Interaction Of Water Waves Research Articles

Water wave interactions with surface-piercing vertical barriers in a rectangular tank: Connections with Bloch waves and quasimodes

Water wave interactions with surface-piercing vertical barriers in a rectangular tank: Connections with Bloch waves and quasimodes

Experimental Modelling of Water-Wave Interactions with a Flexible Beam

A series of fluid-structure-interaction (FSI) experiments is presented for studying water-wave interactions with a flexible beam in a wide range of sea conditions, thereby yielding a repository of FSI test-case data. The aim is to use these experimental data in order to validate FSI solvers commonly employed by the maritime industry in the design of fixed-foundation, offshore wind turbines. The experimental set-up allows simultaneous measurements of beam deflections and their effect on incident and reflected waves. In addition, the study is carried out in a wide range of sea conditions ranging from regular-to-irregular and moderate-to-extreme wave height and steepness. The study of such a wide range of conditions makes the experiments suitable for providing reliable data in the validation of a suite of mathematical and numerical FSI solvers, i.e., linear, nonlinear and high-fidelity. The data from the experiments are made publicly available through open-source data-sharing platforms.

Performance of an oscillating water column wave energy converter device under random ocean waves and ocean currents

The present study investigates the hydrodynamic performance of an onshore oscillating water column (OWC) device placed over an undulated bottom topography by analyzing its hydrodynamic efficiency under the action of combined wave–current interaction. The classical small-amplitude water wave theory is used to model the physical problem. The constant boundary element method is employed to solve the boundary value problem. Significant attention is devoted to describing the hydrodynamic parameters associated with the OWC device by considering the mutual combination of the random waves and ocean currents in the wave propagation phenomena. To examine the complex dynamics of the combined irregular wave current phenomena, the Det Norske Veritas spectrum accompanied by a suitable sea state has been considered for the present study. Considering the existence of opposing and following currents in wave propagation, a comprehensive analysis is conducted on the interactions of regular and irregular water waves with the OWC device. The simulated results demonstrate that the presence of ocean currents in the wave propagation phenomenon strongly influences the resonating patterns of the efficiency and force curves. Additionally, the Doppler shift in the apparent frequency caused by the following currents in the random wave–current interaction significantly improves the device's efficiency for an appropriate structural design.

Transient Shallow Water Wave Interactions with a Partially Fragmented Ice Shelf

This work investigates the interaction between water waves and multiple ice shelf fragments in front of a semi-infinite ice sheet. The hydrodynamics are modelled using shallow water wave theory and the ice shelf vibration is modelled using Euler–Bernoulli beam theory. The ensuing multiple scattering problem is solved in the frequency domain using the transfer matrix method. The appropriate conservation of energy identity is derived in order to validate our numerical calculations. The transient scattering problem for incident wave packets is constructed from the frequency domain solutions. By incorporating multiple scattering, this paper extends previous models that have only considered a continuous semi-infinite ice shelf. This paper serves as a fundamental step towards developing a comprehensive model to simulate the breakup of ice shelves.

Wave trapping by porous breakwater near a rigid wall under the influence of ocean current

The present work investigates the water wave interaction with bottom-standing thick porous trapezoidal-shaped structures and shore-side vertical rigid wall in the presence of uniform ocean currents. This study has been done to understand the impact of different physical parameters like friction, porosity, and ocean currents along with different structural parameters (width and height) on different phenomena like wave energy reflection, wave forces, wave energy dissipation, etc. The quadratic boundary element method-based numerical technique has been used to solve the boundary value problem. The structural porosity is modeled using Sollitt and Cross’s model of water wave interaction with thick porous structures. Several results associated with the wave energy reflection and energy dissipation have been analyzed. Also, the wave force exerted by the incoming waves has been investigated to check the stability and sustainability of the right vertical rigid wall and porous structure. The Doppler-shift effect is observed in wave transformation characteristics due to the presence of ocean currents. The impact of following and opposing ocean currents can be seen in the graph of wave energy reflection, dissipation, and wave forces. The periodic patterns can be observed clearly in wave characteristics like wave energy reflection, dissipation, and wave forces when plotted against the non-dimensional separation gap between the porous breakwater and shore-side rigid seawall.

Nonlinear spatial evolution of degenerate quartets of water waves

In this manuscript we investigate the Benjamin–Feir (or modulation) instability for the spatial evolution of water waves from the perspective of the discrete, spatial Zakharov equation, which captures cubically nonlinear and resonant wave interactions in deep water without restrictions on spectral bandwidth. Spatial evolution, with measurements at discrete locations, is pertinent for laboratory hydrodynamic experiments, such as in wave flumes, which rely on time-series measurements at fixed gauges installed along the facility. This setting is likewise appropriate for experiments in electromagnetic and plasma waves. Through a reformulation of the problem for a degenerate quartet, we bring to bear techniques of phase-plane analysis which elucidate the full dynamics without recourse to linear stability analysis. In particular we find hitherto unexplored breather solutions and discuss the optimal transfer of energy from carrier to sidebands. We show that the maximal energy transfer consistently occurs for smaller side-band separation than the fastest linear growth rate. Finally, we discuss the observability of such discrete solutions in light of numerical simulations.

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.

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.

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.

Modelling the far-field effect of drag-induced dissipation in wave–structure interaction: a numerical and experimental study

In the interaction of water waves with marine structures, the interplay between wave diffraction and drag-induced dissipation is seldom, if ever, considered. In particular, linear hydrodynamic models, and extensions thereof through the addition of a quadratic force term, do not represent the change in amplitude of the waves diffracted and radiated to the far field, which should result from local energy dissipation in the vicinity of the structure. In this work, a series of wave flume experiments is carried out, whereby waves of increasing amplitude impinge upon a vertical barrier, extending partway through the flume width. As the wave amplitude increases, the effect of drag – which is known to increase quadratically with the flow velocity – is enhanced, thus allowing the examination of the far-field effect of drag-induced dissipation, in terms of wave reflection and transmission. A potential flow model is proposed, with a simple quadratic pressure drop condition through a virtual porous surface, located on the sides of the barrier (where dissipation occurs). Experimental results confirm that drag-induced dissipation has a marked effect on the diffracted flow, i.e. on wave reflection and transmission, which is appropriately captured in the proposed model. Conversely, when diffraction becomes dominant as the barrier width becomes comparable to the incoming wavelength, the diffracted flow must be accounted for in predicting drag-induced forces and dissipation.

Interaction of surface water waves with partial porous structure and floating elastic plate in the presence of sea wall

ABSTRACT This study proposes a model composed of either bottom-standing porous structure (BSPS) or surface-piercing porous structure (SPPS) in combination with an elastic plate (EP) placed at a distance from one another to protect a sea wall. The study uses the governing equation and the boundary conditions to coin a system of equations, and the system of equations is solved to identify the hydrodynamics coefficients. Further, it is noticed that length, frictional coefficient, porosity of the porous structure, and flexural rigidity of EP play a crucial role in reducing the force on the sea wall, water elevation and plate deflection. The SPPS exhibits a nearly 60% reduction in wall force coefficient due to a 50% increase in wave-damping when compared to BSPS for k 0 H = 0.85. These results are crucial for developing floating structures that can resist harsh wave environments and minimize the effects of waves close to the shore.

Wave trapping by porous breakwater near a wall under the influence of ocean current

In this paper, oblique water wave interaction with a surface piercing box-type porous structure placed in front of a vertical rigid wall is investigated in the presence of current, which flows parallel to vertical wall. The current speed is considered distinct in different subdomains. However, in a particular subdomain current speed is uniform throughout the water depth. In this analysis, Sollitt and Cross model is used for the study of wave motion inside the porous structure. Employing small amplitude linear water wave theory, the present model of our interest is developed into a boundary value problem and solved analytically using the eigenfunction expansion method. Using the developed solution, the reflection coefficient and hydrodynamic wave forces on porous structure are computed for different values of parameters: the dimension of porous structure, the friction coefficient of porous structure, the current speed of following current and opposing current. This research paper suggests that suitable arrangement of rigid walls and surface-piercing partially extended porous structures can be an effective and economical approach for guiding ocean currents and protecting marine facilities against wave attacks.

Water wave interaction with ice-sheet of variable geometry in the presence of uniform current

Water wave interaction with ice-sheet of variable geometry in the presence of uniform current

Towards High-Performance Linear Potential Flow BEM Solver with Low-Rank Compressions

The interaction of water waves with floating bodies can be modeled with linear potential flow theory and numerically solved with the boundary element method (BEM). This method requires the construction of dense matrices and the resolution of the corresponding linear systems. The cost of this method in terms of time and memory grows at least quadratically with the size of the mesh, and the resolution of large problems (such as large farms of wave energy converters) can, thus, be very costly. Approximating some blocks of the matrix with data-sparse matrices can limit this cost. While matrix compression with low-rank blocks has become a standard tool in the larger BEM community, the present paper provides its first application (to our knowledge) to linear potential flows. In this paper, we assess how efficiently low-rank blocks can approximate interaction matrices between distant meshes when using the Green function of linear potential flow. Due to the complexity of this Green function, a theoretical study is difficult, and numerical experiments are used to test the approximation method. Typical results on large arrays of floating bodies show that 99% of the accuracy can be reached with 10% of the coefficients of the matrix.

Scattering of water waves by multiple segmented concentric semi-closed breakwaters and an interior cylinder: An analytical approach

This study aims to provide a theoretical analytical model for the design of breakwaters like Palm Jumeirah breakwater in Dubai by investigating the hydrodynamic characteristics of segmental semi-enclosed breakwaters simplified from it. An analytical solution to the interaction of water waves and a cylinder and multiple concentric segmented arc-shaped breakwaters has been developed based on linear potential theory. The eigenfunction matching method and separation of variables have been applied to expand the unknown function in terms of Chebyshev polynomials. By considering the boundary conditions, the integral equation has been simplified into a set of algebraic equations, which are then solved to determine the unknown function. The accuracy of the model has been confirmed by comparing the results with those in previous articles. The numerical analysis has revealed the relationship between variations in the hydrodynamic loads, wave elevation of the cylinder, and factors including the gap width between the arcs, opening angle, wave incidence angle, and porous-effect coefficient. The results indicate that segmented breakwaters offer better protection to the internal structure than unsegmented breakwaters. Moreover, segmented breakwaters with smaller gaps are less sensitive to diagonal waves and the gap can serve as a navigational channel, which is an extra benefit.

Wave interactions with a cylinder surrounded by an arc-shaped breakwater

Inspired by the energy island used for energy storage, conversion, and transmission, this study explores the water wave interactions with a bottom-standing cylinder surrounded by an arc-shaped breakwater of negligible thickness. The arc-shaped breakwater can be either impermeable or porous. To analyze the problem, a semi-analytical matched eigenfunction expansion method is developed within the framework of linear potential flow theory. The fluid domain is divided into subdomains, with the velocity potentials in each subdomain expressed as eigenfunction expansions. Matching conditions, ensuring continuity in pressure and normal velocity, are imposed at the juncture boundary. The accuracy of the developed semi-analytical method is verified through comparison with results obtained using the numerically-based boundary element method. Extensive discussions are made on hydrodynamic responses, including wave exciting force and free surface elevations. When the breakwater is impermeable, fluid resonance occurs in the gap between the cylinder and the arc-shaped breakwater, leading to significantly large responses in both free surface elevation and hydrodynamic forces. A simple method is developed to estimate the resonant frequencies and mode shapes associated with these resonances. On the other hand, it is observed that the presence of the porous breakwater considerably reduces the free surface responses in the gap as well as the hydrodynamic loads on the cylinder. The porous breakwater effectively mitigates the occurrence of fluid resonance and offers an efficient means to dampen wave energy, providing valuable insights for wave energy dissipation and coastal engineering applications.

Semi-analytical and CFD formulations of a spherical floater

Today, humanity is facing the great pressure of fossil fuels exhaustion and environmental pollution. This obliges governments and industries to make accelerated efforts on producing green energy. The focus is spotted on marine environment which is a vast source of renewable energy. Among several classes of designs proposed for wave energy conversion, spherical Wave EnergyConverters (WECs) have received considerable attention. The problems of water wave diffraction and radiation by a sphere has been examined by a substantial amount of literature, i.e., [1]–[4], whereas in [5]–[8] linear hydrodynamic effects on a spherical WEC have been examined. All these research works are based on potential flow methodologies. Nevertheless, overthe last decade there has been a significant interest on Computational Fluid Dynamics CFD modelling due to its detailed results, focusing also to spherical WECs [9]–[10].In the present work a semi-analytical model is applied to solve the wave radiation problem around a spherical WEC (Figure 1), in the context of linear potential theory. The outcomes of the theoretical analysis are supplemented and compared with high fidelity CFD simulations (Figure 2 for a semi-submerged sphere). Furthermore, the two methodologies are compared with a theoretical approach for the hydrodynamic analysis of floating bodies with vertical axis as being presented in [11]. The method is based on the discretization of the flow field around the body using coaxial ring elements, which are generated from the approximation of the sphere’s meridian line by a stepped curve.Numerical results are given from the comparison of the three formulations, and some interesting phenomena are discussed concerning the viscous effects on the floater.
 [1] Havelock, T. H. 1955. Wave due to a floating sphere making periodic heaving oscillations. R. Soc. London,A231, 1-7.[2] Hulme, A. 1982. The wave forces acting on a floating hemisphere undergoing force periodic oscillation. J. FluidMech., 121, 443-463.[3] Wang, S. 1986. Motions of a spherical submarine in waves. Ocean Engng., 13, 249-271.[4] Wu, G.X. 1995. The interaction of water waves with a group of submerged spheres. Appl. Ocean. Res., 17, 165-184.[5] Srokosz, M.A. 1979. The submerged sphere as an absorber of wave power. J. Fluid Mech., 95, 717-741.[6] Thomas, G.P., Evans, D.V. 1981. Arrays of three-dimensional wave energy absorbers. J. Fluid Mech., 108, 67-88.[7] Linton, C.M. 1991. Radiation and diffraction of water waves by a submerged sphere in finite depth. Ocean Engng.,18, 61-74.[8] Meng, F., et al. Modal analysis of a submerged spherical point absorber with asymmetric mass distribution.Renew. Energy 130, 223-237.[9] Shami, E.A., et al. 2021. Non-linear dynamic simulations of two-body wave energy converters via identificationof viscous drag coefficients of different shapes of the submerged body based on numerical wave tank CFD simulation.Renew. Energy, 179, 983-997.[10] Katsidoniotaki, E., et al. 2023. Validation of a CFD model for wave energy system dynamics in extreme waves.Ocean Engng., 268, 113320.[11] Kokkinowrachos, K., et al. 1986. Behaviour of vertical bodies of revolution in waves. Ocean Engng., 13, 505-538

A surface-piercing truncated cylindrical meta-structure operating as a wave energy converter

In this paper, we study the interaction of water waves with a surface-piercing truncated cylindrical meta-structure consisting of two overlapping arrays of closely spaced vertical thin plates. The fluid resonance promoted in the narrow vertical channels formed by the cylindrical meta-structure is exploited by a novel design concept of the wave power converter by covering the surface of the cylinder with an array of small cuboid buoys which float in the gaps between the intersecting plate arrays. Each buoy is attached to its own spring and power takeoff damping mechanism, and the vertical displacement of individual buoys is replaced by a continuous two-dimensional function of position which follows from homogenization of the plate/fluid structure of the cylinder. Effective medium equations and boundary conditions are derived under both full depth-dependent theory and shallow-water theory, allowing semi-analytical methods to be developed to investigate the wave scattering and wave energy absorption properties of this cylindrical meta-structure. Results illustrate that the internal resonance of the cylindrical meta-structure can lead to significant wave power capture across a broad range of frequencies.

3D Computational Fluid Dynamic Investigation on Wave Transmission behind Low-Crested Submerged Geo-Bag Breakwater

Wave transmission characteristics behind low-crested submerged breakwaters involve complex-hydrodynamic interaction of water waves on the structures. To properly comprehend the induced-nonlinear wave transformation, the problem necessitates a trustworthy prediction using a computational fluid dynamic (CFD) technique. The goal of this study is to develop a three-dimensional (3-D) computational model of the hydrodynamic performance of a narrow crest behind a submerged breakwater in order to gain a thorough understanding of the wave transmission coefficient, K_t. The simulation took into account a number of wave parameters such as wave steepness (H_i⁄L), relative submergence depth (H_i⁄h), and crest width (c_w⁄L) of the structure. A numerical wave flume model is included, which is based on the full Navier-Stokes solver and includes a shallow water model to account for nonlinearity in the incident wave field. In addition, laboratory measurements were also conducted using a geo-bag dike model as the main breakwater structure. The result shows that the reduction in transmission coefficient correlates highly with the wave steepness and the relative submergence and crest parameters. This can be attributed to most breaking waves over the submerged breakwater. The steeper the incident wave, the greater the reduction in the transmitted wave. And, the greater the principal dimensions of the breakwater, the greater the drop in transmission coefficient. For validation, the CFD results corroborate satisfactorily with measurements

The During Nearshore Event Experiment (DUNEX): A collaborative coastal community experiment to address coastal resilience

The During Nearshore Event Experiment (DUNEX) was a large-scale coastal field effort focused on improving understanding of during-storm nearshore processes to ultimately develop predictive technologies, engineering solutions, and actions to enhance coastal resilience. The experiments were conducted on the North Carolina coast by a multidisciplinary group of over 30 research scientists from 18 academic and federal institutions supporting over 30 graduate students and deploying over 300 instruments from 2019 to 2021. The overarching goal of DUNEX was to gather information collaboratively to improve understanding of the interactions of coastal water levels, waves, currents, beach and dune evolution, soil behavior, vegetation, and groundwater during major coastal storms that affect infrastructure, habitats, and communities. In the short term, these high-quality field measurements will lead to better understanding of during-storm processes and impacts and will enhance U.S. academic coastal research programs by providing opportunities for students to learn about field data collection and to potentially analyze data as part of their studies. Longer-term, DUNEX data and outcomes will improve the ability to predict extreme event physical processes and impacts, validate coastal processes numerical models, and improve coastal resilience strategies and communication methods for coastal communities impacted by storms. The purpose of this paper is to describe the motivation for and science goals of the experiment, how stakeholder needs led to these goals, collaborations amongst researchers, and the knowledge gained that will lead to tools to improve coastal resilience. Herein, we first describe how researchers worked with stakeholders to structure their community-driven needs into science-based requirements. Next, we summarize how federal, academic, and stakeholder researchers worked together to design and execute a multi-organizational experiment aligned with those requirements. Finally, we articulate early findings and lessons learned from the experiment. This paper does not summarize all the research findings from DUNEX, as analyses are still ongoing. An American Geophysical Union (AGU) Special Collection on Coastal Storm Research will be published in 2025 including outcomes from DUNEX research.