Interaction Of Waves Research Articles

Wave transformation across impermeable and porous artificial reefs

Porous artificial reefs can function as nature-based solutions for coastal protection, due to their ability to dissipate wave energy while providing habitat for marine species. However, due to the lack of quantitative understanding of wave interactions with porous artificial reefs, there is uncertainty in how to optimize design for coastal protection applications. To address this gap, physical modelling experiments were conducted in a wave flume to investigate wave transformation across both porous and impermeable artificial reefs exposed to a range of regular wave conditions and submergence depths. The results highlight how key changes to wave kinematics (e.g., wave celerity, wave breaking) and wave energy (through reflection, dissipation and transmission) differ considerably between impermeable and porous artificial reefs. These differences in wave kinematic properties and energy balances across each reef can be well characterized by consideration of the effective crest depth (i.e., the total height of water at a point on the reef, including that in the voids) that accounts for the porosity of the reef structure, rather than the actual depth of the reef crest. The ratio of the effective crest depth to the incident wave height, termed the ‘relative effective crest depth’, was used to develop robust formulations to accurately predict wave reflection and transmission coefficients across both reefs over the range of wave and water depth conditions. The new formulations were also compared to other datasets reported in the literature, and were found to provide accurate predictions of both wave reflection and transmission for the broad range of submerged porous coastal structures considered (including artificial reefs and submerged breakwaters).

Wave Interaction with a Bottom-Mounted Body in Front of a Vertical Wall Using an Exact DtN Boundary Condition

Wave Interaction with a Bottom-Mounted Body in Front of a Vertical Wall Using an Exact DtN Boundary Condition

Interactions of certain localized waves for an extended (3+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics

Currently, there is much interest in the study on the localized waves and their interactions in fluid mechanics. An extended (3+1)-dimensional Kadomtsev-Petviashvili equation is considered here. By means of the Hirota method, we obtain the N-soliton solutions, with N as a positive integer. The higher-order breather solutions are obtained from the N-soliton solutions through the complex conjugated transformations. Making use of the long-wave limit method, we determine the higher-order lump solutions via the N-soliton solutions. Besides, some hybrid solutions are presented. Three kinds of the localized waves, namely, the solitons, breathers and lumps, along with their interactions, are investigated via the above solutions. Amplitudes, shapes and velocities of those localized waves remain invariant after the interactions, which indicate that the interactions are elastic. Fluid-mechanically meaningful, all our results rely on the coefficients in that equation.

Sum-frequency triad interactions among surface waves propagating through an ice sheet

We study nonlinear resonant wave–wave interactions which occur when ocean waves propagate into a thin floating ice sheet. Using multiple-scale perturbation analysis, we obtain theoretical predictions of the wave amplitude evolution as a function of distance travelled past the ice edge for a semi-infinite ice sheet. The theoretical predictions are supported by a high-order spectral (HOS) method capable of simulating nonlinear interactions in both open water and the ice sheet. Using the HOS method, the amplitude evolution predictions are extended to multiple (coupled) triad interactions and a single ice sheet of finite length. We relate the amplitude evolution to mechanisms with strong frequency dependence – ice bending strain, related to ice breakup, as well as wave reflection and transmission. We show that, due to sum-frequency interactions, the maximum strain in the ice sheet can be more than twice that predicted by linearised theory. For an ice sheet of finite length, we show that nonlinear wave reflection and transmission coefficients depend on a parameter in terms of wave steepness and ice length, and can have values significantly different than those from linear theory. In particular, we show that nonlinear sum-frequency interactions can appreciably decrease the total wave energy transmitted past the ice sheet. This work has implications for understanding the occurrence of ice breakup, wave attenuation due to scattering in the marginal ice zone and the resulting ice floe size distribution.

TOSCA – an open-source, finite-volume, large-eddy simulation (LES) environment for wind farm flows

Abstract. The growing number and growing size of wind energy projects coupled with the rapid growth in high-performance computing technology are driving researchers toward conducting large-scale simulations of the flow field surrounding entire wind farms. This requires highly parallel-efficient tools, given the large number of degrees of freedom involved in such simulations, and yields valuable insights into farm-scale physical phenomena, such as gravity wave interaction with the wind farm and farm–farm wake interactions. In the current study, we introduce the open-source, finite-volume, large-eddy simulation (LES) code TOSCA (Toolbox fOr Stratified Convective Atmospheres) and demonstrate its capabilities by simulating the flow around a finite-size wind farm immersed in a shallow, conventionally neutral boundary layer (CNBL), ultimately assessing gravity-wave-induced blockage effects. Turbulent inflow conditions are generated using a new hybrid off-line–concurrent-precursor method. Velocity is forced with a novel pressure controller that allows us to prescribe a desired average hub-height wind speed while avoiding inertial oscillations above the atmospheric boundary layer (ABL) caused by the Coriolis force, a known problem in wind farm LES studies. Moreover, to eliminate the dependency of the potential-temperature profile evolution on the code architecture observed in previous studies, we introduce a method that allows us to maintain the mean potential-temperature profile constant throughout the precursor simulation. Furthermore, we highlight that different codes do not predict the same velocity inside the boundary layer under geostrophic forcing owing to their intrinsically different numerical dissipation. The proposed methodology allows us to reduce such spread by ensuring that inflow conditions produced from different codes feature the same hub wind and thermal stratification, regardless of the adopted precursor run time. Finally, validation of actuator line and disk models, CNBL evolution, and velocity profiles inside a periodic wind farm is also presented to assess TOSCA’s ability to model large-scale wind farm flows accurately and with high parallel efficiency.

Utilization of a Genetic Algorithm to Identify Optimal Geometric Shapes for a Seismic Protective Barrier

The utilization of seismic barriers for protection against the hazardous impact of natural or technogenic waves is an extremely promising emerging technology to secure buildings, structures and entire areas against earthquake-generated seismic waves, high-speed-transport-induced vibrations, etc. The current research is targeted at studying the effect of seismic-barrier shape on the reduction of seismic-wave magnitudes within the protected region. The analytical solution of Lamb’s problem was used to verify the adopted numerical approach. It was demonstrated that the addition of complementary geometric features to a simple barrier shape provides the possibility of significantly increasing the resulting seismic protection. A simple genetic algorithm was employed to evaluate the nontrivial but extremely effective geometry of the seismic barrier. The developed approach can be used in various problems requiring optimization of non-parameterizable geometric shapes. The applicability of genetic algorithms and other generative algorithms to discover optimal (or close to optimal) geometric configurations for the essentially multiscale problems of the interaction of mechanical waves with inclusions is discussed.

Oceanic internal solitary wave interactions via the KP equation in a three-layer fluid with shear flow

Oceanic internal solitary wave interactions via the KP equation in a three-layer fluid with shear flow

Low-frequency air-coupled transducer based damage detection in composite materials

In this paper results of simulations of non-contact elastic wave generation in the composite panel based on acoustic to elastic wave transformation are presented. For this purpose simulations of acoustic wave generation and processing are based on the FEM method in COMSOL. Elastic wave generation and propagation are based on the spectral element method (SEM) in the time domain. The SEM model utilises time-varying acoustic pressure distributions calculated in the FEM. The SEM allows to simulate the interactions of elastic waves with the delamination. Damage localization is based on RMS elastic wave energy maps. In this research a panel made of carbon fibre-reinforced polymer composite is investigated. Research related to low-frequency air-coupled transducer (ACT) is presented. The utilisation of low-frequency waves allows for the reduction of the effects of the wave attenuation in composite material. The proposed combination of FEM and SEM gives an efficient tool for the simulation of non-contact wave generation for non-destructive testing analysis.

On the dynamics of soliton interactions in the stellar environments

The effects of trapping of relativistically degenerate electrons are studied on the formation and interaction of nonlinear ion-acoustic solitary waves (IASWs) in quantum plasmas. These plasmas are detected in high-density astrophysical entities and can be created in the laboratory by interacting powerful lasers with matter. The formula for the number density of electrons in a state of relativistic degeneracy is provided, along with an analysis of the non-relativistic and ultra-relativistic scenarios. While previous studies have delved into specific aspects of relativistic effects, there needs to be a more detailed and systematic examination of the fully relativistic limit, which is essential for gaining a holistic perspective on the behavior of solitons in these extreme conditions. The aim of this work is to comprehensively investigate the fully relativistic limit of the system to fill this gap. The reductive perturbation technique is utilized to deduce the Korteweg–de Vries (KdV) equation, which is used to analyze the properties of the IASWs. Hirota bilinear formalism is applied to obtain single- and multi-soliton solutions for the KdV equation. The numerical analysis is focused on the plasma properties of the white dwarf in the ongoing investigation. The amplitude of the IASWs is found to be maximum for the non-relativistic, intermediate for the ultra-relativistic, and minimum for the fully relativistic limit. Most importantly, it is found that the fastest interaction occurs in the non-relativistic limit and the slowest in the fully relativistic limit.

Self-consistent interaction of linear gravitational and electromagnetic waves in non-magnetized plasma

This paper explores the hybridization of linear metric perturbations with linear electromagnetic (EM) perturbations in non-magnetized plasma for a general background metric. The local wave properties are derived from first principles for inhomogeneous plasma, without assuming any symmetries of the background metric. First, we derive the effective (“oscillation-center”) Hamiltonian that governs the average dynamics of plasma particles in a prescribed quasimonochromatic wave that involves metric perturbations and EM fields simultaneously. Then, using this Hamiltonian, we derive the backreaction of plasma particles on the wave itself and obtain gauge-invariant equations that describe the resulting self-consistent gravito-electromagnetic (GEM) waves in a plasma. The transverse tensor modes of gravitational waves are found to have no interaction with the plasma and the EM modes in the geometrical-optics limit. However, for longitudinal GEM modes with large values of the refraction index, the interplay between gravitational and EM interactions in plasma can have a strong effect. In particular, the dispersion relation of the Jeans mode is significantly affected by electrostatic interactions. As a spin-off, our calculation also provides an alternative resolution of the so-called Jeans swindle.

On the shock wave boundary layer interaction in slightly rarefied gas

The shock wave and boundary layer interaction (SWBLI) plays an important role in the design of hypersonic vehicles. However, discrepancies between the numerical results of high-temperature gas dynamics and experiment data have not been fully addressed. It is believed that the rarefaction effects are important in SWBLI, but the systematic analysis of the temperature-jump boundary conditions and the role of translational/rotational/vibrational heat conductivities are lacking. In this paper, we derive the three-temperature Navier–Stokes–Fourier (NSF) equations from the gas kinetic theory, with special attention paid to the components of heat conductivity. With proper temperature-jump boundary conditions, we simulate the SWBLI in the double cone experiment. Our numerical results show that, when the three heat conductivities are properly recovered, the NSF equations can capture the position and peak value of the surface heat flux, in both low- and high-enthalpy inflow conditions. Moreover, the separation bubble induced by the separated shock and the reattachment point induced by impact between transmitted shock and boundary layer are found to agree with the experimental measurement.

Two-Dimensional Wave Interaction with a Rigid Body Floating near the Marginal Ice Zone

The interaction problem of waves with a body floating near the marginal ice zone is studied, where the marginal ice zone is modeled as an array of multiple uniformly sized floating ice sheets. The linear velocity potential theory is applied for fluid flow, and the thin elastic plate mode is utilized to describe the ice sheet deflection. A hybrid method is used to solve the disturbed velocity potential; i.e., around the floating body, a boundary integral equation is established, while in the domain covered by ice sheets, the velocity potential is expanded into an eigenfunction series, and in the far-field with a free surface, a similar eigenfunction expansion is used to satisfy the radiation condition. The boundary integral equation and the coefficients of the eigenfunction expansions are solved together based on the continuous conditions of pressure and velocity on the interface between the sub-domains. Extensive results for the equivalent Young’s modulus of the ice sheet array and hydrodynamic force on the body are provided, and the effect of individual ice sheet length as well as wave parameters are investigated in detail.

Switching via wave interaction in topological photonic lattices.

A honeycomb Floquet lattice with helically rotating waveguides and an interface separating two counter-propagating subdomains is analyzed. Two topologically protected localized waves propagate unidirectionally along the interface. Switching can occur when these interface modes reach the edge of the lattice and the light splits into waves traveling in two opposite directions. The incoming mode, traveling along the interface, can be adjusted and routed entirely or partially along either lattice edge with the switching direction based on a suitable mixing of the interface modes.

Quasi-phase-matched nonlinear Lamb waves in composite laminates for material degradation monitoring

Monitoring material degradation and in-service damage in fibrous composites at an early stage is challenging, yet critical for many industrial applications. Second harmonic Lamb waves, which result from the interaction of fundamental waves with material microstructural defects, have great potential for Structural Health Monitoring (SHM) applications. However, understanding of the second harmonic generation in composite laminates remains largely insufficient, which hinders practical SHM applications. This issue is investigated in this study to highlight the quasi-cumulative second harmonic B2 mode Lamb wave in the low frequency range. Theoretical analyses are conducted to ascertain how anisotropy affects the quasi-cumulative effect, followed and validated by numerical simulations and analyses considering different wave propagation angles. The characteristics of the second harmonic B2 mode Lamb waves are further explored in terms of the cumulative feature, robustness to wave beam divergence, and excitability. Experiments are finally carried out to monitor material degradation during the thermal aging of a carbon fiber reinforced panel. The results confirm the omnidirectional cumulative effect of quasi-phase-matched second harmonic B2 mode Lamb waves. It is revealed that the 0° propagating Lamb waves exhibit superior cumulative effect, high robustness to wave beam divergence, and good excitability, rendering them an ideal tool for SHM applications. Furthermore, the high sensitivity of the second harmonic B2 mode waves to material degradation is demonstrated, confirming their promise for material degradation monitoring applications in composite structures.

Experimental investigation of cylindrical shock wave interactions

Experimental investigation of cylindrical shock wave interactions

Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves

Physics-Informed Neural Networks with Two Weighted Loss Function Methods for Interactions of Two-Dimensional Oceanic Internal Solitary Waves

Electrostatic wave interaction via asymmetric vector solitons as precursor to rogue wave formation in non-Maxwellian plasmas

An asymmetric pair of coupled nonlinear Schrödinger (CNLS) equations has been derived through a multiscale perturbation method applied to a plasma fluid model, in which two wavepackets of distinct (carrier) wavenumbers (k1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_1$$\\end{document} and k2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k_2$$\\end{document}) and amplitudes (Ψ1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Psi _1$$\\end{document} and Ψ2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Psi _2$$\\end{document}) are allowed to co-propagate and interact. The original fluid model was set up for a non-magnetized plasma consisting of cold inertial ions evolving against a κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document}-distributed electron background in one dimension. The reduction procedure resulting in the CNLS equations has provided analytical expressions for the dispersion, self-modulation and cross-coupling coefficients in terms of the two carrier wavenumbers. These coefficients present no symmetry whatsoever, in the general case (of different wavenumbers). The possibility for coupled envelope (vector soliton) solutions to occur has been investigated. Although the CNLS equations are asymmetric and non-integrable, in principle, the system admits various types of vector soliton solutions, physically representing nonlinear, localized electrostatic plasma modes, whose areas of existence is calculated on the wavenumbers’ parameter plane. The possibility for either bright (B) or dark (D) type excitations for either of the (2) waves provides four (4) combinations for the envelope pair (BB, BD, DB, DD), if a set of explicit criteria is satisfied. Moreover, the soliton parameters (maximum amplitude, width) are also calculated for each type of vector soliton solution, in its respective area of existence. The dependence of the vector soliton characteristics on the (two) carrier wavenumbers and on the spectral index κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document} characterizing the electron distribution has been explored. In certain cases, the (envelope) amplitude of one component may exceed its counterpart (second amplitude) by a factor 2.5 or higher, indicating that extremely asymmetric waves may be formed due to modulational interactions among copropagating wavepackets. As κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document} decreases from large values, modulational instability occurs in larger areas of the parameter plane(s) and with higher growth rates. The distribution of different types of vector solitons on the parameter plane(s) also varies significantly with decreasing κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document}, and in fact dramatically for κ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\kappa$$\\end{document} between 3 and 2. Deviation from the Maxwell-Boltzmann picture therefore seems to favor modulational instability as a precursor to the formation of bright (predominantly) type envelope excitations and freak waves.

Small-scale Magnetic Fields Are Critical to Shaping Solar Gamma-Ray Emission

The Sun is a bright gamma-ray source due to hadronic cosmic-ray interactions with solar gas. While it is known that incoming cosmic rays must generally first be reflected by solar magnetic fields to produce outgoing gamma rays, theoretical models have yet to reproduce the observed spectra. We introduce a simplified model of the solar magnetic fields that captures the main elements relevant to gamma-ray production. These are a flux tube, representing the network elements, and a flux sheet, representing the intergranular sheets. Both the tube and sheet have a horizontal size of order 100 km and serve as sites where cosmic rays are reflected and gamma rays are produced. While our simplified double-structure model does not capture all the complexities of the solar-surface magnetic fields, such as Alfvén turbulence from wave interactions or magnetic fluctuations from convection motions, it improves on previous models by reasonably producing both the hard spectrum seen by Fermi Large Area Telescope at 1–200 GeV and the considerably softer spectrum seen by the High Altitude Water Cherenkov Observatory (HAWC) at near 103 GeV. We show that lower-energy (≲10 GeV) gamma rays are primarily produced in the network elements and higher-energy (≳few × 10 GeV) gamma rays in the intergranular sheets. Notably, the spectrum softening observed by HAWC results from the limited effectiveness of capturing and reflecting ∼104 GeV cosmic rays by the finite-sized intergranular sheets. Our study is important for understanding cosmic-ray transport in the solar atmosphere and will lead to insights into small-scale magnetic fields at the photosphere.

Blast effect on layered polyurethane foam

The shock wave interaction with solids has been a classical problem of interest for a long time in various domains due to its diverse applications. One such application is energy dissipation using polymeric foam. Since the mechanical compression of polymeric foam exhibits an extended plateau region, it is a primary choice of interest in any form of energy dissipation, particularly blast wave energy. Density-based layered foam has a higher chance of more blast energy absorption compared to a single layer of the same density. Hence, in this study, the response of the blast-induced compression of three different polyurethane (PU) foam densities such as 29.201 kg/m3, 59.692 kg/m3, and 107.720 kg/m3, say D1, D2, and D3, respectively, are carried as single layer and bilayer of the same thickness using a Blast Wave Simulator (BWS). Here, we experimentally record the incident and reflected blast pressure near the blast-hitting face and the reaction force at the rear face of the foam. The full-field displacement of PU foam because of the blast wave is measured using a 2D DIC method. In the bilayer PU foam B2 (D2/D1←, the arrow represents the blast direction), the peak displacement of 10.478 mm, the reaction force, FT of 3.75 kN, reflection coefficient, Cr of 1.99, and energy absorption Eabs of 18.68 J was observed. The increase in energy absorption of the bilayer B3 (D2/D1←) compared to a single layer D1 is 83.03 %, and for the bilayer B1 (D1/D2←) it is 18.90 %. This observation helps to utilize the foam for the blast and shock-prone zone more effectively. The force exerted on the reaction wall of the PU foam helps in deciding the type of material to be used as the blast barrier wall. Also, this study proposes an outline to examine the material’s response in a uni-directional compression because of blast wave impact.

Bragg Resonance of Surface Gravity Waves by Surface-Piercing Vertical Multi-Plate Breakwaters

Abstract The interaction between surface gravity waves and surface-piercing vertical multi-plate breakwaters in finite water depth is investigated under the assumption of potential flow theory. The time-domain desingularized boundary integral equation method (DBIEM) is adopted to solve the boundary value problem. A decomposition method based on the superposition principle is used to obtain reflected waves. The effect of the vertical plates as a floating breakwater by making full use of Bragg resonance is analyzed. Initially, the waveforms calculated without breakwaters are compared with second-order Stokes regular wave to obtain the appropriate desingularization distance. Then, the interaction of surface gravity waves with the breakwaters with the single plate, double, and triple plates are analyzed. The transmission and reflection coefficients of the breakwater with the single plate are verified with the analytical solutions of previous literature. The transmission and reflection coefficients of the breakwaters with double and triple plates are verified with experimental results. Finally, the transmission and reflection coefficients of surface-piercing vertical multi-plate breakwaters with different plate numbers and drafts are also calculated. The occurring condition of Bragg resonance and its values affected by the plate number and the draft are analyzed. The present results are reference values for the optimal design of vertical plates as a floating breakwater for offshore and coastal engineering applications by fully using Bragg resonance.