Interaction Of Waves Research Articles

On oblique interaction of water waves with semi-infinite submerged elastic plate

Abstract This article relates with the interaction of water waves obliquely incident on a semi-infinite submerged elastic plate of insignificant thickness. The solution is obtained using method of mode matching. Reflection coefficients under the variation of various physical parameters: submergence depth, angle of incidence, stiffness of elastic plate and Poisson’s ratio, for two different edge conditions (i) pinned edge condition and (ii) sliding edge condition are discussed. Convergence and validation of results is also given. Behaviour of the velocity potentials around semi-infinite submerged elastic plate for different physical parameters are also analyzed. The consequences are explained through numerical and graphical results. More over energy balance relation is also discussed.

Design and aerodynamic characteristics of variable-geometry hypersonic inlet based on shock wave elimination

To solve the problem that the control of shock wave elimination is weakened under off-design conditions, the design concept of a variable-geometry inlet scheme that combines the variable-geometry cowl (translating and diagonalizing) with regulating shock wave elimination is introduced in this paper. The variable-geometry inlet is designed by the theories of oblique shock wave and isentropic wave as well as the Oswatitsch theory. Regulatory law of the variable-geometry cowl based on shock wave elimination is obtained by the geometric relationships between cowl compression angle, cowl shock wave angle, and optimal control point or range. Numerical simulations are conducted to investigate flow field characteristics, control mechanism, and working performance of the inlet. Results reveal that expansion waves have a significant impact on the cowl shock wave and boundary layer interaction, and flow separation. Furthermore, variable-geometry inlet with translating and diagonalizing cowl based on the regulation of shock wave elimination effectively controls and even completely eliminates the flow separation. In terms of inlet performance, the total pressure loss of the variable-geometry inlet decreases such that the total pressure recovery coefficients of the translating cowl and diagonalizing cowl inlets are increased by maximum values of 3.39 % and 9.97 %, respectively. However, the mass flow coefficient of translating cowl inlet decreases, whereas that of the diagonalizing cowl inlet is equivalent to that of the fixed-geometry inlet. The working range can be widened by changing the internal contract ratio of the inlet through translating or diagonalizing the cowl. The results confirm that the scheme of variable geometry inlet with diagonalizing cowl is practicable and reliable and has important guiding significance and value for inlet design.

Study on Aerodynamic Performance and Wake Characteristics of a Floating Offshore Wind Turbine in Wind–Wave Coupling Field

Floating offshore wind turbines (FOWTs) exhibit complex motion with multiple degrees of freedom due to the interaction of wind and waves. The aerodynamic performance and wake characteristics of these turbines are highly intricate and challenging to accurately capture. In this study, dynamic fluid body interaction (DFBI) and overset grid technology are employed to investigate the dynamic motion of a 5 MW FOWT. We use the volume of fluid (VOF) method and improved delayed detached eddy simulation (IDDES) model to investigate the aerodynamic performance and wake evolution mechanism for various wave periods and heights. According to the findings, the magnitude of the pitch motion increases with the period and height of the waves, leading to a decrease in both the power output and thrust; the maximum power was reduced by nearly 6.8% compared to a wind turbine without motion. The value of power and thrust reduction varies for different wave periods and heights, and is influenced by the relative speed and pitch angle, which play a crucial role. Wind–wave coupling has a significant impact on the evolution of both wake and vortex structures for FOWT. The wake shape downstream is also dynamically influenced by the waves. In the presence of wind and wave coupling, the interaction between the wind turbine and the wake is heightened, leading to the merger of two unstable vortex rings into a single, larger vortex ring. The research unveils a comprehensive picture of the offshore wind energy dynamics and wake field, which holds immense significance for the design of floating wind turbines and the optimization of wind farm layout.

Global transonic solutions of hot-Jupiter model for exoplanetary atmosphere

In this paper, we make modifications to the original hot-Jupiter model, which addresses the problem of hydrodynamic escape for the planetary atmosphere. The model involves the Euler equation with gravity, tidal effect, and heat. We employ the generalised Glimm technique to prove the presence of transonic solutions to the problem. By adjusting the dilation of the characteristic fields, we enhance the accuracy of the Glimm–Goodman wave interaction estimates. This allows us to establish a more general admissible condition for stabilizing the generalised Glimm scheme. Additionally, we derive the exact relationship between the lower bound of the gas velocity in the subsonic state and the adiabatic constant of the gas. Under certain constraints on the transonic initial and boundary data, the limit of the approximation solutions represents an entropy transonic solution with bounded variations. Furthermore, we are able to determine the feasible hydrodynamical region directly from the equation itself, without the need for any additional state equation.

Wave interaction with multiple thin flexible porous barriers in water of uniform finite depth

The interaction of water waves with multiple flexible porous barriers partially immersed in a uniform finite-depth fluid is investigated in the present study. Using linear theory, the physical problem is mathematically modeled as a boundary value problem. The eigenfunction expansion approach is used to generate the velocity potential function in terms of orthogonal eigenfunctions. The Havelock’s inversion formula is then used to convert the boundary value problem into a set of Fredholm-type integral equations. By choosing a suitable weight function, the multi-term Galerkin’s approximation technique is used to obtain the mathematical solutions of these integral equations in terms of the Chebyshev polynomial. Numerical solutions regarding the reflection and transmission coefficients, hydrodynamic forces, and dissipated wave energy at the barriers are obtained and graphically represented in several figures for various non-dimensional parameters. It is observed from the graphical representations that the permeability and flexibility of the barriers play a crucial role in the modeling of efficient breakwaters.

Model of bores interaction in the swash

This paper examines the impact of wave interactions in the inner-surf zone, including the swash, on shoreline excursion dynamics. Specifically, the study focuses on how the time lag between consecutive waves and the slope of the beachface affect shoreline dynamics. To investigate this, a laboratory experimental setup is developed to study the behaviour of two consecutive bore-type waves travelling over a fluid layer with constant depth, representing an idealized inner-surf zone, before impacting an inclined solid plane with slope β, representing the beachface. Bore waves are generated using two dam-break flow devices, with a controlled time lag Δt between them. This simplified physical model allows for the assessment of semi-theoretical predictive models based on shallow water approximation, resulting in ballistic-type models for shoreline motion. By combining these approaches, the study characterizes different flow regimes in the (Δt,β) parameter space. It is observed that varying Δt at a fixed β distinguishes four interaction regimes, either wave–wave interaction in the inner-surf zone or wave-swash interaction in the swash, with possibilities of merging or collision depending on wave orientation. In particular, increasing Δt leads to either bore–bore merging in the inner-surf, bore-runup merging in the swash, bore-backwash collision in the swash or bore–bore collision in the inner-surf. Bore–bore merging and bore-runup merging enhance runup, peaking when Δt is such that merging occurs near the transition from the inner-surf to the swash. On the contrary, bore-backwash collision results in additional dissipation of the second bore’s dynamics, leading to a reduced shoreline extension compared to that induced by the first bore. All processes within the swash, including the transition between bore-runup and bore-backwash regimes, as well as the enhancement and extra dissipation of the second bore’s swash excursion, exhibit some level of dependence on β. Overall, the results from this physical model help characterize and explain local mechanisms triggered by wave interaction near the shoreline. Validating this model’s relevance warrants specific attention through comparisons with field data. As an initial validation attempt, field data extracted from the literature are compared to the physical model, showing promising agreement.

Failure Analysis and Piezo-resistance Response of Intralaminar Glass/Carbon Hybrid Composites Under Blast Loading Conditions

Abstract In this study, damage mechanisms and the piezo-resistance response of glass/carbon intralaminar hybrid composites are examined under blast loading conditions. Two-ply orientations are considered, namely a repeating ((G45C45)R) and an alternating ((G45C45)A) +/− 45° glass/carbon layers, along with three boundary condition configurations: simply supported, partially fixed, and fully fixed are applied. A shock tube apparatus and the three-dimensional digital image correlation technique are utilized to investigate the interaction of shock waves with the composites and gather a comprehensive deformation field during the loading. A modified four-probe resistivity measurement method is implemented to comprehend the piezo-resistance response associated with damage evolution. The results underscore the substantial influence of boundary conditions on the blast mitigation capacity of the composites. Analysis following the experiments reveals that the damage to the specimens primarily involves the fracture of fibers accompanied by internal delamination. Thermal imaging of the tested composite specimens provides enhanced insight into the precise occurrences of internal fiber breakage and delamination. Composites of (G45C45)A type demonstrate an increased energy dissipation ranging from 18% to 33% compared to (G45C45)R composites, depending on the specific boundary conditions among the three types considered. Furthermore, the findings indicated a strong correlation between changes in piezo-resistance and the fracture of carbon fibers, coupled with the sustained deformation of the composites. Notably, (G45C45)A composites exhibited 100% ∼ 300% higher change in piezo-resistance compared to (G45C45)R composites, indicative of the superior damage-sensing capabilities of the former.

Forward modeling of quake’s infrasound recorded in the stratosphere on board balloon platforms

Acoustic waves generated by seismic waves contain information on the internal structure of planets, and can be sensed by pressure sensors onboard high-altitude balloons. To identify the various contributions (infrasound signal, noise, balloon response, etc.) in such pressure records, a full waveform modeling is implemented and completed by infrasound ray tracing and additional data analysis. Here, we analyze the Stratéole-2 pressure data associated with two earthquakes (Garcia et al. Geophys. Res. Lett. 49(15):e98844, 2022) and compared these to full waveform simulations by SPECFEM2D-DG-LNS software. Even if our simulations do not precisely reproduce the waveform observed in the frequency range [0.05, 0.3] Hz, we show that the waveform presents more sensitivity to quake and internal structure parameters than to atmospheric structure, and that seismic surface wave dispersion is observed in balloon pressure records. The long-duration pressure oscillations observed after the main infrasonic signal cannot be fully reproduced by our one-dimensional input model even when source time function complexity and aftershocks are considered. These features are ascribed mainly to the complex vertical ground movements below the balloon and partly to late secondary infrasound arrivals excited by the interactions of seismic waves with the topography. These results enhance the advantages and limitations of quake-related infrasound observations on board terrestrial and planetary balloon platforms.Graphical

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

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

Real Gas Corrections Based on the Interaction of One-Dimensional Unsteady Waves in a Shock Tube

There are multiple unsteady wave system interactions such as shock waves, expansion waves, and reflection, transmission, and intersection of the contact surface inside a shock tube. Studying the law of unsteady wave system interaction has important guiding significance for the design of gas wave equipment. This paper proposes a solution method for the interaction law of unsteady wave systems based on real gas equation of state (EoS) and applies it to shock tubes. The results show that the temperature maximum error between the code based on ideal gas EoS and simulation results is 3.64%, and the error of wave velocity results is between 2.99% and 18.27%. While the error of temperature results between code based on real gas EoS and simulation is not exceed 3%. More importantly, the wave velocity calculated by the code based on real gas EoS is pretty consistent with the simulation results. The code based on the real gas model can help to solve the problem of offset design point. Research has also shown that as pressure and temperature gradually increase, the deviation between ideal and real gases increases, which also proves that the influence of real gas effects is becoming increasingly significant.

Synchronized shock wave and compliant wall interactions: Experimental characterization and aeroelastic modeling

The static and dynamic interaction of a normal shock wave (upstream Mach number 1.35) with a compliant wall is characterized experimentally by schlieren visualizations and an optical displacement sensor. Depending on the location of the shock wave along the compliant wall, three different regimes of interaction are found: large-amplitude synchronized regime, small-amplitude synchronized regime and unsynchronized regime. The regime of large-amplitude synchronized oscillations is found for shock locations close to the mid-point of the compliant wall along the streamwise direction; at this location, the coupled system locks to the second vibration frequency of the structure. Three regimes of small-amplitude synchronized oscillations are found depending on the shock position. When the shock is located upstream the center of the compliant wall, the shock may oscillate either periodically at the frequency of the first vibration mode or quasi-periodically with highest amplitudes at the three frequencies of the vibration modes. When the shock is located downstream the center of the compliant wall, the shock oscillates periodically at the frequency of the third vibration mode. Finally, close to the trailing edge of the compliant wall, the shock oscillation is not synchronized with the compliant wall which oscillates with a very small amplitude. An empirical model is proposed to investigate the energy exchange between the flow and the compliant wall during the limit cycle oscillations. A negative aerodynamic damping – and, hence, the possibility of a limit cycle – is observed when a sufficiently extended separation is considered in the model for the pressure distribution at the wall.

Revealing physical interactions of ultrasound waves with the body through photoelasticity imaging

Ultrasound is a ubiquitous technology in medicine for screening, diagnosis, and treatment of disease. The functionality and efficacy of different ultrasound modes relies strongly on our understanding of the physical interactions between ultrasound waves and biological tissue structures. This article reviews the use of photoelasticity imaging for investigating ultrasound fields and interactions. Physical interactions are described for different ultrasound technologies, including those using linear and nonlinear ultrasound waves, as well as shock waves. The use of optical modulation of light by ultrasound is presented for shadowgraphic and photoelastic techniques. Investigations into shock wave and burst wave lithotripsy using photoelastic methods are summarized, along with other endoscopic forms of lithotripsy. Photoelasticity in soft tissue surrogate materials is reviewed, and its deployment in investigating tissue-bubble interactions, generated ultrasound waves, and traumatic brain injury, are discussed. With the continued growth of medical ultrasound, photoelasticity imaging can play a role in elucidating the physical mechanisms leading to useful bioeffects of ultrasound for imaging and therapy.

Chaotic behavior, bifurcations, sensitivity analysis, and novel optical soliton solutions to the Hamiltonian amplitude equation in optical physics

This study, highlights the exact optical soliton solutions in the context of optical physics, centering on the intricate Hamiltonian amplitude equation with bifurcation and sensitivity analysis. This equation is pivotal in optics which underpins the understanding of optical manifestations, encompassing solitons, nonlinear consequences, and wave interactions. Applying an analytical expansion approach, we extract diverse optical solutions, having trigonometric, hyperbolic, and rational functions. Next, we utilize concepts from the principle of planar dynamical systems to investigate the bifurcation processes and chaotic behaviors present in this derived system. Additionally, we use the Runge–Kutta scheme to carry out a thorough sensitivity analysis of the dynamical system. It has been verified through this analytical process that small variations in beginning conditions have negligible effects on the stability of the solution using bifurcation analysis. Validation via Mathematica software ensures the accuracy of these findings. Furthermore, we employ dynamic visualizations, such as 2D, 3D, and contour plots, to illustrate various soliton patterns, including kink, multi-kink, single periodic, multi-periodic, singular, and semi-bell-shaped configurations. These visual representations provide a glimpse into the fascinating behavior of optical phenomena. The solutions obtained via this proposed method showcase its efficacy, dependability, and simplicity in comparison to various alternative approaches.

Semi-analytical approach to study wave interaction with a pair of obliquely submerged heterogeneous flexible structures

ABSTRACT Analyzing inclined flexible plates of varying thickness is crucial for optimising and attaining precise control over wave reflection and transmission. This is particularly significant in the context of breakwater construction. In contrast to horizontal breakwaters, inclined barriers can penetrate multiple layers of fluid with varying particle velocities, facilitating interactions and causing wave breaking, which results in the dissipation of wave energy. Moreover, compared to vertical structures, inclined ones demonstrate more effective wave attenuation. In the context of the present study, we investigate the interaction of water waves with a pair of obliquely submerged flexible thin plates characterised by non-uniform thickness. In order to model this complex physical scenario, we employ the principles of linear water wave theory in conjunction with Kirchhoff's thin plate theory. By employing repeated integration and Green's integral theorem, we reduce the boundary value problem to a system of coupled integral equations. Through appropriate approximations, we solve this system and obtain numerical values for various hydrodynamic quantities. This model provides comprehensive results for both horizontal and vertical plates, making it highly versatile. We examine the impact of varying thickness and the inclination of the two flexible plates to understand their roles in the wave scattering process and the associated physical parameters. The results obtained from this study shed light on the intricate dynamics involved in wave-structure interactions and can inform the design and optimisation of breakwater systems.

Numerical modeling of bamboo fences with various infill porosities deployed for mangrove restoration

As part of mangrove restoration initiatives eco-friendly fence has been implemented in eroded coastal areas in recent years. These fences provide the capacity to mitigate incoming wave energy and facilitate sediment deposition, thereby promoting the establishment and maintenance of mangrove habitats. Nevertheless, it is crucial to investigate the influence of the infill porosity on the wave dissipation performance of these fences, as the infill porosity can vary considerably across different restoration projects. The aim of this research is to explore the relationship between the infill porosity and wave dissipation effectiveness to identify more efficient designs for these eco-friendly restoration measures. The experiments involving wave interactions with fence models were conducted in a wave flume measuring 0.8 m in width and 25 m in length. Four wooden fences with distinct infill porosities ranging from 0.60 to 0.90 were strategically positioned to assess wave transmission, reflection, and dissipation phenomena under 18 distinct wave conditions. Additionally, the simulating waves till shore (SWASH)model was employed to calibrate critical bulk drag coefficient parameters and simulate the flow velocity distribution surrounding the fences under the experimental wave conditions. The findings indicated that a fence with a reduced infill porosity exhibits a higher wave transmission coefficient. However, this is accompanied by a higher reflection coefficient and lower wave energy dissipation within the fence. Both the infill porosity and incident wave conditions influence the flow velocity distribution characteristics in the vicinity of the fences. The area where the interaction between waves and fences is the most prominent is concentrated in the upper water layer immediately adjacent to the frontal section of the fences. Understanding the velocity distribution and hydrodynamic characteristics of the fence area aids in better determining the suitable porosity of fill materials for engineering applications.

Effect of perforated wall in controlling the separation due to SWBLI at Mach no. 5 to 9

Abstract The mixed compression scramjet engine intake was numerically simulated to study the characteristic of shock wave induced boundary layer separation leading to the formation of the separation bubble (SB). The analysis employed a 2D-RANS method with SST k-ω turbulence model at different Mach numbers. The intake is designed as a three-ramp intake for improved performance. As the Mach number varies, the size of the separation bubble formed due to the interaction of oblique shock waves with the boundary layer also varies, affecting both intake the efficiency and overall efficiency of the engine. Apart from traditional control techniques, the most preferred bleed technique is incorporated. Localised & distributed bleed techniques are designed and analysed within the intake at different locations. These techniques result in a reduction in the size of the separation bubble within the intake. Establishing perforation in the engine intake also increases the intake efficiency and overall engine performance.

The characteristics of bubbly shock waves in a cavitating axisymmetric venturi via time-resolved X-ray densitometry

The bubbly shock-driven partial cavitation in an axisymmetric venturi is studied with time-resolved two-dimensional X-ray densitometry. The bubbly shock waves are characterised using the vapour fraction and pressure changes across it, propagation velocity, and Mach number. The sharp changes in vapour fraction measured with X-ray densitometry, combined with high-frequency dynamic pressure measurements, reveal that the interaction of the pressure wave with the vapour cavity dictates the shedding dynamics. At the lowest cavitation number ( $\sigma \sim 0.47$ ), the condensation shock front is the predominant shedding mechanism. However, as $\sigma$ increases ( $\sigma \sim 0.78$ ), we observe an upstream travelling pressure discontinuity that changes into a condensation shock as it approaches the venturi throat. This coincides with the increasing strength of the bubbly shock wave as it propagates upstream, manifested by the increasing velocity of the shock front and the pressure rise across it. Consequently, the Mach number of the shock front increases and surpasses the critical value 1, favouring condensation shocks. Further, at higher $\sigma$ ( ${\sim }0.84\unicode{x2013}0.9$ ), both the re-entrant jet and pressure wave can cause cavity detachment. However, at such $\sigma$ , the pressure wave likely remains subsonic. Hence cavity condensation is not favoured readily. This leads to the re-entrant jet causing the cavity detachment at higher $\sigma$ . The shock front is accelerated as it propagates upstream through the variable cross-section of the venturi. This enhances its strength, favouring cavity condensation and eventual shedding. These observations explain the existence of shock fronts in an axisymmetric venturi for a large range of $\sigma$ .

Tsunami Squares: Leapfrog scheme implementation and benchmark study on wave–shore interaction of solitary waves

Impulse waves are generated by rapid subaerial mass movements including landslides, avalanches and glacier break-offs, which pose a potential risk to public facilities and residents along the shore of natural lakes or engineered reservoirs. Therefore, the prediction and assessment of impulse waves are of considerable importance to practical engineering. Tsunami Squares, as a meshless numerical method based on a hybrid Eulerian–Lagrangian algorithm, have focused on the simulation of landslide-generated impulse waves. An updated numerical scheme referred to as Tsunami Squares Leapfrog, was developed which contains a new smooth function able to achieve space and time convergence tests as well as the Leapfrog time integration method enabling second-order accuracy. The updated scheme shows improved performance due to a lower wave decay rate per unit propagation distance compared to the original implementation of Tsunami Squares. A systematic benchmark testing of the updated scheme was conducted by simulating the run-up, reflection and overland flow of solitary waves along a slope for various initial wave amplitudes, water depths and slope angles. For run-up, the updated scheme shows good performance when the initial relative wave amplitude is smaller than 0.4. Otherwise, the model tends to underestimate the run-up height for mild slopes, while an overestimation is observed for steeper slopes. With respect to overland flow, the prediction error of the maximum flow height can be limited to ± 50% within a 90% confidence interval. However, the prediction of the front propagation velocity can only be controlled to ± 100% within a 90% confidence interval. Furthermore, a sensitivity analysis of the dynamic friction coefficient of water was performed and a suggested range from 0.01 to 0.1 was given for reference.

Study of the reflection of a plane electromagnetic wave from a layer of chiral metamaterial located on a conducting plane, taking into account the inhomogeneity and dispersion of material parameters

To reduce the radar signature of moving objects, such as cars, boats, manned and unmanned aircraft systems, technologies for creating broadband radio-absorbing materials are being actively developed and improved. Among such materials are composites and chiral metamaterials, which have unique characteristics that make it possible to effectively control the reflection and rotation of the plane of polarization of electromagnetic waves. In addition, devices included in the structure of infocommunication systems are subject to electromagnetic radiation, which can cause undesirable effects and interference. Radio-absorbing coatings based on metamaterials can significantly reduce the reflection of electromagnetic waves and effectively counteract the effects of electromagnetic radiation. The purpose of this study is to solve the scientific and technical problem of determining the reflection coefficients of electromagnetic waves from a radio-absorbing material consisting of a chiral metamaterial located on a conducting surface. The main objective of the work is to study the interaction of a plane electromagnetic wave with the specified layer of metamaterial located on a conducting plane, taking into account the inhomogeneity and dispersion of material parameters.

Non-diffusive neural network method for hyperbolic conservation laws

In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately computing weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bounded by discontinuity lines (DLs), the latter defined from the Rankine-Hugoniot jump conditions. The proposed approach allows to efficiently consider an arbitrary number of entropic shock waves, shock wave generation, as well as wave interactions. Some numerical experiments are presented to illustrate the strengths and properties of the algorithms.