Linear Wave Theory Research Articles

Self-healing of a heralded single-photon Airy beam.

Self-healing of an Airy beam during propagation is of fundamental interest and also promises important applications. Despite many studies of Airy beams in the quantum regime, it is unclear whether an Airy beam only including a single photon can heal after passing an obstacle because the photon may be blocked. Here we experimentally observe self-healing of a heralded single-photon Airy beam. Our observation implies that an Airy wave packet is robust against obstacle caused distortion and can restore even at the single-photon level.

Analysis of wave-induced submarine landslides in nearly saturated sediments at intermediate water depths

Evaluation of wave impacts on submarine landslides is an essential element in geohazard studies. The slight desaturation of sediments (due to dissociation of gas hydrates) has been found to adversely impact the slide of the sloping seabed in the Fraser River Delta in Canada. In this study, to investigate the role of wave action on the slide of partially saturated seabed slopes, an integrated FEM model is developed. Despite most earlier studies that used a simplified decoupled undrained analysis, in this article, a more realistic model for coupled flow-and-deformation processes (within the sediments) and fluid-seabed interaction is utilized. Linear wave theory and Biot’s poroelasticity for the fluid and seabed domains are considered, respectively, and continuity of flux and traction is enforced along the interface of the media. The instability of the sloping seabed is investigated using strength reduction finite element method (SRFEM) with Mohr-Coulomb failure criterion. The limitation of limit equilibrium methods in the evaluation of submarine landslides is shown through comparison with SRFEM analyses where partly-dynamic and quasi-static idealizations of seabed response are considered. Finally, the adverse impacts of slight desaturation on seabed instability are assessed, and the reduction of the stability number with seabed steepness is presented.

Remarks on the Boundary Conditions for a Serre-Type Model Extended to Intermediate-Waters

Numerical models are useful tools for studying complex wave–wave and wave–current interactions in coastal areas. They are also very useful for assessing the potential risks of flooding, hydrodynamic actions on coastal protection structures, bathymetric changes along the coast, and scour phenomena on structures’ foundations. In the coastal zone, there are shallow-water conditions where several nonlinear processes occur. These processes change the flow patterns and interact with the moving bottom. Only fully nonlinear models with the addition of dispersive terms have the potential to reproduce all phenomena with sufficient accuracy. The Boussinesq and Serre models have such characteristics. However, both standard versions of these models are weakly dispersive, being restricted to shallow-water conditions. The need to extend them to deeper waters has given rise to several works that, essentially, add more or fewer terms of dispersive origin. This approach is followed here, giving rise to a set of extended Serre equations up to kh ≈ π. Based on the wavemaker theory, it is also shown that for kh > π/10, the input boundary condition obtained for shallow-waters within the Airy wave theory for 2D waves is not valid. A better estimate for the input wave that satisfies a desired value of kh can be obtained considering a geometrical modification of the conventional shape of the classic piston wavemaker by a limited depth θh, with θ≤ 1.0.

Relation between Orbital Velocities, Pressure, and Surface Elevation in Nonlinear Nearshore Water Waves

AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of nonlinear shoaling and breaking waves in the nearshore has long been recognized. Yet, it remains widely used with linear wave theory to convert between subsurface pressure, wave orbital velocities, and the free surface elevation associated with nonlinear nearshore waves. Here, we present a nonlinear fully dispersive method for reconstructing the free surface elevation from subsurface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea state composed of both free and forced components. The present approach is effective starting from intermediate water depths—where nonlinear interactions between triads intensify—up to the surf zone, where most wave components are forced and travel approximately at the speed of nondispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the nonlinear fully dispersive method successfully reconstructs sea surface energy levels at high frequencies in diverse nonlinear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea surface energy levels at high frequencies and wave-by-wave statistics (e.g., wave extrema). Through its control on the efficiency of nonlinear energy transfers between triads, the spectral bandwidth is shown to greatly influence nonlinear effects in the transfer functions between subsurface hydrodynamics and the sea surface elevation.

A new type connection with optimum stiffness configuration for very large floating platforms

A novel connection for super-scale modularized floating platforms is put forward for the purposes of suppressing the oscillation of the platform. The platform consists of multiple blocks where semi-submergible modules are flexibly connected with upper decks by elastic cushions. For the connection between adjacent blocks, neighboring decks are linked by rigid hinges and neighboring floating modules are connected by flexible linkages. Based on the linear wave theory and rigid-module-flexible-connection (RMFC) model, the governing equation of motions for the modularized floating platform is derived by using a network modeling method. In numerical case studies, a five-block platform is investigated. Taking combined responses of the platform and the connector loads as an objective function, the stiffness configuration of the connection and the elastic cushion is optimally determined by using a genetic algorithm. At last, the short-term extreme responses of the floating platform with the optimum setting of the stiffness configuration of the connection are analyzed.

Numerical modelling of new flap-gate type breakwater in regular and solitary waves using one-fluid formulation

Breakwater is commonly used infrastructure for protecting coastal zones from waves and tsunamis. Computational modelling is frequently employed for prediction and validation of the breakwater design. Potential flow based models may not be ideal for such applications due to large energy dissipation. We apply the Computational Fluid Dynamics (CFD) to study the waves and breakwater interaction problem. In this work, we benchmark the performance of a new type of flap-gate breakwater in regular waves (airy wave theory and second order Stokes wave theory), where the multiphase Navier–Stokes equations are solved and the structure of breakwater is considered as one phase of fluid within the ‘one-fluid’ framework. In this way, the computational costs will be reduced to the same level as the numerical wave tank alone. We conduct a grid refinement study and compare results to experiments to investigate accuracy. The result shows a good agreement with the experimental data. Further, we use the validated model for sensitivity studies for different settings of flap-gate, and the solitary waves paradigm for tsunamis. The proposed novel numerical tool allows us to study large parametric spaces, impact of breaking waves, load and pressure producing process and interaction time.

Field-angle anisotropy of proximate Kitaev systems under an in-plane magnetic field

We have investigated the field-angle behaviors of magnetic excitations under an in-plane magnetic field for proximate Kitaev systems. By employing the exact diagonalization method in conjunction with the linear spin wave theory, we have demonstrated that the magnetic excitation gap in the polarized phase is determined by the magnon excitation at $M$ points and has a strong anisotropy with respect to the field direction in the vicinity of the critical field limit. The specific heat from this magnon excitation bears qualitatively the same anisotropic behaviors as expected one for the non-Abelian spin liquid phase in the Kitaev model and experimentally observed one of the intermediate phases in $\alpha$-RuCl$_3$.

Estimation of Relations between Representative Wave Heights Using Measured Wave Data for the West Sea of Korea

Ko, D.-H.; Lee, U.-J.; Cho, H., and Lee, B.W., 2021. Estimation of relations between representative wave heights using measured wave data for the west sea of Korea. In: Lee, J.L.; Suh, K.-S.; Lee, B.; Shin, S., and Lee, J. (eds.), Crisis and Integrated Management for Coastal and Marine Safety. Journal of Coastal Research, Special Issue No. 114, pp. 51–55. Coconut Creek (Florida), ISSN 0749-0208. The Rayleigh distribution was first defined as the distribution of individual wave heights for irregular waves. The relationships between representative wave heights have since been determined by manipulating the probability density function of the Rayleigh distribution. However, since the Rayleigh distribution is based on the linear wave theory assumption for narrow-band spectra, it is necessary to examine its applicability to shallow water. Thus, in this study, individual wave heights were calculated using water surface elevation data (2013.08.01 - 31) obtained from the HeMOSU-1 offshore measurement tower. The zero-up crossing method was used to define individual waves, and representative wave heights of highest, significant, highest one-tenth, mean, and root mean square waves were calculated using individual waves for 20 minutes. The Kolmogorov-Smirnov (K-S) test was used to determine the goodness of fit of the Rayleigh distribution for individual wave heights. Relationships between representative wave heights were also estimated and compared to the theoretical relationships. Approximately 91% of the total data did not follow the Rayleigh distribution. Meanwhile, the estimated coefficients of relationships (y = α × x) were compared to theoretical coefficients. The estimates obtained are greater than the theoretical estimates derived from the Rayleigh distribution with an error range of 1.68% to 13.25%.

Efficient asymptotics of solutions to the Cauchy problem with localized initial data for linear systems of differential and pseudodifferential equations

We say that the initial data in the Cauchy problem are localized if they are given by functions concentrated in a neighbourhood of a submanifold of positive codimension, and the size of this neighbourhood depends on a small parameter and tends to zero together with the parameter. Although the solutions of linear differential and pseudodifferential equations with localized initial data constitute a relatively narrow subclass of the set of all solutions, they are very important from the point of view of physical applications. Such solutions, which arise in many branches of mathematical physics, describe the propagation of perturbations of various natural phenomena (tsunami waves caused by an underwater earthquake, electromagnetic waves emitted by antennas, etc.), and there is extensive literature devoted to such solutions (including the study of their asymptotic behaviour). It is natural to say that an asymptotics is efficient when it makes it possible to examine the problem quickly enough with relatively few computations. The notion of efficiency depends on the available computational tools and has changed significantly with the advent of Wolfram Mathematica, Matlab, and similar computing systems, which provide fundamentally new possibilities for the operational implementation and visualization of mathematical constructions, but which also impose new requirements on the construction of the asymptotics. We give an overview of modern methods for constructing efficient asymptotics in problems with localized initial data. The class of equations and systems under consideration includes the Schrödinger and Dirac equations, the Maxwell equations, the linearized gasdynamic and hydrodynamic equations, the equations of the linear theory of surface water waves, the equations of the theory of elasticity, the acoustic equations, and so on. Bibliography: 109 titles.

Effects of a Hole on Uplifting Forces on a Submerged Horizontal Thin Plate

The effect of a hole on uplifting forces acting on a submerged horizontal thin plate are examined using the boundary element method. To deal with the submerged thin plate case, which is a degenerate boundary problem, a hypersingular integral equation is employed to overcome some troubles when the boundary element method is used. Two-dimensional problems are considered, and the linear gravity wave theory is adopted. Several examples are calculated and the numerical results are presented to show the influence of a hole on uplifting forces.

Effects of a Hole on Uplifting Forces on a Submerged Horizontal Thin Plate

The effect of a hole on uplifting forces acting on a submerged horizontal thin plate are examined using the boundary element method. To deal with the submerged thin plate case, which is a degenerate boundary problem, a hypersingular integral equation is employed to overcome some troubles when the boundary element method is used. Two-dimensional problems are considered, and the linear gravity wave theory is adopted. Several examples are calculated and the numerical results are presented to show the influence of a hole on uplifting forces.

Extent of frustration in the classical Kitaev- Γ model via bond anisotropy

In the pseudospin-$\frac{1}{2}$ honeycomb Mott insulators with strong spin-orbit coupling, there are two types of bond-dependent exchange interactions, named Kitaev ($K$) and $\Gamma$, leading to strong frustration. While the ground state of the Kitaev model is a quantum spin liquid with fractionalized excitations, the ground state of the $\Gamma$ model remains controversial. In particular, the phase diagram of the $K\Gamma$ model with ferromagnetic $K$ and antiferromagnetic $\Gamma$ interactions has been intensively studied because of its relevance to candidate materials such as $\alpha$-RuCl$_{3}$. Numerical studies also included the effects of tuning the bond strengths, i.e., $z$-bond strength different from the other bonds. However, no clear consensus on the overall phase diagram has been reached yet. Here we study the classical $K\Gamma$ model with the anisotropic bond strength using Monte Carlo simulations to understand the emerging phases out of competition between the two frustrated limits. We also address how the anisotropic bond strength affects the phase diagram and strength of quantum fluctuations. We found various large unit cell phases due to the competing frustrations, and analyzed their intrinsic degeneracy based on the symmetry of the Hamiltonian. Using the linear spin wave theory we showed that the anisotropic bond strength enhances quantum fluctuations in the $\Gamma$-dominant regime where a small reduced moment is observed. The implications of our findings in relation to the quantum model are also discussed.

A Theoretical Study of the Hydrodynamic Performance of an Asymmetric Fixed-Detached OWC Device

The chamber configuration of an asymmetric, fixed-detached Oscillating Water Column (OWC) device was investigated theoretically to analyze its effects on hydrodynamic performance. Two-dimensional linear wave theory was used, and the solutions for the associated radiation and scattering boundary value problems (BVPs) were derived through the matched eigenfunction expansion method (EEM) and the boundary element method (BEM). The results for the hydrodynamic efficiency and other important hydrodynamic properties were computed and analyzed for various cases. Parameters, such as the length of the chamber and the thickness and submergence of the rear and front walls, were varied. The effects on device performance of adding a step under the OWC chamber and reflecting wall in the downstream region were also investigated. A good agreement between the analytical and numerical results was found. Thinner walls and low submergence of the chamber were seen to increase the efficiency bandwidth. The inclusion of a step slightly reduced the frequency at which resonance occurs, and when a downstream reflecting wall is included, the hydrodynamic efficiency is noticeably reduced at low frequencies due to the near trapped waves in the gap between the OWC device and the rigid vertical wall.

Nonlinear wave effects on the oscillatory pore pressure induced forces on buried pipelines

ABSTRACT The present study investigates the influence of nonlinear waves on the oscillatory pore pressure-induced response around buried pipes. The study is carried out considering the applicable wave theories namely: linear, Stokes, cnoidal and solitary wave theories. The soil modelling is based on Biot’s consolidation equations which are solved using Finite Element tool COMSOL Multiphysics. Two case studies are considered for the investigation where the parameters of wave height and water depth are varied respectively for each case study to increase the wave nonlinearity. The hydrodynamic pressure on the seabed is based on the applicable wave theory which is chosen from Le-Mehaute’s diagram. The pore pressures, stresses and forces developed on the buried pipe are evaluated considering different wave theories. As the wave transforms from linear to cnoidal through stokes waves a gradual variation in the wave-induced soil response is observed, whereas the soil response from cnoidal to solitary waves is found to be considerably abrupt. It is observed that the magnitude of these wave-induced forces and stresses due to a solitary wave can be about twice that of a linear wave under a wave crest. Similarly, for the case of pipe under wave trough, linear wave theory gives a very high estimate of uplift force as compared to highly nonlinear solitary waves.

Surface manifestation of stochastically excited internal gravity waves

ABSTRACT Recent photometric observations of massive stars show ubiquitous low-frequency ‘red noise’ variability, which has been interpreted as internal gravity waves (IGWs). Simulations of IGWs generated by convection show smooth surface wave spectra, qualitatively matching the observed red noise. Theoretical calculations using linear wave theory by Shiode et al. and Lecoanet et al. predict IGWs should manifest at the surface as regularly spaced peaks associated with standing g modes. In light of the apparent discrepancy between these theories and simulations/observations, we test the theories with simplified 2D numerical simulations of wave generation by convection. The simulations agree with the transfer function calculations presented in Lecoanet et al., demonstrating that the transfer function correctly models linear wave propagation. However, there are differences between our simulations and the g-mode amplitude predictions of Shiode et al. This is because that work did not take into account the finite width of the g-mode peaks; after correcting for this finite width, we again find good agreement between theory and simulations. This paper verifies the theoretical approach of Lecoanet et al. and strengthens their conclusion that IGWs generated by core convection do not have a surface manifestation consistent with observed low-frequency variability of massive stars.

Theoretical Hydrodynamic Analysis of a Surface-Piercing Porous Cylindrical Body

In the present study, the diffraction and the radiation problems of water waves by a surface-piercing porous cylindrical body are considered. The idea conceived is based on the capability of porous structures to dissipate the wave energy and to minimize the environmental impact, developing wave attenuation and protection. In the context of linear wave theory, a three-dimensional solution based on the eigenfunction expansion method is developed for the determination of the velocity potential of the flow field around the cylindrical body. Numerical results are presented and discussed concerning the wave elevation and the hydrodynamic forces on the examined body for various values of porosity coefficients. The results revealed that porosity plays a key role in reducing/controlling the wave loads on the structure and the wave run-up, hence porous barriers can be set up to protect a marine structure against wave attack.

Predicting the Radiated Noise of a Submarine Propeller with Different Types of Control Surfaces

_ The objective of this paper is to predict the noise radiated from submarine propellers with different control surface types (the cross- and X-type). When the propellers are free from cavitation, such as those of submarines at a diving depth, the radiated noise dominate, due to unsteady propeller forces. A well-known submarine model (DARPA SUBOFF) is taken as the computing sample. Simulations for hydrodynamics, including stern wakes and unsteady propeller forces, are carried out by using CFD (Computational Fluid Dynamics) technology, and the results are compared with the experimental data. The accuracy of the predicted noise depends on the CFD results. Comparisons between the CFD results and the experimental data are in good agreement. The CFD results are treated as dipole strengths in the linear wave theory to predict the radiated noise caused by the unsteady forces of the propeller. It is found that, when the control surface is of the X-type, the propeller inflow is more uniform, and the radiated noise can be decreased by about 5 dB compared to the cruciform control surface. Introduction When submarines are at diving depth, the noise generated by unsteady propeller forces (i.e., dipole strengths) will dominate. Because the juncture vortex caused by the sail makes the propeller inflow more nonuniform, the dipole strength will be enhanced and the radiated noise will be more noticeable. The uniformity of the wake field at the stern should be controlled well in order to restrain the radiated noise.

Can Short‐Wave Nonlinearity Affect the Prediction of Wave Setup?

AbstractBased on high‐resolution laboratory data of instantaneous surface elevation and fluid velocity associated with the propagation of short waves over a gently sloping beach (GLOBEX project), the present work compares two methods for predicting the wave setup. A one‐dimensional (cross‐shore) model is considered to solve the balance equation that links the pressure gradient induced by the mean surface elevation profile with the wave radiation stress (including wave roller) and bottom stress profiles. When compared to measurements and using a wave‐by‐wave approach, the mean elevation appears to be significantly better predicted with a nonlinear approach based on stream function theory than with the commonly used linear approach based on Airy wave theory. At the shoreline, the linear method overestimates the wave setup by at least about while this error is globally reduced by a factor 2 to 4 in the nonlinear case. In the framework of this study, the combined contribution of bottom stress and wave roller to the wave setup appears secondary since it accounts for about of the predicted setup at the shoreline. Alternative computational methods are also considered to model the wave setup. In the linear case, using a spectral instead of the wave‐by‐wave approach greatly improves the wave setup predictions. This improvement is related to the disparity between the representative wave height (and thus the wave energy) obtained from spectral and wave‐by‐wave analysis when short‐wave nonlinearity becomes significant.

Variation of Wave Forces Along a Semi-Infinite Breakwater Due to Wave Diffraction

Abstract This paper investigates distribution of wave forces along a semi-infinite breakwater considering wave diffraction using the analytical solutions derived from linear wave theory. It is foun...

Wave attenuation properties of rubble mound breakwater in tandem with a floating dock against oblique regular waves

This work examines the impact of oblique wave action on a combination of a rubble mound breakwater and a floating dock. The influence of the breakwater on safety of the floating dock is examined in various configurations. The breakwater is approximated by a submerged trapezoidal structure and the floating dock by a surface piercing rigid rectangular structure. A numerical solution is developed combining the eigenfunction expansion method and the multi-domain boundary element method while assuming linear water wave theory. Reflection and transmission coefficients along with wave forces on the dock are evaluated and analyzed over a wide parameter range. The study reveals that the sloping angle of the trapezoidal breakwater plays a vital role in dissipating the wave load on the floating dock and the case of a trapezoidal breakwater with a vertical lee side faces is also examined. The reflection and transmission of waves are found to be dominated by the floating dock parameters in the system, while the wave forces on the dock are reduced by increasing the length and breadth of the breakwater and frictional coefficient of the porous structure, respectively. The combination of two structures in different tandem configurations is proposed as an effective coastal protection system.