Wave force on vertically submerged circular thin plate in shallow water

The paper presented is a solution of shallow water wave force, using small amplitude linear wave theory on two-dimensional vertically submerged circular thin plates under three different configurations: (1) a surface-piercing circular thin plate, (2) a submerged circular thin plate, and (3) a bottom-standing circular thin plate. Finally Morison's equation is used for the determination of wave force which is based on the linear wave theory. The plate is submerged in water near the shore on uniformly sloping bottom. The solution method is confined in a finite domain, which contains both the region of different depth of water and the plate. Laplace's equation and boundary value problems are solved in a finite domain, by the method of separation of variables and the small amplitude linear wave theory. The variation of horizontal force by single particle, total horizontal force and moment with respect to the wave amplitude are obtained at different depth of water and at different wave period. It is observed that the force and moment are converging with the increase of wave period and the gradients of force and moment with respect to the wave amplitude are extremely high for lower wave period.     

Wave reflection by a vertical wall with a horizontal submerged porous plate

By applying the linear water wave theory and the eigenfunction expansion method, the wave reflection by a vertical wall with a horizontal submerged porous plate is investigated in this paper. The numerical results, concerning the effects of the dimensionless plate length, the relative water depth, and the porous effect parameter of the plate on the wave loads on the plate and the wave height near the wall as well as the reflection coefficient, are discussed. It is found that the submerged plate increases the complexity of the phenomenon related to the wave reflection and refraction in the close region of the wall, and leads to the occurrence of the phenomenon of wave trapping. The results indicate that there may exist a process of focusing wave energy near the wall for small dimensionless porous effect parameters, whereas the increase of the dimensionless porous effect parameter decreases gradually the wave height until setdown occurs. The behavior of a larger plate with proper porosity is similar to that of a wave absorber which can significantly suppress not only the wave height above the plate but also the reflection waves. The ability of the porous plate to reduce the wave height on the wall surface is, in general, directly proportional to the dimensionless plate length and may be strongest for a proper value of the dimensionless porous effect parameter. It is also demonstrated that the wave loads on a porous plate are smaller than those on an impermeable plate.     

Experiments on Surface Waves Interacting with Flexible Aquatic Vegetation

Surface wave interaction with aquatic vegetation appears to play a key role in coastal hydro-morpho-dynamics. As an example, the presence of a dense meadow at intermediate water depth is usually associated with a stable and resilient shore. Wave-meadow interactions are investigated here by means of physical modelling, with a focus on wave height distribution and hydrodynamics. The central part of a wave flume is covered by flexible artificial seagrass, composed of polyethylene leaves. This vegetation is tested in both near emergent and submerged conditions. The wave height reduction is evaluated by means of a drag coefficient defined from linear wave theory, which contains all the unknowns of the adopted methodology. The behaviour of such a coefficient is investigated as a function of a wave related Reynolds number. The influence of the flexibility of the leaves is also considered, together with a wave frequency parameter. The results show a complex behaviour with three different trends for near rigid, intermediate or highly flexible leaves. Amplitudes of the orbital velocities are investigated and show a fairly good match with the linear wave theory. On the contrary, the mean velocity along the water column appears to be modified by the seagrass for submerged leaves.     

The Relative Trough Froude Number for initiation of wave breaking: Theory,experiments and numerical model confirmation

It is important to accurately locate the wave breaking region for the calculation of nearshore hydrodynamics. Energy from breaking waves drives hydrodynamic phenomena such as wave set-up, set-down, wave run-up, longshore currents, rip currents, and nearshore circulation. Numerous studies have been undertaken to describe when and where wave breakings occurs. Recent development of computer resources permits the use of phase-resolving numerical models for the study of wave propagation, transformation, and nearshore hydrodynamics. This requires new types of wave breaking criteria for the numerical model. The Relative Trough Froude Number (RTFN) is a new wave breaking criterion. This model is based on the moving hydraulic jump concept, therefore it satisfies properly posed boundary-value conditions. It has been experimentally proved that a critical RTFN at the initiation of wave breaking is consistent with and without the presence of an opposing current, but previous efforts did not investigate the theory for the critical value. This paper provides a theoretical analysis and a numerical analysis to demonstrate why the RTFN theory works as a wave breaking initiation (trigger) index. The theoretical analysis provides a universal constant for the initiation of wave breaking for all water depths assuming the Miche formula properly describes the wave breaking condition. A subroutine for wave breaking in a numerical model, FUNWAVE was modified to include the RTFN trigger. The numerical model was calibrated with data from wave tank experiments, and it was found that the critical condition is very close to the theoretical number, CTFN = 1.45. A second paper (in preparation) provides details of the theory and experiments for a second criterion for termination of wave breaking. The time scale for the establishment of the breaking region i.e., between the initiation position and termination position, depends upon the additional momentum present under turbulent condition within the breaking wave. This subject is not considered herein.     

Internal flow structure of short wind waves

Characteristic features of the internal flow field of short wind waves are described mainly on the basis of streamline patterns measured for four different cases of individual wave. In some waves a distinct high vorticity region, with flow in excess of the phase speed in the surface thin layer, is formed near the crest as shown in Part I of this study, but the streamlines are found to remain quite regular even very near the water surface. The characteristics of flow in the high vorticity region are investigated, and it is argued that the high vorticity region is not supported steadily in individual waves but that growth and attenuation in individual waves repeats systematically, without no severe wave breaking. Below the surface vorticity layer a quite regular wave motion dominates. However, this wave motion is strongly affected by the presence of the high vorticity region. By comparing the measured streamline profiles with those predicted from wave profiles by the use of a water-wave theory, it is found that the flow of the wind waves studied cannot be predicted, even approximately, from the surface displacements, in contrast to the case of pure irrotational water waves.     

Run-up of surface waves on a sea wall built on a convex bottom profile

Wave run-up on a sea wall built on a convex bottom profile is studied in the framework of linear shallow water theory. When the wall is located in “deeper water,” a wave is reflected from the wall without changing its shape and phase, which is fully consistent with classical considerations. If the wall is shifted towards the shore, the shape of the wave changes in a complex way. Note that the wave phase changes to the opposite in the limiting case when the wall is located right on the shore. The role of nonlinear effects is studied by means of numerical simulations using nonlinear shallow water theory. It is shown that the contribution of nonlinear effects and breaking is high on a convex-shaped beach, which makes the structure of the wave field rather complicated.     

Water wave interaction with a floating porous cylinder

The interaction of water waves with a freely floating circular cylinder possessing a side-wall that is porous over a portion of its draft is investigated theoretically. The porous side-wall region is bounded top and bottom by impermeable end caps thereby resulting in an enclosed fluid region within the structure. The problem is formulated based on potential flow and linear wave theory and assuming small-amplitude structural oscillations. An eigenfunction expansion approach is then used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented which illustrate the effects of the various wave and structural parameters on these quantities. It is found that the permeability, size and location of the porous region may have a significant influence on the horizontal components of the hydrodynamic excitation and reaction loads, while its influence on the vertical components in most cases is relatively minor.     

埕岛油田海域波—底相互作用

基于1976，1993年埕岛油田海域测深资料，应用HISWA浅水海浪数值计算模式，研究风暴浪入侵该海域导致的波-底相互作用后果。数值计算结果表明，海区固定点海底冲刷导致波场强化；波参数增量与冲刷深度有关；海底水质点轨道流速峰值，底摩擦耗散峰值及临界波高值相对水深分布均表明，该海域深水区海底冲刷将减弱，浅水区海底冲刷将加强。     

Numerical Simulation of Breaking Wave Based on Higher-Order Mild Slope Equation

The "surface roller" to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation including diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well. This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natu ral topography.     

有限长正弦地形上的波浪传播问题研究

应用基于势流理论的频域边界元方法,研究了波浪在有限长正弦周期地形上的传播问题.开展了网格收敛性分析,并与物理模型试验结果做了对比,验证了数值方法的准确性.研究了正弦地形长度和幅度对水波反射率的影响,以及波浪在周期性地形上传播时的沿程波幅变化.研究发现,波浪反射系数随波数的变化及波浪幅值沿程的变化均呈包络状;当频率处于布拉格共振区域边缘且反射率为零时,周期地形上会出现极大的波幅;随海床波幅增大,第一布拉格共振带变宽且向低频移动.     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

Representing frequency spectra for shallow water waves

Wind waves recorded in water from 1.4 to 3.8 m deep near the southeastern shore of Lake Erie during 1981 were used to compare two methods for representing wave spectra in shallow water. The results show that the semi-theoretical Wallops model, which requires total energy, peak energy frequency, and depth as parameters, provides fair agreement with observed spectra at the deeper stations but only marginal agreement in very shallow water. The general empirical model, which requires average frequency and energy density at the spectral peak as additional parameters, provides closer agreement with observed wave spectra for all depths.     

Generalized Mean-Flow Theory of Wave-Current-Bottom Interactions

1 .IntroductionAveraging has beenconsidered as anactive ,effective and precise methodinthe studyof fluid dy-namics ,andthe governing macroscopic variables like velocity are the averagingresults inthemselves .Consequently,for a special purpose ,the fluid m…     

山东半岛东北部海域悬浮体季节分布及控制因素

基于2018年山东半岛东北部海域冬、夏两季悬浮体浓度、浊度及水温和盐度调查资料,分析了研究区水体悬浮体浓度的季节性变化,探讨了其控制因素。结果表明:夏季浊度在0.2~37.8FTU之间变化,冬季浊度在1.5~100.1FTU之间变化,均表现为底高表低、东高西低的特征。夏季水温分层明显,表现为表层高、底层低的特征,盐度整体无明显变化;冬季温盐垂向上混合均匀,平面上表现为近岸低温低盐水体向远岸高温高盐水体的过渡。悬浮体浓度分布受潮流、波浪、温跃层和温盐锋面等因素影响。夏季,悬浮体垂向上受到温跃层影响,底层悬浮体难以向表层输运;平面上潮混合和波浪差异性作用阻碍了悬浮体的水平输运。冬季,强风浪促使悬浮体垂向混合剧烈,表层悬浮体浓度明显较夏季变高;平面上沿岸流和黄海暖流形成的温、盐锋面阻碍了水团间悬浮体的输运。     

Wave-induced response of seabed: Various formulations and their applicability

In this study, a set of generalized analytical solutions are developed for the wave-induced response of a saturated porous seabed under plane strain condition. When considering the water waves originating in deep water and travelling towards the shore, their velocities, lengths and heights vary. Depending on the characteristics of the wave and the properties of the seabed, different formulations (fully dynamic, partly dynamic, quasi-static) for the wave-induced response of the seabed are possible. The solutions for the response with these formulations are established in terms of non-dimensional parameters. The results are presented in terms of pore pressure, shear stress and vertical effective stress distributions within the seabed. For typical values of wave period and seabed permeability, the regions of applicability of the three formulations are identified and plotted in parametric spaces. With given wave and seabed characteristics, these regions provide quick identification of the appropriate formulation for an adequate evaluation of the wave-induced seabed response.     

副高对黄渤海夏季异常海温影响的数值试验

副热带高压是黄、渤海夏季异常海温的重要成因之一。根据该海区夏季的气候特点 ,构造了一个典型的副高天气过程 ,利用“近海异常海温数值预报模式”对海表层温度进行了数值试验。对该形势下引起黄、渤海夏季异常高温的各因子进行了定量分析 ,给出了副高中心及其附近两点由各因子引起的增温率变化。试验表明 ,副热带高压控制的天气情况下 ,短波辐射对该海区夏季异常高温的形成起主要作用 ,暖水辐聚的贡献占第二位。     

对应分析方法在粤西水东湾动力沉积环境分析的应用

本文以粤西水东湾表层沉积物样品的粒度分布为基本数据,使用对应分析方法并结合地形与波流特征,分析了海湾动力沉积环境。分析结果表明,海湾现代沉积环境可划分为4个动力沉积区。     

Wave Action on Structures of Combined Cylinders

1.Introduction Owingtoitssignificanteffectofreductionofwaveloadsandwaverun up,theperforatedwallon anarrayofcylindricalstructureshasreceivedconsiderableattentioninrecentyears.Manyresearches havebeencarriedoutinthisfield.Anexactsolutionforthediffractionoflinearwaterwaveswithan arrayofimpermeablecylinderswasfirstgivenbySpringandMonkmeyer(1974)usinganeigenfunction expansionapproach.Subsequently,LintonandEvans(1990)madeamajorsimplificationtothetheo ry,whichallowedthenear fieldquantitiessuchasload…     

Reflection of long internal waves of small amplitudes from an underwater slope

The dynamics of long waves in the vicinity of a transition point of a two-layer flow into a single-layer one is studied within the linear theory of shallow water. The analogy between this problem and the classical problem of surface wave runup on the shore is shown. Conditions for breaking internal waves on a slope are discussed.     

On the response of a Coulomb‐damped poroelastic bed to water waves

Abstract

The problem of forced vibration of a slightly inelastic porous bed by water waves is treated analytically on the basis of a linearized expression of the nonlinear damping term for the grain‐to‐grain friction in bed soils and the linear theory by Biot (1962a [Jour. Appl. Physics, 33:1482–1498]) on the elastic wave propagation in porous media. A dispersion relation of water waves is obtained as a function of wave frequency, water depth, permeability, Poisson's ratio, rigidity, and specific loss of bed soil. Three types of elastic waves are induced in a bed by water waves: a shear wave and a compressional wave in the skeletal frame of soil, and a compressional wave in the pore fluid. The compressional wave, due to the motion of the pore fluid relative to the skeletal frame of soil, is highly damped by the viscosity of pore fluid and only a short range effect near the boundaries of discontinuity, such as a sea‐seabed interface. The seabed response to water waves is characterized by the two Mach numbers, i.e., the ratio of water‐wave speed to shear‐wave speed in soil and the ratio of water‐wave speed to compressional‐wave speed in soil. Most of the water‐wave propagation problems fall into the subsonic flow condition, where elastic waves in the bed travel faster than water waves.

For sandy beds, generally the speeds of compressional and shear waves are much higher than the phase velocity of the water wave. For this case, the solution of the Coulomb‐damped poroelastic bed response presented in this paper approaches the solution of the massless poroelastic bed response in Yamamoto et al. (1978 [Jour. Fluid Mech., 87(1): 193–206]). The damping of water waves due to internal grain‐to‐grain friction is equally or more significant than the damping due to percolation in sand beds.

For clay beds, the speed of the shear wave in soil becomes low and comparable to the phase speed of the water wave. The bed motion for this case is considerably amplified due to the near‐resonance vibration of shear mode of bed vibration. The water wavelength on a clay bed is significantly shortened compared to the water wavelength over a rigid bed. The water wave damping due to internal grain‐to‐grain friction in soil becomes much larger compared to the water wave damping due to percolation in clay beds. Long water waves over a soft clayey bed attenuate within several wavelengths of travel distance.