater fronts, showing that there are two main classes of flow. One class is an essentially two-dimensional flow with a single wave front traversing the entire deck, while the second type has multiple wave fronts originating from all sides of the platform. We characterize each type with respect to wave conditions and describe the transition between the two types. We then discuss two modeling approaches that can be used to simulate the kinematic of the overtopping fronts. A simple linear model, based on linear wave theory and on the assumption of the overtopping as a dam break, to predict the type and the propagation of the overtopping wave on the deck. The second is a three-dimensional nonlinear numerical hydrodynamics model, based on Smoothed Particle Hydrodynamics method, which reproduces the geometry of the overtopping in the laboratory more accurately. We compare the outputs of these models with laboratory observations and discuss their applicability.

Observation of Bohm trajectories and quantum potentials of classical waves

In 1952 David Bohm proposed an interpretation of quantum mechanics, in which the evolution of states results from trajectories governed by classical equations of motion but with an additional potential determined by the wave function. There exist only a few experiments that test this concept and they employed weak measurement of non-classical light. In contrast, we reconstruct the Bohm trajectories in a classical hydrodynamic system of surface gravity water waves, by a direct measurement of the wave packet. Our system is governed by a wave equation that is analogous to the Schrödinger equation which enables us to transfer the Bohm formalism to classical waves. In contrast to a quantum system, we can measure simultaneously their amplitude and phase. In our experiments, we employ three characteristic types of surface gravity water wave packets: two and three Gaussian temporal slits and temporal Airy wave packets. The Bohm trajectories and their energy flows follow the valleys and bounce off the hills in the corresponding quantum potential landscapes.

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.