Measurement of water particle velocities in waves

Water surface profiles and horizontal and vertical water particle velocity components have been measured to investigate the properties of intermediate depth waves generated in the laboratory. The data has been compared with linear wave theory. It was found that linear theory predicted the attenuation of velocity field with depth successfully and that it overestimates both components of velocity slightly.     

Enhancement of biological productivity by internal waves: observations in the summertime in the northern South China Sea

Streaks of elevated concentrations of surface chlorophyll a (Chl_a) of various spacing were found to be associated with internal waves in their transmission zone and dissipation zone in the summertime in the deep open northern South China Sea. At an anchored station in the dissipation zone north of the Dongsha Atoll with a water depth of ca. 600?m, undulations of the mixed layer depth with an amplitude of ca. 30?m and a periodicity of ca. 12?h were observed, and they were accompanied by similar undulation in the isotherm and isopleth of the nutrients. These observations are consistent with the enhancement of vertical mixing by internal waves and the resulting transfer of cold, nutrient-rich subsurface water to the surface mixed layer to fuel biological productivity. In the transmission zone and dissipation zone, respectively, the summertime (May–October) average sea surface temperature was 0.5 and 0.8?°C lower and Chl_a was 19 and 43?% higher than those in a nearby subregion that was minimally affected by internal waves. The mean net primary productivity was elevated by 15 and 37?%. These results indicate that the enhancement of biological activity by internal waves is not confined to the shallow waters on the shelf. The effect can be detected in all phases of the internal waves although it may be especially prominent in the dissipation zone where mixing between subsurface and surface waters is more effective.     

Laboratory study of the dynamics of a layer of turbulence excited by standing surface waves

The evolution of a turbulent layer excited by standing surface parametric waves is studied experimentally. The time dependence of the depth of the turbulized region is obtained. It is found that the thikness of the layer is described by a nonlinear dependence as distinguished from the previously obtained theoretical results. The dynamics of turbulent-layer embedding is described on the basis of a semiempirical theory and the assumption that the outer scale of turbulence is constant. Satisfactory agreement with experimental data is obtained. In the context of the proposed model, a relationship is found between the quantities characterizing the turbulence and surface waves. The dependence of the steepness of surface waves on the acceleration of the bottom is obtained experimentally. The data obtained in this study can be used for estimation of turbulence generation during a submarine earthquake.     

2009 年夏季东沙群岛附近内孤立波的现场观测

通过对东沙群岛附近2009年夏季测到的三个孤立波事件的分析, 结合现场的X 波段雷达、ADCP和CTD 观测, 发现内孤立波经过时, 伴有突发性强流, 最大水平东西分量U大于0.5 m/s, 周期大约15 min, 各深度层海流均为西向。第三个孤立波事件中, 雷达后向散射影像中包含至少4个亮条带, 其中最后的条带雷达表面信号最强。而内波表面信号强弱不仅与内波的振幅有关, 还可能与潮流、混合层深度等环境条件有关, 该研究可加深对内波遥感观测的理解。     

Penetration depth of the dynamic response of seabed induced by internal solitary waves

We use flume experiments and numerical modeling to examine the penetration depth of internal solitary waves (ISWs) on partially saturated porous sandy silt and clayey silt seabed. The results of the experiment and model showed that the instantaneous excess pore water pressure in both the sandy silt and clayey silt seabed followed the same trend of decreasing with the seabed depth. In general, the excess pore water pressure generated by the sandy silt was bigger than that by clayey silt at the same depth. The ISW-induced excess pore water pressure greatly influenced the surface seabed and showed a linear relationship. The penetration depth was approximately one order of magnitude smaller than the half-wavelength of the ISWs, which might be larger than the penetration depth induced by surface waves. Our study results are helpful for understanding the damage that ISWs inflict upon the seabed and for informing future field experiments designed to directly measure the interaction between ISWs and seabed sediments.     

Numerical modelling of the propagation of tsunami waves in the crimean peninsula shelf zone

The paper analyses the effect of non-linearity and bottom friction on propagation of tsunami-type surface waves from the abyssal part of the Black Sea towards the shelf zone. The study relies, on numerical solution of unidimensional non-linear equations for long waves, using the finite-difference technique. Numerical experiments have been conducted for the bottom profile continental slope and shelf, with the full wave reflection being prescribed at a 10-m depth contour. It has been shown that the major role in transforming solitary waves belongs to non-linear topographic factors rather than to dissipation. The reflected wave has been found to be non-linearly distorted, and wave heights in the Black Sea coastal zone have been found to increase by many times. Translated by Vladimir A. Puchkin.     

数值波浪水槽中完全非线性浅水波仿真特性研究

应用基于势流理论的时域高阶边界元方法,建立一个完全非线性的三维数值波浪水槽,通过实时模拟推板造波运动的方式产生波浪。通过混合欧拉-拉格朗日方法和四阶Runge-Kutta方法更新自由水面和造波板的瞬时位置。利用所建模型分别模拟了有限水深波和浅水波,与试验结果、相关文献结果和浅水理论结果吻合较好,且波浪能够稳定传播。系统地讨论造波板的运动圆频率、振幅和水深等对波浪传播和波浪特性的影响,并对波浪的非线性特性进行分析,研究发现造波板运动频率、运动振幅以及水深均将对波浪形态和波浪非线性产生显著影响。结果为真实水槽造波机的运动控制以及波浪生成试验提供了依据,便于实验室设置更合理的参数来准确模拟不同条件下的波浪。     

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.     

Wave particle velocities measured with a Doppler current meter

A newly developed three-dimensional Doppler current meter is described and the results of preliminary field experiments are presented where simultaneous measurements of surface elevation and water velocity associated with wave orbital motion were made. The phase difference between the surface elevation and the vertical velocity measured at 1.0 and 0.45 meters below the mean water level is found to be approximately 90, in accord with the theory for surface waves of infinitesimally small amplitudes. The spectral (frequency) density distribution for velocity is also found to agree with that we would expect from the linear theory for the observed frequency distribution of surface elevation. However, the amplitude of velocity is consistently smaller (about 10 %) than that we would expect. This reduction of amplitude is more pronounced in cases where waves are high and the water depth is shallow.     

Wave interaction with partially immersed twin vertical barriers

The wave transmission, reflection and energy dissipation characteristics of partially immersed twin vertical barriers and the water surface fluctuations in between the barriers were studied using physical models. Regular and random waves of wide ranges of wave heights and periods, nine different immersions of the barriers and a constant water depth were used for the investigation. The coefficient of transmission, and the coefficient of reflection were obtained from the measurements and coefficient of energy dissipation is estimated using the law of conservation of energy. It is found in general that the twin barrier is better in reducing the coefficient of transmission and increasing the coefficient of dissipation in random waves than with the regular waves, especially for increasing incident wave energy levels. The coefficient of transmission reduces significantly with the increased relative water depth. Increase of relative water depth from 0.09 to 0.45 resulted in reduction of transmission coefficient from 0.65 to 0.05. It is possible to achieve a transmission coefficient less than 0.20 for six immersion configurations with relative depth of immersions of the barrier less than (0.28, 0.43), especially in the region closer to deep water conditions. Coefficient of dissipation ranging from 0.65 to 0.85 can be obtained due to random wave interaction.     

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied.     

高频表面波对定常Ekman流解的影响

基于Jenkins(1989)建立的包含Stokes漂流、风输入和波耗散影响的修正Ekman模型,采用Paskyabi等(2012)使用的推广的Donelan等(1987)中的谱和波耗散函数,并利用Paskyabi等(2012)中修正方法给出的包含高频波的风输入函数,在粘性不依赖于水深及粘性随深度线性变化的条件下,研究了包含高频毛细重力波的随机表面波对Stokes漂流和Song(2009)导出的波浪修正定常Ekman流解的影响。结果表明高频表面波使Stokes漂流在海表面剪切加强,对定常Ekamn流解的影响通常不能忽略,但对Ekman流场的角度偏转影响很小。最后,将考虑高频表面波尾谱影响所估算的定常Ekman流解与已有观测结果以及经典Ekman解进行了比对分析。     

Remote sensing of breaking wave phase speeds with application to non-linear depth inversions

A number of existing models for surface wave phase speeds (linear and non-linear, breaking and non-breaking waves) are reviewed and tested against phase speed data from a large-scale laboratory experiment. The results of these tests are utilized in the context of assessing the potential improvement gained by incorporating wave non-linearity in phase speed based depth inversions. The analysis is focused on the surf zone, where depth inversion accuracies are known to degrade significantly. The collected data includes very high-resolution remote sensing video and surface elevation records from fixed, in-situ wave gages. Wave phase speeds are extracted from the remote sensing data using a feature tracking technique, and local wave amplitudes are determined from the wave gage records and used for comparisons to non-linear phase speed models and for non-linear depth inversions. A series of five different regular wave conditions with a range of non-linearity and dispersion characteristics are analyzed and results show that a composite dispersion relation, which includes both non-linearity and dispersion effects, best matches the observed phase speeds across the domain and hence, improves surf zone depth estimation via depth inversions. Incorporating non-linearity into the phase speed model reduces errors to O(10%), which is a level previously found for depth inversions with small amplitude waves in intermediate water depths using linear dispersion. Considering the controlled conditions and extensive ground truth, this appears to be a practical limit for phase speed-based depth inversions. Finally, a phase speed sensitivity analysis is performed that indicates that typical nearshore sand bars should be resolvable using phase speed depth inversions. However, increasing wave steepness degrades the sensitivity of this inversion method.     

Upwelling by a wave pump

A rigid open-ended pipe is submerged in the ocean below the troughs of the surface waves and held fixed in the vertical position, the lower end being at or below the depth of wave influence. When surface gravity waves propagate past the pipe, water flows up as long as waves are present. The steady upward vertical velocity in the center of the pipe is calculated to be proportional to the square of both the average wave steepness and the pipe’s radius. An application is to bring nutrient rich waters up into the sunlit surface layers of the open oceans.     

Capillary-Gravitational Waves of Finite Amplitude on the Surface of a Homogeneous Liquid

The method of multiple scales is used to deduce equations for three nonlinear approximations of the capillary-gravitational disturbances of the free surface of a layer of a homogeneous liquid of constant depth. In these equations, the space-time variations of the wave profile in the expression for the velocity potential on the liquid surface are taken into account. On this basis, we construct asymptotic expansions up to the quantities of the third order of smallness for the velocity potential and elevations of the liquid surface induced by running periodic waves of finite amplitude. Furthermore, we analyze the dependences of the amplitude-phase characteristics of wave disturbances on the surface tension, depth of the liquid, and the length and steepness of waves of the first harmonic. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 5, pp. 25–34, September–October, 2005.     

Seiches in a circular basin of variable depth

Free waves (seiches) in a circular basin of variable depth are studied numerically within the framework of the linear theory of long waves taking into account the action of the Coriolis force. We determine the frequencies of axisymmetric and circular waves, study the structure of the modes of elevation of the free surface and wave velocities, and establish the dependences of the phase velocities of circular waves on the number of mode and wavelength. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

A probabilistic analysis of random wave-induced liquefaction

Seabed instability caused by soil liquefaction due to build-up of excess pore pressure within the sedimentary seabed represents a serious threat to coastal structures. Models of varying sophistication exist for predicting the liquefaction process but most previous calculations are limited to regular waves while the real waves are random. In this study, a numerical study of liquefaction potential of a sand bed under narrow-band random waves is carried out employing ensemble modelling techniques. The aim of the work is to investigate the effect of random waves on excess pore pressure build-up and liquefaction processes and study the probability distribution of the maximum liquefaction depth. The computational results using a 1D liquefaction model indicate that the random wave-induced liquefaction can be much deeper than that of the corresponding regular waves with the largest individual waves in the random wave time series playing a dominant role in determining the maximum liquefaction depth. It is also found that the time for the maximum liquefaction depth to be reached can vary considerably from one random wave series to another, which suggests that in random waves notable densification may occur within the same timeframe as that for liquefaction.     

Sinking/floatation of pipelines and other objects in liquefied soil under waves

This paper presents the results of an experimental study where the sinking and floatation of a pipeline and other objects (namely, a sphere and a cube) in a silt bed was investigated. The bed was exposed to progressive waves. Two kinds of experiments were made: The undisturbed-flow experiments, and the experiments with the structure model (a pipeline, a sphere, and a cube). In the former experiments, the pore-water pressure was measured across the soil depth. The pore-water pressure built up, as the waves progressed. The soil was liquefied for wave heights larger than a critical value. Regarding the experiments with the structure model, the displacement of the structure (sinking or floatation) was measured simultaneously with the pore-water pressure. The influence of various parameters (such as the initial position of the object, the specific gravity, the soil layer thickness, and the wave height) was investigated. It was found that while the pipe sank in the soil to a depth of 2–3 times the pipe diameter, the sphere sank to even larger depths. The pipe with a relatively small specific gravity, initially buried, floated to the surface of the soil. The drag coefficients for the objects sinking in the liquefied soil were obtained.     

On the possible generation of low-frequency microseisms by internal waves in the ocean

The conditions under which the interaction between internal waves and the rough bottom topography may be the reason for synchronous fluctuations of pressure at the bottom have been studied. Disturbances of the depth are assumed to be small compared with the mean depth of the ocean, and the Väisälä-Brunt frequency is constant. It is shown that synchronous fluctuations of pressure exist with a frequency equal to that of internal waves. The amplitude of pulsations can be approximately an order lower than the amplitude of fluctuations generated by standing surface waves. However, local maxima can exist in the low-frequency minimum of the spectrum of microseisms (in the range of 20–1000 s).Translated by Mikhail M. Trufanov.