Forced Waves in a Bounded Basin with Two Pycnoclines

The behavior of waves induced in a continuously stratified fluid with two pycnoclines by periodic variations of pressure on the free surface is studied within the framework of the linear theory by taking into account the action of the Coriolis force. The fluid fills a bounded basin of constant depth. We establish the dependences of the amplitudes and velocities of waves on the period of disturbing pressure. The process of transition of generated waves from the barotropic character of propagation to baroclinic with changes in the period of disturbing pressure is studied in detail.     

Influence of the Space Distribution of Atmospheric Pressure on the Structure of Free Wave Surface in a Basin of Variable Depth

Within the framework of the linear theory of long waves, we study forced oscillation of liquid in a ring basin of variable depth by using numerical methods. As a generator of waves, we use periodic (in time) variations of atmospheric pressure. The action of the Coriolis force is taken into account. The liquid is regarded as homogeneous and inviscid. We analyze the dependences of the structure of the free wave surface (the number and location of nodal lines) on the period and space distribution of disturbing pressures. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 2, pp. 11–23, March–April, 2005.     

VERIFICATION OF INTERNAL WAVES IN OFFSHORE AREAS BY MEANS OF CURRENT OBSERVATIONS

Based on the shear effect of internal wave currents in stratified fluid, the necessary condition for the possible existence of an internal wave and the sufficient condition under which there will be no internal wave are deduced starting from the continuity equation of incompressible fluid. The above two conditions are verified by the measured results from vertical current meter arraies at some observation stations in the Bohai Sea and the South Huanghai Sea. In the treatment of measured results, first of all, the tidal period components are separated from the measured currents by Fourier-analysis method, and then the internal wave currents of tidal period from the tidal period components in the light of some considerations. The analytical results of observed currents are well consistent with theoretical analysis. Furthermore, one can also deduce some features of internal waves therefrom. Consequently, it is concluded that the observation from a vertical current meter array is an important means to verif     

Generation of a double Kelvin wave resulting from the reflection of the Rossby wave by the jump layer

This paper considers the evolution of a spatially-localized divergent Rossby wave field near the depth jump. If the jump magnitude is comparable to the depth, Rossby waves are fully reflected and a double Kelvin wave is then generated. The Rossby waves and the double Kelvin wave are described by the first- and zero-approximation fields of the asymptotic expansion, respectively. Over the characteristic Rossby wave period, the level elevation produced by the double Kelvin wave spreads over an extensive area, theraby making up for the change in the total fluid mass of the Rossby waves.Translated by Vladimir A. Puchkin.     

Study on Transient Gap Resonance with Consideration of the Motion of Floating Body

In this paper, the transient fluid resonance phenomenon inside a narrow gap between two adjacent boxes excited by the incident focused waves with various spectral peak periods and focused wave amplitudes is simulated by utilizing the open-sourced computational fluid dynamics software, OpenFOAM. The weather-side box is allowed to heave freely under the action of waves, and the lee-side box keeps fixed. This paper mainly focuses on how both the spectral peak period and the focused wave amplitude affect the free-surface amplification inside the gap, the motion of the weather-side box, and the wave loads (including the vertical and the horizontal wave forces) acting on both boxes. For comparison, another two-box system with both boxes fixed is also considered as a control group. It is found that the motion of the weather-side box significantly changes the characteristics of the transient gap resonance, and it would cause that the fluid resonant period becomes 1.4–1.6 times that of the two-box system with both boxes fixed. All the concerned physical quantities (i.e., the free-surface amplification in the gap, the motion of the weather-side box, the wave loads) are found to closely depend on both the spectral peak period and the focused wave amplitude.

     

张力腿平台内孤立波作用特性数值模拟

依据三类内孤立波理论KdV、eK dV和MCC的适用性条件,采用Navier-Stokes方程为流场控制方程,以内孤立波诱导上下层深度平均水平速度作为入口边界条件,建立了两层流体中内孤立波对张力腿平台强非线性作用的数值模拟方法。结果表明,数值模拟所得内孤立波波形及其振幅与相应理论和实验结果一致,并且在内孤立波作用下张力腿平台水平力、垂向力及力矩数值模拟结果与实验结果吻合。研究同时表明,张力腿平台内孤立波载荷由波浪压差力、粘性压差力和摩擦力构成,其中摩擦力很小,可以忽略;水平力的主要成分为波浪压差力和粘性压差力,粘性压差力与波浪压差力相比较小却不可忽略,流体粘性的影响较小;垂向力中粘性压差力很小,流体粘性影响可以忽略。     

Prediction of impact pressure induced by breaking waves on vertical cylinders in random seas

This paper presents a method to statistically predict the magnitude of impact pressure (including extreme values) produced by deep water waves breaking on a circular cylinder representing a column of an ocean structure. Breaking waves defined here are not those whose tops are blown off by the wind but those whose breaking is associated with steepness. The probability density function of wave period associated with breaking waves is derived for a specified wave spectrum, and then converted to the probability density function of impact pressure. Impacts caused by two different breaking conditions are considered; one is the impact associated with waves breaking in close proximity to the column, the other is an impact caused by waves approaching the column after they have broken. As an example of the application of the present method, numerical computations are carried out for a wave spectrum obtained from measured data in the North Atlantic.     

Very small waves and associated sediment resuspension on an estuarine intertidal flat

Field data from a microtidal estuarine intertidal flat (Tamaki estuary, New Zealand) are used to analyse very small waves (height <10 cm; period 1.0–1.8 s) and associated sediment resuspension under light winds. Mean spectral period at the bed varied over the tidal cycle, driven by changes in surface-wave spectrum and depth-attenuation of orbital motions. Wave-orbital currents exceeded 30 cm/s, disturbing the fine-sand (100–200 μm) matrix of the seabed and resulting in the release of fine silt (particle size <20 μm) at concentrations >120 mg/L. Resuspension was initiated when ∼40% of the maximum zero-downcrossing orbital speeds in a burst exceeded the critical speed for initiation of sediment motion. Sediment concentrations were highest around low tide, when waves were smaller compared to high tide because of a reduced fetch but depth-attenuation of orbital motions was less because the water was shallower. Wave period exerted a control on sediment resuspension through the wave friction factor. There was a hysteresis in the wave Reynolds number such that it was greater on the ebbing tide compared to on the flooding tide: since it did not exceed 3 × 10⁵ the bed was hydraulically smooth, and the wave friction factor therefore is inversely proportional to wave period. Hence, the tidal-cycle hysteresis in wave Reynolds number translated into a smaller wave friction factor on the ebbing tide, and accounting for this caused the ebb and flood sediment concentration data to collapse onto one curve when plotted against wave-induced skin friction. A simple model is presented to evaluate the relative contribution to sediment resuspension of waves associated with weak and strong winds. At the base of the flat (waves competent to resuspend sediment for 5% of the inundation time), waves associated with stronger, infrequent winds dominate resuspension. At the top of the flat (waves competent to resuspend sediment for 30% of the inundation time), waves associated with lighter, frequent winds dominate resuspension. Moderate winds – neither the strongest nor most frequently occurring – dominate resuspension integrated across the profile. The mass of sediment resuspended by waves is greatest towards the top of the flat: shoreward of this, resuspension is smaller because of wave dissipation; seaward of this, resuspension is smaller because of greater depth-attenuation of orbital motions. The location of maximum sediment mass resuspended by waves and the location of maximum duration of resuspension are not necessarily the same.     

Effect of a submerged plate on the near-bed dynamics underincoming waves in deep water conditions

It is well known that wave induced bottom oscillations become more and more negligible when the water depth exceeds half the wavelength of the surface gravity wave. However, it was experimentally demonstrated for regular waves that the bottom pressure oscillations at both first and second wave harmonic frequencies could be significant even for incoming waves propagating in deep water condition in the presence of a submerged plate [16]. For a water depth h of about the wavelength of the wave, measurements under the plate (depth immersion of top of plate h/6, length h/2) have shown bottom pressure variations at the wave frequency, up to thirty times larger than the pressure expected in the absence of the plate. In this paper, not only regular but also irregular wave are studied together with wave following current conditions. This behavior is numerically verified by use of a classical linear theory of waves. The wave bottom effect is explained through the role of evanescent modes and horizontally oscillating water column under the plate which still exist whatever the water depth. Such a model, which allows the calculation of the velocity fields, has shown that not only the bottom pressure but also the near bed fluid velocity are enhanced. Two maxima are observed on both sides of the location of the plate, at a distance of the plate increasing with the water depth. The possible impact of such near bed dynamics is then discussed for field conditions thanks to a scaling based on a Froude similarity. It is demonstrated that these structures may have a significant impact at the sea bed even in very deep water conditions, possibly enhanced in the presence of current.     

Experimental study on the performance of the multiple-layer breakwater

Based on the idea of disturbing the water motion in the upright direction, a new kind of multiple-layer breakwater is proposed in this article, which mainly consists of several horizontal plates. The breakwater's performance of dissipating waves has been investigated in detail in the regular wave tests. The factors identified with the characteristics of the breakwater are discussed, such as the relative width, the wave steepness and the models geometrical parameters (the width and the gap). The comparison and analysis of the transmission and reflection coefficients with respect to different factors are presented. The model test results indicate that the multiple-layer breakwater has the good characteristic of dissipating waves. Further more, only in a little extent can it reflect the waves. The multiple-layer breakwater proposed in the paper is very significative to promote the open type breakwater to be the permanent wave attenuator in the application.     

Hydroelastic interaction between obliquely incident waves and a semi-infinite elastic plate on a two-layer fluid

The hydroelastic response of a semi-infinite thin elastic plate floating on a two-layer fluid of finite depth due to obliquely incident waves is investigated. The upper and lower fluids with different densities separated by a sharp and stable interface are assumed to be inviscid and incompressible and the motion to be irrotational. Simply time-harmonic incident waves of the surface and interfacial wave modes with a given angular frequency are considered within the framework of linear potential flow theory. With the aid of the methods of matched eigenfunction expansion and the inner product of the two-layer fluid, a closed system of simultaneous linear equations is derived for the reflection and transmission coefficients of the series solutions. Based on the dispersion relations for the gravity waves and the flexural–gravity waves in a two-layer fluid and Snell’s law for refraction, we obtain a critical angle for the incident waves of the surface wave mode and three critical angles for the incident waves of the interfacial wave mode, which are related to the existence of the propagating waves. Graphical representations of the series solutions show the interaction between the water waves and the plate. The effects of several physical parameters, including the density and depth ratios of the fluid and the thickness of the plate, on the wave scattering and the hydroelastic response of the plate are studied. It is found that the variation of the thickness of the plate may change the wave numbers and the critical angles. The density ratio is the main factor to influence the wave numbers of the interfacial wave modes. Finally, the stress state is considered.     

On waves propagating over poro-elastic seabed

In this study, an analytical solution is developed for the problem of periodic waves propagating over a poro-elastic seabed of infinite depth. Water waves above the seabed are described using the linear wave theory. The poro-elastic seabed is modelled based on the Biot theory in which the inertia effect and Darcy's friction are added. Continuity of dynamic pressure and flow flux at the interfacial seabed surface are considered. Adopting an approach similar to Hsu et al. (1993), the governing equations for the pore pressure and displacements of the poro-elastic medium are derived. The present analytic solution compares favorably well with experimental results by Yamamoto et al. (1978), and analytical results by Song (1993) for the case of fine sand. Using the present theory, variations of the wavelength and fluid pressure caused by coupling of waves and the poro-elastic seabed are discussed. Results show that higher elasticity of the poro-elastic seabed induces larger interface pressure, but higher permeability causes smaller pressure on the seabed interface. The wave length is affected by the poro-elastic seabed and becomes shorter for softer seabed and shallower water depth.     

Numerical simulation of nonlinear dispersive waves propagating over a submerged bar by IB–VOF model

It is a good test for a numerical model to simulate progressive waves propagating over a submerged bar with a relatively high ratio of slopes. In this paper, the combined IB–VOF model is used to predict nonlinear dispersive waves propagating over a submerged bar with both slopes of 1:2. The predicted free surface elevations are compared with the experimental data and numerical results presented by other researchers. The comparison shows that the IB–VOF model is able to provide satisfactory wave profiles in the shallow water with strong nonlinear effects and in the wave transmitted region with strong wave dispersion in particular. Moreover, the wave evolution behind the submerged bar is described in detail, including the spatial wave profile modulation, spectral analysis of the time-series waves, flow velocity and pressure fields, and kinetic energy distribution. The effect of fluid viscosity on the numerical simulations is also studied, and it is found that the effect on the wave evolution considered in this paper is not significant. Finally, the hydrodynamic force acting on the bar is calculated using the IB–VOF model.     

Ship waves in a continuously stratified basin with ice cover

Ship waves generated in an exponentially stratified fluid when an axisymmetrical area of pressure of constant intensity moves over a floating ice cover are studied in a linear statement. The influence of ice rigidity on the distribution of amplitudes of the internal wave disturbances along the constant phase lines is analysed.Translated by Mikhail M. Trufanov.     

Comparisons of Computational and Experimental Results of Solitary Wave Breaking

- In this paper, the solitary wave deformation along a gentle slope and the impact pressure, on the wall are investigated experimentally and the results are compared with numerical results obtained based on the volume of fluid (VOF) method. The topography used in the experiment consists of three segments. The left segment is a 1:4 slope, the middle segment 1 :SO slope and the right segment a horizontal bed. Both the wave heights and breaking points obtained from numerical simulation and experiments are in good agreement. Numerical results give reasonable pressure distributions of breaking waves on the wall.     

A field experiment on the small-scale model of a gravity offshore platform

The 1:50 scale model of a big offshore gravity platform was placed off the beach at Reggio-Calabria, where the wind waves typically have significant height ranging from 0.20 to 0.40 m and peak period from 1.8 to 2.6 sec. A first set of pressure transducers was assembled at the boundary of the platform and a second set, with the same configuration as the first one, was assembled in the undisturbed wave field, in order to compare the force amplitude on the platform to the force amplitude on an ideal equivalent mass of water (Froude-Krylov force amplitude). Along with the pressure transducers, a few wave gauges were functioning in the undisturbed wave field. It was found that the time histories of the pressure induced by the highest waves, at the columns and at the platform base, were very similar to the measured covariances of the pressure fluctuations. The statistical distribution of the forces on the platform proved to be coincident with the statistical distribution of the Froude-Krylov forces. The spectrum of the force process proved always to be narrow even in the case of the broad wave spectrum. The diffraction coefficient (ratio of the actual force amplitude to the Froude-Krylov force amplitude) was found to depend essentially on a marked reduction of the propagation speed of the pressure head waves, both at the columns and at the platform base.     

一种实体嵌入的三维海浪可视化方法

针对实体嵌入对海面的随机干扰问题,提出一种海浪三维可视化方法。该方法采用扰动的思想改进了海浪的数学模型,并利用信息更加全面的方向谱描述海浪,进而将方向谱和改进海浪模型共同应用于海浪的三维可视化,形象展示实体嵌入时对海浪的随机性影响,并给出了三维实体的建模方法。通过多组实体嵌入的海浪可视化仿真试验的比较与分析,验证了本文提出方法的有效性。     

Wave forces acting on a submerged horizontal circular cylinder in oblique waves and on a vertical cylinder in deep waves

This paper presents a method of estimating wave forces acting on a submerged horizontal circular cylinder fixed in oblique waves.The experiments show that drag and inertia coefficients in beam sea are available for calculating the wave forces in oblique waves.Wave forces exerted on a vertical circular cylinder in deep waves are also investigated.The experimental results show that wave forces acting on the vertical cylinder coincide approximately with hydrodynamic forces acting on a submerged circular cylinder in an oscillating fluid.     

The near field of internal waves after the moving area of atmospheric pressures

The near wave field generated by the travelling atmospheric pressure zone over a stratified fluid is studied within the framework of the linear theory of long waves allowing for the Coriolis force. The exact solution of the problem as a set of single integrals is deduced for the model distribution of pressures. The characteristics of the near wave field have been computed for the Väisälä-Brunt frequency profile takeu from observations. Their dependences on the geographical latitude and the wave generator travelling rate are analysed.Translated by Mikhail M. Trufanov.