Irregular wave transmission over a submerged breakwater

Irregular wave tests were conducted in a laboratory flume with an ‘Odessa-type’ bevelled-block submerged breakwater on a sloping bottom. The incident and transmitted waves were subjected to probabilistic and spectral analysis. Although the incident wave heights and periods are described respectively by the Gluhovski and the Rayleigh distributions, for the square of the wave periods, the transmitted heights and periods conform to the Rayleigh distribution irrespective of the depth of submergence of the breakwater. The significant wave heights (H _s) give transmission coefficients comparable to the corresponding monochromatic waves, but theH _max and give 50% higher and upto 28% lower values respectively, the difference increasing with the depth of submergence of the breakwater. The peak frequency of the spectrum does not vary on transmission. Resonant frequencies, where the wave energy is transmitted almost completely, are observed in the process. The resonance occurs at frequencies 1·4, 3·8, 5·6 and 7·0 rad/s, and they remain constant for different submergences of the breakwater. The presence of similar frequencies is also found in the case of monochromatic waves, although the tests are limited. Application of irregular wave tests is recommended in the design of submerged breakwaters. The laboratory studies were conducted under the guidance of Prof A V Mihailov and Dr I S Halfin of the Moscow Civil Engineering Institute,ussr, as a part of the author’s Ph. D. dissertation.     

Longshore Submerged Wave Breaker for a Reflecting Beach

This paper considers the effect of a hard-wall beach on the downstream side of submerged parallel bars in a breakwater. In previous research, it was assumed that the beach can absorb all of the transmitted wave energy, when an optimal dimension for a submerged parallel bar is obtained and the wave amplitude is reduced as more bars are installed. However, for a hard-wall beach there are waves reflected from the beach that change the long-term wave interaction. We adopt the linear shallow water equations in Riemann invariant form and use the method of characteristics, in a procedure applicable to various formations of submerged rectangular bars. The distance from the parallel bar (or bars) to the beach determines the phase differences between right running waves in the beach basin and whether they superpose destructively or constructively before hitting the beach, to define the safest and the most dangerous cases. Our numerical calculations for one bar, two bars and for periodic rectangular bars confirm the analytical formulae obtained.     

Wave interaction with a floating and submerged elastic plate system

Surface gravity wave interaction with a floating and submerged elastic plate system is analyzed under the assumption of small-amplitude surface water wave theory and structural response. The plane progressive wave solution associated with the plate system is analyzed to understand the characteristics of the flexural gravity waves in different modes. Further, linearized long-wave equations associated with the wave interaction with the elastic plate system are derived. The dispersion relations are derived based on small-amplitude wave theory and shallow-water approximation and are compared to ensure the correctness of the mathematical formulation. To deal with various types of problems associated with gravity wave interaction with a floating and submerged flexible plate system, Fourier-type expansion formulae are derived in the cases of water of both finite and infinite depths in two dimensions. Certain characteristics of the eigensystems of the developed expansion formulae are derived. Source potentials for surface wave interaction with a floating flexible structure in the presence of a submerged flexible structure are derived and used in Green’s identity to obtain the expansion formulae for flexural gravity wavemaker problems in the presence of submerged flexible plates. The utility of the expansion formulae and associated orthogonal mode-coupling relations is demonstrated by investigating the diffraction of surface waves by floating and submerged flexible structures of two different configurations. The accuracy of the computational results is checked using appropriate energy relations. The present study is likely to provide fruitful solutions to problems associated with floating and submerged flexible plate systems of various configurations and geometries arising in ocean engineering and other branches of mathematical physics and engineering including acoustic structure interaction problems.     

Gravity wave interaction with porous structures in two-layer fluid

Oblique wave interaction with rectangular porous structures of various configurations in two-layer fluid are analyzed in finite water depth. Wave characteristics within the porous structure are analyzed based on plane wave approximation. Oblique wave scattering by a porous structure of finite width and wave trapping by a porous structure near a wall are studied under small amplitude wave theory. The effectiveness of three types of porous structures—a semi-infinite porous structure, a finite porous structure backed by a rigid wall, and a porous structure with perforated front and rigid back walls—in reflecting and dissipating wave energy are analyzed. The reflection and transmission coefficients for waves in surface and internal modes and the hydrodynamic forces on porous structures of the aforementioned configurations are computed for various physical parameters in two-layer fluid. The eigenfunction expansion method is used to deal with waves past the porous structure in two-layer fluid assuming the associated eigenvalues are distinct. An alternate procedure based on the Green’s function technique is highlighted to deal with cases where the roots of the dispersion relation in the porous medium coalesce. Long wave equations are derived and the dispersion relation is compared with that derived based on small amplitude wave theory. The present study will be of significant importance in the design of various types of coastal structures used in the marine environment for the reflection and dissipation of wave energy.     

An alternative analytical solution for water-wave motion over a submerged horizontal porous plate

This study gives an alternative analytical solution for water-wave motion over an offshore submerged horizontal porous-plate breakwater in the context of linear potential theory. The matched-eigenfunction-expansions method is used to obtain the solution. The solution consists of a symmetric part and an antisymmetric part. The symmetric part is also the solution of wave reflection by a vertical solid wall with a submerged horizontal porous plate attached to it. In comparison with previous analytical solutions with respect to finite submerged horizontal porous plates, no complex water-wave dispersion relations are included in the present solution. Thus, the present solution is easier for numerical implementation. Numerical examples show that the convergence of the present solution is satisfactory. The results of the present solution also agree well with previous results by different analytical approaches, as well as previous numerical results by different boundary-element methods. The present solution can be easily extended to the case of multi-layer submerged horizontal porous plates, which may be more significant in practice for meeting different tide levels.     

An analytical solution for long-wave scattering by a submerged circular truncated shoal

An analytical solution of the long-wave (or shallow-water) equation in closed-form is obtained for simple harmonic waves scattered by a submerged circular truncated shoal. This analytical solution is firstly validated against Longuet-Higgins’s classical analytical solution for a submerged cylinder, and then validated against numerical solutions obtained by using the DRBEM (dual reciprocity boundary-element method) model for a submerged circular truncated cone. Finally, the analytical solution is used to investigate the changing trend of maximum wave amplification, the trace pattern of focal position of wave-energy versus the wave period and the influence of shoal submergence on wave-energy trapping.     

非饱和地基中Love波的传播特性

基于非饱和多孔介质的波动方程,考虑了土中水,气体与土骨架之间的粘性耦合作用,建立了弹性半空间上非饱和土层中Love波的弥散方程。首先分析了饱和度与频率对非饱和孔隙介质中剪切波速的影响。然后运用数值方法得到了不同饱和度下土层中多种Love模态波的弥散特性和位移分布情况,并用图表的形式给出。数值计算结果表明,上覆非饱和土层中Love波的传播速度和衰减系数不仅具有频散性,而且与土层的饱和度有关。在不同饱和度时的高模态(n≥2)的Love波的截止频率值不同。此外,讨论了饱和度对Love波水平位移幅值的影响。     

聚焦波浪在潜堤上传播变形的数值模拟

该文以一组色散关系得到改进的完全非线性Boussinesq方程建立了一个波浪模型,通过与均匀水深条件下聚焦波浪的实验结果进行对比说明该模型可以很好的模拟聚焦波浪,然后应用该模型聚焦波浪在一前后坡度对称的潜堤上的非线性传播变形。结果表明：随着水深的减小波峰越来越尖,波谷越来越平坦,所对应的能谱在高次谐频部分也有较大的增长,但在堤顶部分和反变浅区域,波浪的群性随着水深的增大而越来越不明显,对应的频谱表明在这段区域内有反向能量传递存在。另外,在反变浅区域主波频率附近的自由波能量有所增加,这说明频率的峰度也会减小。     

防波堤帷幕尺度对波浪力和消浪性能的影响研究

帷幕式防波堤下部透水,利于港内外的海水交换,防止水质恶化,维持原始水域生态平衡,因此模拟波浪与防波堤的相互作用具有重要的现实意义。该文基于高阶紧致插值CIP(Constrained Interpolation Profile)方法的二维波浪数值模型水槽,通过与文献结果进行比较,结果表明：该文数值模型能够有效地模拟孤立波在冲击帷幕式防波堤过程中的波浪破碎等强非线性现象。通过数值模拟,描述了帷幕式防波堤在不同的宽度和浸没深度情况下与孤立波之间的相互作用中流速和涡度的演变过程,并讨论了孤立波波高和帷幕式防波堤结构尺寸对反射、透射、耗散系数以及在帷幕式防波堤上冲击力的影响。研究表明：帷幕式防波堤的相对浸没深度越大时,消浪效果良好,同时帷幕式防波堤的相对宽度对消浪效果的影响较大。     

Wave interaction with a perforated circular breakwater of non-uniform porosity

Wave interaction with a porous cylindrical breakwater is studied analytically by linear potential wave theory. The breakwater is assumed to have a thin skin, is bottom-mounted and surface-piercing. The porosity of the breakwater is uniform vertically but varies in the circumferencial direction. This allows the choice of a partially impermeable wall or a vertical slot in the breakwater. Three different basic configurations of the breakwater are investigated, namely, (1) uniformly porous cylinder; (2) porous cylinder with partial impermeable wall; and (3) porous cylinder with an opening. The performance of these types of breakwaters is studied vs. wave parameters and breakwater configurations including angle and position of opening or partial impermeable wall as well as porosity. Parametric studies with regard to the wave-amplification factor, wave forces, and elevation contours are made. The results should be found useful in the design of coastal and offshore structures.     

波浪在潜堤上传播的非线性参数分析

利用完全非线性Boussinesq方程数值模型,通过与不规则波浪理论谱、物理模型实验进行了对比验证,证明了该模型模拟不规则波浪的有效性。应用该模型研究了不规则波浪在缓坡潜堤上传播时,波浪非线性参数的变化。波浪在经过缓坡潜堤过程中,波浪的不对称度有一个由负变正的过程,并且最小值出现在堤顶前部区域,最大值出现在堤顶后部区域。波浪的偏度在变浅区逐渐增大,在堤顶中部区域达到最大值,之后偏度在反变浅区逐渐减小到零附近。极值出现的位置可能是潜堤受波浪冲刷破坏比较严重的位置。基于几个典型位置波面过程线的波形变化及其波浪谱变化分析了这些参数变化的原因。分析了变浅区、反变浅区、堤顶区三个区域不对称度和偏度随Ursell数的变化关系,并给出了变浅区和反变浅区波浪的不对称度和偏度与Ursell数之间的经验公式,并与相关研究进行了对比。     

On the stability of lumps and wave collapse in water waves

In the classical water-wave problem, fully localized nonlinear waves of permanent form, commonly referred to as lumps, are possible only if both gravity and surface tension are present. While much attention has been paid to shallow-water lumps, which are generalizations of Korteweg-de Vries solitary waves, the present study is concerned with a distinct class of gravity-capillary lumps recently found on water of finite or infinite depth. In the near linear limit, these lumps resemble locally confined wave packets with envelope and wave crests moving at the same speed, and they can be approximated in terms of a particular steady solution (ground state) of an elliptic equation system of the Benney-Roskes-Davey-Stewartson (BRDS) type, which governs the coupled evolution of the envelope along with the induced mean flow. According to the BRDS equations, however, initial conditions above a certain threshold develop a singularity in finite time, known as wave collapse, due to nonlinear focusing; the ground state, in fact, being exactly at the threshold for collapse suggests that the newly discovered lumps are unstable. In an effort to understand the role of this singularity in the dynamics of lumps, here we consider the fifth-order Kadomtsev-Petviashvili equation, a model for weakly nonlinear gravity-capillary waves on water of finite depth when the Bond number is close to one-third, which also admits lumps of the wave packet type. It is found that an exchange of stability occurs at a certain finite wave steepness, lumps being unstable below but stable above this critical value. As a result, a small-amplitude lump, which is linearly unstable and according to the BRDS equations would be prone to wave collapse, depending on the perturbation, either decays into dispersive waves or evolves into an oscillatory state near a finite-amplitude stable lump.     

板-网结构浮式防波堤消浪性能的试验研究

水深较大时,固定式防波堤不再适用,而相比之下,浮式防波堤具有轻便、机动、经济及良好的海水交换功能等特点。因此为保障深水养殖网箱在风浪中的安全,采用浮式防波堤进行掩护是唯一可行的工程措施。提出了一种新型的浮式防波堤结构型式——板-网浮式防波堤。通过实验室物理模型试验,研究波浪周期、平板宽度、网衣数目、平板刚度以及水流方向和速度对波浪透射系数的影响。试验采用规则波浪,水深为20m,波高为2.5m、4.5m和6.0m,周期为6s～10s。试验结果表明,采用该种浮式防波堤具有较好的消浪效果,但具体参数需根据当地波浪、水流条件而定。     

直立堤上任意方向入射波的波压力研究

为了研究在不同入射波向时直立堤上的波压力,基于FLOW-3D,该文建立了三维数值波浪水池,并进行了物理模型试验。模型采用推板造波及孔隙消波的方法形成稳定的波浪场,数值模拟结果与试验结果吻合较好。研究表明：墙面测点的波压力与波吸力均随入射角度的增大而增大;墙底各测点浮托力的变化规律较为复杂,合田公式不能准确描述;墙面波压力的分布与合田公式基本相符;墙底浮托力的分布并不是合田公式描述的三角形,而是近似梯形分布;斜向波作用下的墙面波吸力分布图相似于正向入射时的分布。研究结论可为防波堤设计提供参考依据。     

Modulation of nonlinear waves in a viscous fluid contained in a tapered elastic tube

In the present work, treating the arteries as a tapered, thin walled, long and circularly conical prestressed elastic tube and the blood as a Newtonian fluid, we have studied the amplitude modulation of nonlinear waves in such a fluid-filled elastic tube, by use of the reductive perturbation method. The governing evolution equation is obtained as the dissipative nonlinear Schrödinger equation with variable coefficients. It is shown that this type of equations admit solitary wave solutions with variable wave amplitude and speed. It is observed that, the wave speed increases with distance for tubes of descending radius while it decreases for tubes of ascending radius. The dissipative effects cause a decay in wave amplitude and wave speed.     

Net flow of compressible viscous liquids induced by travelling waves in porous media

The influence of ultrasonic radiation on the flow of a liquid through a porous medium is analyzed. The analysis is based on a mechanism proposed by Ganiev et al. according to which ultrasonic radiation deforms the walls of the pores in the shape of travelling transversal waves. Like in peristaltic pumping, the travelling transversal wave induces a net flow of the liquid inside the pore. In this article, the wave amplitude is related to the power output of an acoustic source, while the wave speed is expressed in terms of the shear modulus of the porous medium. The viscosity as well as the compressibility of the liquid are taken into account. The Navier–Stokes equations for an axisymmetric cylindrical pore are solved by means of a perturbation analysis, in which the ratio of the wave amplitude to the radius of the pore is the small parameter. In the second-order approximation a net flow induced by the travelling wave is found. For various values of the compressibility of the liquid, the Reynolds number and the frequency of the wave, the net flow rate is calculated. The calculations disclose that the compressibility of the liquid has a strong influence on the net flow induced. Furthermore, by a comparison with the flow induced by the pressure gradient in an oil reservoir, the net flow induced by a travelling wave can not be neglected, although it is a second-order effect.     

Wave radiation by a submerged source undergoing large amplitude periodic motion

Equations are derived to calculate the water waves radiation at infinity bya submerged source undergoing large amplitude motion. These equations do not require the full solution of the velocity potential itself, as demonstrated by a number of two- and three-dimensional examples. The results obtained are used to derive a far field equation for calculating the steady force (the drift force) on a submerged body undergoing large amplitude motion. It is concluded that the equations derived are useful to cases such as a deeply submerged body for which the source distribution may be taken as those obtained in an unbounded fluid domain.     

The wave characteristics of a nonisothermal film of liquid under conditions of jets forming on its surface

An eight-channel capacitive sensor is used for the first time, which enables one to investigate the dynamics of three-dimensional wave flows and the variation of the transverse profile of a nonisothermal film of liquid during formation of jets. Measurements are performed of the wave characteristics of the flow of a film of water on a vertical plate with a heater 150 × 150 mm in size. During the heating of falling liquid, the thermocapillary forces cause the formation of jets and of a thin film between them. The film thickness and wave amplitude in the interjet region decrease with increasing heat flux. Two ranges of the effect of the heat flux on the characteristics of wave flow are identified. Under conditions of low heat fluxes, the film flow hardly differs from isothermal. Under significant heat loads, an intensive formation of jets occurs. Three-dimensional waves propagate over the jet crests, where the film thickness and wave amplitude increase with increasing heat flux. In the interjet region of the film being heated, the average relative amplitude of waves increases with decreasing average thickness, and in the isothermal region this amplitude decreases. Comparison of the obtained results with experimental data for isothermal film reveals that the values of relative amplitude differ significantly in the interjet region at high densities of heat fluxes. Transverse temperature gradients cause a decrease in the liquid film thickness, and longitudinal gradients cause an increase in the relative amplitude of waves compared to isothermal flows. In the end, this leads to the emergence of dry spots and breakdown of film. The relative amplitude of waves on the jet surface decreases with increasing heat flux; this is true of isothermal film flows.     

用改进的Boussinesq方程模拟潜堤上的波浪变形

研究了一种改进的Boussinesq方程,采用预报校正格式对该方程进行了数值离散,并对淹没潜堤上的波浪变形进行了数值模拟,从数值模拟结果和实测值的比较结果来看,该方程能较好地模拟波浪在潜堤上传播时波面的变形过程,可以用于实际中的波浪问题计算。这种改进的Boussinesq方程本身及其求解方法需做进一步的完善。研究结果为实际应用Boussinesq方程来研究复杂地形上的波浪传播提供一定的理论指导。