Interaction Of Water Waves Research Articles

Rotational Motion Due to the Interaction of Water Waves with a Pair of Coaxial Cylinders in Water of Finite Depth

Rotational Motion Due to the Interaction of Water Waves with a Pair of Coaxial Cylinders in Water of Finite Depth

Interaction of water waves with small undulations on a porous bed in a two-layer ice-covered fluid

The scattering problem involving water waves by small undulation on the porous ocean-bed in a two-layer fluid, is investigated within the framework of the two-dimensional linear water wave theory where the upper layer is covered by a thin uniform sheet of ice modeled as a thin elastic plate. In such a two-layer fluid there exist waves with two different modes, one with a lower wave number propagate along the ice-cover whilst those with a higher wave number propagate along the interface. An incident wave of a particular wave number gets reflected and transmitted over the bottom undulation into waves of both modes. Perturbation analysis in conjunction with the Fourier transform technique is used to derive the first-order corrections of reflection and transmission coefficients for both the modes due to incident waves of two different modes. One special type of bottom topography is considered as an example to evaluate the related coefficients in detail. These coefficients are depicted in graphical forms to demonstrate the transformation of wave energy between the two modes and also to illustrate the effects of the ice sheet and the porosity of the undulating bed.

부유식 원형 실린더 배열에 의한 파 상호작용

The water wave interactions on any three-dimensional structure of arbitrary geometry can be calculated numerically through the use of source distribution or Green's function techniques. However, such a method can be computationally expensive. In the present study, the water wave interactions in floating circular cylinder arrays were investigated numerically using the eigenfunction expansion method with the three- dimensional potential theory to reduce the computational expense. The wave excitation force, added mass coefficient, radiation damping coefficient, and wave run-up are presented with the water wave interactions in an array of 5 or 9 cylinders. The effects of the number of cylinders and the spacing between them are examined because the water wave interactions in floating circular cylinder arrays are significantly dependent upon these.

Numerical simulation of interactions between water waves and inclined-moored submerged floating breakwaters

This paper studies the interactions of water waves with submerged floating breakwaters moored by inclined tension legs, using a numerical wave tank model proposed by Lee and Mizutani (2009) and based on the Navier–Stokes solver. This model combines a direct-forcing immersed boundary (IB) method, volume of fluid (VOF) method, and the mechanics model of the floating breakwater. The floating breakwaters are free on three degrees of freedoms, namely, surge, heave and pitch. Two floating breakwater shapes, rectangular and circular, are used in the experimental and numerical investigations to validate that the model is capable of treating solid boundaries with complex shapes. The non-breaking and breaking waves are carefully chosen to study the nonlinear interactions between water waves and the submerged floating breakwaters. Comparisons of the computed and measured results reveal a favorable agreement in terms of the free water surface, tension force acting on the mooring line, and dynamics of the floating body. A slight phase discrepancy is found between the offshore and onshore mooring forces in the case of a circular floating breakwater, whereas this phenomenon is not observed in the rectangular case. In addition, fully nonlinear phenomena and viscous process in the flow field such as wave breaking, the boundary layer separation on the interface, vortex formation, and motion can be reproduced and captured accurately using the numerical model.

Nonlinear water wave interaction with floating bodies in SPH

A weakly compressible SPH solver is presented for applications involving nonlinear interaction between water waves and floating bodies. A complete algorithm able to compute fully coupled viscous Fluid–Solid interactions is described. No slip boundary condition on the solid surface is enforced through a ghost–fluid technique and the global loads are evaluated through the momentum exchange between fluid and ghost particles. A dedicated algorithm is developed to manage the intersection between the free surface and the solid profile. An explicit synchronous algorithm is proposed for the full coupling between fluid and rigid bodies. Stability, convergence and conservation properties are tested on several freely floating test cases and a final validation of the full algorithm is performed for the interaction between a 2-D box and a wave packet.

Full wave solution for hydrodynamic behaviors of pile breakwater

Rayleigh expansion is used to study the water-wave interaction with a row of pile breakwater in finite water depth. Evanescent waves, the wave energy dissipated on the fluid resistance and the thickness of the breakwater are totally included in the model. The formulae of wave reflection and transmission coefficients are obtained. The accuracy of the present model is verified by a comparison with existing results. It is found that the predicted wave reflection and transmission coefficients for the zero order are all highly consistent with the experimental data (Hagiwara, 1984; Isaacson et al., 1998) and plane wave solutions (Zhu, 2011). The losses of the wave energy for the fluid passing through slits play an important role, which removes the phenomena of enhanced wave transmission.

Excitation of rogue waves in a variable medium: An experimental study on the interaction of water waves and currents

We show experimentally that a stable wave propagating into a region characterized by an opposite current may become modulationally unstable. Experiments have been performed in two independent wave tank facilities; both of them are equipped with a wavemaker and a pump for generating a current propagating in the opposite direction with respect to the waves. The experimental results support a recent conjecture based on a current-modified nonlinear Schrödinger equation which establishes that rogue waves can be triggered by a nonhomogeneous current characterized by a negative horizontal velocity gradient.

Resonance theory of water waves in the long-wave limit

AbstractThe instability due to resonant interactions of finite-amplitude water waves is examined in the long-wave limit. In contrast to the well-known case of a small-amplitude limit in which the resonance is considered for a flat surface, here we consider a periodic approximate of the finite-amplitude solitary wave which is the long-wave limit of the periodic wave. The resonance conditions for the corresponding perturbations yield a new family of resonance curves that are totally different from those of the small-amplitude limit obtained by Phillips and Mclean. Under these resonance conditions, we conduct a systematic asymptotic analysis for small wavenumbers to obtain the growth rates of the perturbations explicitly and clarify whether each resonance curve is associated with instability. These results are verified numerically by showing that the instability bands for finite-amplitude periodic waves in shallow water are located along these unstable resonance curves.

Finite Element Based Viscous Numerical Wave Flume

A two-dimensional numerical wave flume (NWF) for viscous fluid flows with free surface is developed in this work. It is based on the upwind finite element solutions of Navier-Stokes equations, CLEAR-volume of fluid method for free surface capture, internal wave maker for wave generation, and sponge layer for wave absorbing. The wave generation and absorption by prescribing velocity boundary conditions along inlet and radiation boundary condition along outlet are also incorporated. The numerical model is validated against several benchmarks, including dam-breaking flow, liquid sloshing in baffled tank, linear water wave propagation and reflection from vertical wall, nonlinear solitary wave fission over sharp step, and wave-induced fluid resonance in narrow gap confined by floating structures. The comparisons with available experimental data, numerical results, and theoretical solutions confirm that the present numerical wave flume has good performance in dealing with complex interface flows and water wave interaction with structures.

航空機の離着陸に伴う大型浮体構造物の非線形振動の数値解析

Interaction of surface water waves with a floating platform is discussed considering nonlinearity of fluid motion and flexibility of oscillating structure. The set of nonlinear shallow water equations is applied to water motion interacting with a horizontally very large and elastic thin plate floating on the water surface. Calculation results of the floating thin-plate displacement due to the propagation of a tsunami, in terms of a solitary wave, are compared with the existing experimental data. Surface waves generated by the takeoff or landing of an airplane are simulated, such that when the offshore airport is constructed in shallower water, the slope of runway becomes larger and the complicated oscillation is harder to be damped down because of the reflection of floating thin-plate waves at the ends of the offshore airport.

Bottom pressure distribution due to wave scattering near a submerged obstacle

AbstractThe dynamic pressure distribution on the bottom of a wave flume, due to the interaction of water waves with a submerged structure, is investigated experimentally and analytically, for both first- and second-order gravity waves of finite amplitude. The dynamic pressure excess is found to be very important, even for incoming waves propagating in deep water conditions. In this depth condition, a high pressure zone, thirty times larger than the dynamic pressure excess expected in the absence of the obstacle, is found in its vicinity. On the other hand, a low pressure zone is observed in the vicinity of the submerged obstacle for incoming waves propagating in smaller depth conditions. In any case, pressure gradients remain important. The second-order disturbance is found to be larger than first order in deep water conditions, for some specific conditions and locations. This result is interpreted in terms of nonlinear coupling of first-order components, including local modes.

On physical and numerical resonances for water wave problems using the dual boundary element method

Abstract Scattering problems of water waves impinging on bottom-mounted vertical cylinders are solved by using the dual boundary element method (DBEM). Both resonances due to near-trapped mode (physics) and fictitious frequency (mathematics) are examined. It is found that the near-trapped mode is a physical phenomenon and the fictitious frequency stems from the numerical instability. A trapped mode is associated with a singularity that lies on the real axis of complex wave number. A near-trapped mode means a localized behavior that energy is trapped in a truncated periodical structure. Critical wave number for the near-trapped mode and fictitious frequency of numerical instability are detected in this work. Numerical oscillation of the resultant force near the fictitious frequency is also observed by using the DBEM. Fictitious frequencies depend on the formulation instead of the specified boundary condition. Both the Burton and Miller approach and the CHIEF method are employed to alleviate the problem of irregular frequencies. Highly rank-deficiency matrices for four identical cylinders are numerically examined and the rank is promoted by adding valid CHIEF constraints. Parameter study of spacing and radius of cylinders on the near-trapped mode and fictitious frequency is also addressed. Several examples of water wave interaction by circular and square cylinders are demonstrated to see the validity of the present formulation.

On near-trapped modes and fictitious frequencies for water wave problems containing an array of circular cylinders using a null-field boundary integral equation

To avoid using the addition theorem to translate the Bessel function, scattering of water waves by an array of circular cylinders is solved by using the null-field boundary integral equations, in conjunction with the adaptive observer system. Both the near-trapped modes (physics) and fictitious frequencies (mathematics) are observed. To alleviate the resonance problem of fictitious frequency for multiple cylinders, Combined Helmholtz Interior integral Equation Formulation (CHIEF) approach and Burton and Miller formulation are both considered. Regarding the Burton and Miller approach, hypersingular integrals can be easily calculated by using series summability without any difficulty owing to the introduction of degenerate kernels. The highly rank-deficient matrices for equal radius of cylinders are numerically examined and the rank is improved by adding valid CHIEF constraints. Besides, the selection of location and number for CHIEF points is addressed instead of trial and error. Parameter study of the incident angle on the resultant force is investigated. The effect of spacing and radius of cylinders on the near-trapped mode and fictitious frequency is also discussed. Several examples of water wave interaction by circular cylinders were demonstrated to see the validity of the present formulation.

Analysis of wave interaction with submerged perforated semi-circular breakwaters through multipole method

This study gives a solution of water wave interaction with submerged perforated semi-circular breakwaters in the context of linear potential theory. The multipole expansion with singularities located on the seabed is developed for the solution. It is found that the expanded series converges very rapidly as the number of terms increase. The wave reflection and transmission coefficients, the horizontal and vertical wave forces and the hydrodynamic pressure distribution over the semi-circular breakwaters are obtained and the results are carefully examined. Their significance for practical engineering is discussed.

Exciting forces due to interaction of water waves with a submerged sphere in an ice-covered two-layer fluid of finite depth

Abstract Scattering of water waves by a sphere in a two-layer fluid, where the upper layer has an ice-cover modelled as an elastic plate of very small thickness, while the lower one has a rigid horizontal bottom surface, is investigated within the framework of linearized water wave theory. The effects of surface tension at the surface of separation is neglected. There exist two modes of time-harmonic waves – the one with lower wave number propagating along the ice-cover and the one with higher wave number along the interface. Method of multipole expansions is used to find the particular solution for the problem of wave scattering by a submerged sphere placed in either of the layers. The exciting forces for vertical and horizontal directions are derived and plotted against different values of the wave number for different submersion depths of the sphere and flexural rigidity of the ice-cover. When the flexural rigidity and the density of the ice-cover are taken to be zero, the numerical results for the exciting forces for the problem with free surface are recovered as particular cases.

Wave interaction with a wave absorbing double curtain-wall breakwater

This study examines the hydrodynamic performance of a wave absorbing double curtain-wall breakwater. The breakwater consists of a seaward perforated wall and a shoreward impermeable wall. Both walls extend from above the seawater to some distance above the seabed. Then the below gap allows the seawater exchange, the sediment transport and the fish passage. By means of the eigenfunction expansion method and a least square approach, a linear analytical solution is developed for the interaction of water waves with the breakwater. Then the reflection coefficient, the transmission coefficient and the wave forces acting on the walls are calculated. The numerical results obtained for limiting cases agree very well with previous predictions for a single partially immersed impermeable wall, the double partially immersed impermeable walls and the bottom-standing Jarlan-type breakwater. The predicted reflection coefficients for the present breakwater also agree reasonable with previous experimental results. Numerical results show that with appropriate structure parameters, the reflection and transmission coefficients of the breakwater may be both below 0.5 at a wide range of the relative water depth. At the same time, the magnitude of wave force acting on each wall is small. This is significant for practical engineering.

Water wave interaction with surface-piercing porous cylinders using the null-field integral equations

Following the successful experiences of solving water wave scattering problems for multiple impermeable cylinders by the authors' group, we extend the null-field integral formulation in conjunction with the addition theorem and the Fourier series to deal with the problems of surface-piercing porous cylinders in this paper. In the implementation, the null-field point can be exactly located on the real boundary free of calculating the Cauchy and Hadamard principal values, thanks to the introduction of degenerate kernels (or separable kernels) for fundamental solutions. This method is a semi-analytical approach, since errors attribute from the truncation of the Fourier series. Not only a systematic approach is proposed but also the effect on the near-trapped modes due to porous cylinders and disorder of layout is examined. Several advantages such as mesh-free generation, well-posed model, principal value free, elimination of boundary-layer effect and exponential convergence, over the conventional boundary element method (BEM) are achieved. It is found that the disorder has more influence to suppress the occurrence of near-trapped modes than the porosity. The free-surface elevation is consistent with the results of William and Li and those using the conventional BEM. Besides, the numerical results of the force on the surface of cylinders agree well with those of William and Li. Besides, the present method is a semi-analytical approach for problems containing circular and elliptical shapes at the same time.

Theoretical and Experimental Study on a Porous Cylinder Floating in Waves

Abstract In the present work, theoretical and experimental studies on the interaction of water waves with a truncated circular cylinder were performed. The cylinder, which is partly made of porous materials, possesses a porous sidewall and an impermeable bottom. A nondimensional parameter b is adopted in the theoretic formulation to describe the porosity, which is not directly related to the opening ratio τ of the porous materials. To validate the theoretical work and computed results, a series of model tests are carried out in a wave basin. Effort is made to establish an empirical relation between b and τ based on the comparison of the calculation and experimental data. The phenomenon of the sloshing mode that occurred at a certain wave number is observed, which might have an application in breakwaters. The validation of the Haskind relations is examined for the porous body. It is found that the damping coefficient consists of two parts. In addition to the component of conventional wave-radiating damping, there exists a second component caused by the porous effects.

Short and long waves over a muddy seabed

The available experimental results have shown that in time-periodic motion the rheology of fluid mud displays complex viscoelastic behaviour. Based on the measured rheology of fluid mud from two field sites, we study the interaction of water waves and fluid mud by a two-layered model in which the water above is assumed to be inviscid and the mud below is viscoelastic. As the fluid-mud layer in shallow seas is usually much thinner than the water layer above, the sharp contrast of scales enables an approximate analytical theory for the interaction between fluid mud and small-amplitude waves with a narrow frequency band. It is shown that at the leading order and within a short distance of a few wavelengths, wave pressure from above forces mud motion below. Over a much longer distance, waves are modified by the accumulative dissipation in mud. At the next order, infragravity waves owing to convective inertia (or radiation stresses) are affected indirectly by mud motion through the slow modulation of the short waves. Quantitative predictions are made for mud samples of several concentrations and from two different field sites.

Modelling of water wave interaction with multiple cylinders of arbitrary shape

This paper describes the development of an efficient numerical model, namely scaled boundary finite-element method (SBFEM) for linear waves interaction with cylindrical structures of arbitrary shapes. The two-dimensional Helmholtz equation is firstly weakened in the circumferential direction, so that the governing partial differential equation is transformed to an ordinary matrix differential equation in radial direction, and is solved fully analytically. As a key element, a virtual porous circular cylinder surrounding the cylindrical structures is introduced so that the entire computational domain is partitioned along the virtual cylinder into an unbounded and several bounded sub-domains with common interfaces. The principle innovation is that, the present SBFEM model chooses Hankel function as a base solution for the unbounded sub-domain, while a power series is used for the internal bounded sub-domains. The approach discretises only the common interfaces of the sub-domains with surface finite-elements, and fewer elements are required to obtain very accurate results. Numerical simulations show that the new SBFEM model offers a considerable improvement by far in its numerical performance, as well as in the range of physical phenomena that is capable of simulating. The wave forces and run-ups are presented for a single and multiple cylindrical structures of different cross sectional shapes. Influences of the incident wave parameters and structural configurations on the hydrodynamics are examined.