An investigation on internal solitary waves in a two-layer fluid: Propagation and reflection from steep slopes

Experimental investigations on internal solitary wave (ISW) propagation and their reflection from a smooth uniform slope were conducted in a two-layered fluid system with a free surface. A 12-meter-long wave flume was in use which incorporated with: (1) a movable vertical gate for generating ISW; (2) six ultrasonic probes for measuring the fluctuation of an ISW; and (3) a steep uniform slope (from one of θ=30°, 50°, 60°, 90°, 120° and 130°) much greater than those ever published in the literature. This paper presents the wave profile properties of the ISW recorded in the flume and their nonlinear features in comparison with the existing Korteweg de Vries (KdV) and modified Korteweg-de Vries (MKdV) theories. Experimental results show that the KdV theory is suitable for most small-amplituded ISWs and MKdV theory is appropriate for the reflected ISWs from various uniform slopes. In addition, both the amplitude-based reflection coefficient and reflected energy approach a constant value asymptotically when plotted against the slope and the characteristic length ratio, respectively. The reflected wave amplitudes calculated from experimental data agree well with those reported elsewhere. The optimum reflection coefficient is found within the limit of 0.85 for wave amplitude, among the test runs from steep normal slope of 30° to inverse angle of 130°, and around 0.75 for the reflected wave energy, produced by an ISW on a vertical wall.     

Dynamic response and sliding distance of composite breakwaters under breaking and non-breaking wave attack

Over the last 15 years improved awareness of wave impact induced failures has focused attention on the need to account for the dynamic response of maritime structures to wave impact load. In this work a non-linear model is introduced that allows evaluating the effective design load and the potential sliding of caisson breakwater subject to both pulsating and impulsive wave loads. The caisson dynamics is modelled using a time-step numerical method to solve numerically the equations of motion for a rigid body founded on multiple non-linear springs having both horizontal and vertical stiffness. The model is first shown to correctly describe the dynamics of caisson breakwaters subject to wave attack, including nonlinear features of wave–structure–soil interaction. Predictions of sliding distances by the new method are then compared with measurements from physical model tests, showing very good agreement with observations. The model succeeds in describing the physics that stands behind the process and is fast, accurate and flexible enough to be suitable for performance design of caisson breakwaters.     

An investigation of breaking wave pressures on inclined walls

Shoreline structures are subjected to breaking wave loads which may reach 690 KN/m². One possibility to reduce these loadings is to slope the exposed surface backwards. The possible amount of reduction in breaking wave loads is, however, unclear, and recent model tests indicated that sloped walls might be exposed to higher loads than are vertical walls. Within the Wave Energy Group at Queen's University Belfast, tests on a 1/36 model of a shoreline wave power station were conducted in order to assess the influence of front wall inclination on the magnitude of breaking wave pressures. It was found that breaking wave pressures decrease from 100% for the vertical wall to 44% for a 32.7° backwards inclined wall and to 64% for a 32.7° forward inclined wall. From the results it was concluded that a maximum pressure of 105% can be expected for a 10° forward inclined wall. Design recommendations were found to be conservative.     

Influence of wave approach angle on TLP's response

The current study focuses on the response analysis of triangular tension leg platform (TLP) for different wave approach angles varying from 0° through 90° and its influence on the coupled dynamic response of triangular TLPs. Hydrodynamic loading is modeled using Stokes fifth-order nonlinear wave theory along with various other nonlinearities arising caused by change in tether tension and change in buoyancy caused by set down effect. Low frequency surge oscillations and high frequency tension oscillations of tethers are ignored in the analysis. Results show that wave approach angle influences the coupled dynamic response of triangular TLP in all degrees of freedom except heave. Response in roll and sway degrees of freedom are activated which otherwise are not present in TLP's response to unidirectional waves. Pitch and roll responses are highly stochastic in nature indicating high degree of randomness. Variation in surge, sway and heave responses are nonlinear and are not proportional to change in wave height for the same period.     

An evaluation of model estimates of ocean wave directions

The potential accuracy of local models is investigated to determine the mean direction of waves from the time history of locally observed significant wave height (or peak frequency) and locally observed wind. This is done by comparing results of such models with observations at a location in the southern North Sea for a period of six weeks. The model results are also compared with results of two synoptic models which require large scale wind information to estimate the local mean wave direction.For significant wave heights larger than 1.5 m the rms-error of the estimated mean wave direction was about 30° for the best performing local model and about 15° for the best performing synoptic model.     

Variations in wave direction estimated using first and second order Fourier coefficients

In most design applications such as alignment of the berthing structure and breakwater alignment, it becomes necessary to determine the direction of design wave. There are two different approaches to determine wave direction. One involves the use of first order Fourier coefficients (mean wave direction) while the other uses second order Fourier coefficients (principal wave direction). Both the average wave direction over the entire frequency range (0.03–0.58 Hz) and the direction corresponding to the peak frequency are used in practice. In the present study, comparison is made on wave directions estimated based on first and second order Fourier coefficients using data collected at four locations in the west and east coasts of India. Study shows that at all locations, the mean and principal wave directions for frequencies ranging from 0.07 to 0.25 Hz (±0.5 times peak frequency) co-vary with a correlation coefficient of 0.99 but at lower and higher frequencies, difference between the parameters is large. Average difference between the mean wave direction at peak frequency and the average over the frequency related to spectral energy more than 20% of maximum value is less, around 13°. Study shows that average difference in the sea and swell directions is around 39°.     

The wave plus current flow over vortex ripples at an arbitrary angle

This work concerns the wave plus current flow over a sand bed covered by vortex ripples, with the current and the waves coming from different angles. Experiments were performed in a basin, where current and waves were perpendicular, in order to determine the conditions (current strength) leading to a regular ripple pattern formation. Numerical simulations were conducted changing the direction between the waves and the current from 0° to 90° and the ratio between the current strength and the wave orbital velocity from 0.2 to 1.5. Close to the bed, the current aligns parallel to the ripple crests, leading to a veering current profile with the vertical coordinate. The current-related friction coefficient was calculated. It was found that it decreases as the angle approaches 90°, while it increases for decreasing values of the current with a trend that can be described by a power law.     

近破波作用下沉箱式防波堤运动特性的模型实验研究

对近破波作用下沉箱式防波堤的运动特性进行了模型实验研究。实验中测量了沉箱模型与基床的摩擦系数、基床刚度和阻尼系数;不同水位情况下作用于沉箱模型上的近破波波压力时程;近破波作用下沉箱模型的位移和转角响应时程等,并与数学模型计算结果进行了比较分析。实验结果表明,若沉箱的滑移力大于沉箱与基床间的摩擦力,在连续波浪作用下,沉箱将连续出现间歇式滑移运动,数学模型可较好地模拟这一运动过程。     

The Rossby wave as a key mechanism of Indian Ocean climate variability

We analyze the time-longitude structure of composite cases from model-assimilated ocean data in the period 1958–1998, following on from earlier work by Huang and Kinter (J. Geophys. Res. 107(C11) (2002) 3199) that studied east–west thermocline variability in the Indian Ocean. Our analysis focuses on the Rossby wave signal along the thermocline ridge in the tropical SW Indian Ocean (10°S, 60–80°E), where wind stress curl is important. Anomalous winds in the equatorial east Indian Ocean force successive Rossby waves westward at speeds of 0.1 m s⁻¹±30%. With a wavelength of 7000 km, the period of oscillation is in the range 1.9–5.2 years. The Indian Ocean Rossby wave is partially resonant with the global influence of the El Nino–Southern Oscillation, except during quasi-biennial rhythm. The presence of the Rossby wave offers potential predictability for east–west atmospheric circulation systems and climate that affect resources in countries surrounding the Indian Ocean.     

沉箱基础对摇板式波浪能装置水动力性能影响研究

摇板式波浪能转换装置具有频率响应范围广、可靠性好、常规海况下转换效率高、建造成本低等优点。基于势流理论建立具有沉箱基础的摇板式波浪能装置水动力性能的解析解。将解析结果与文献中已有结果和边界元数值结果进行了对比,验证了解析解求解过程的正确性。通过算例分析,研究了波浪入射频率、沉箱基础高度、沉箱基础宽度、摇板位置、摇板厚度和摇板密度对装置能量俘获效率的影响。研究结果表明：采用合适高度的沉箱基础能显著提升装置性能;长波海况下,摇板铰接在沉箱基础背浪侧上表面时装置性能更佳,而短波海况下,摇板铰接在沉箱基础迎浪侧上表面更为合理;沉箱基础宽度的推荐值为0.5到1.0倍水深;适当减小摇板厚度能够提升装置性能;应优先选用密度较大的摇板。     

新型直立式透空堤消浪性能数值研究

为使防波堤同时具有良好的掩护效果和水体交换能力,提出了两种带有透浪通道的新型直立式防波堤。基于Fluent求解器建立了三维数值波浪水槽,通过与试验结果对比,验证了该数值水槽求解波浪与透空堤作用具有较高的精度。对两种防波堤在规则波作用下的透浪特性进行了研究,结果表明:透射系数K_t与透空率呈正线性相关,且可通过调整透浪通道间距,使相同透空率下K_t降低20%～30%。对同一结构,K_t随相对波长的增大而显著增大,但受相对波高的影响较小。在透空率大于0.16后,异型沉箱防波堤的消浪性能明显优于错位沉箱。基于数值计算结果,给出了以上两种透空堤波浪透射系数的经验公式。     

开孔沉箱式结构内部波浪冲击压力试验研究

为研究在不同比尺模型下,透空式海洋结构中开孔沉箱内部受力与入射波浪的关系及差异,针对简化的上部开孔箱体海洋结构,选取两组不同尺寸模型进行了多组规则波物理模型试验。首先采用低通滤波方法分析了冲击力的不同组分,然后对比了两组模型内部所受冲击力的分布及波要素与箱体内部受力的关系。研究发现,波面对开口的淹没程度是影响冲击过程的主要因素;当模型尺寸发生变化时,开孔箱体内部所受波浪力与入射波要素的关系也发生了变化。     

Design of a caisson plate under wave impact

From the laboratory experiments and field studies it has been shown that when a wave breaks directly on a vertical wall, impact pressures of high magnitude and short duration, are produced. Despite the recent advances made in collecting data on impact pressure histories and their spatial distributions, analyses on the structural behaviour of the walls loaded by the impact forces do not seem adequate. In the present study the theoretical analysis of the response characteristics of a caisson plate, having different aspect ratios, under the wave impact loading is investigated. Numerical results for the dynamic values of moments and transverse displacements are obtained by the method of finite elements. Some prerequisite experimental data for wave breaking and resulting impact pressures are provided. The static results for moments and deflections are also computed for comparing them with the dynamic values. The dynamic results are found significantly greater than the static values. The ratio between the dynamic and static values is called “Dynamic magnification factor” that varies with plate aspect ratio. Based on this factor a procedure is proposed which may have practical consequences in the design of caisson plates.     

带横隔板局部开孔沉箱在斜向波作用下的受力研究

基于线性势流假定,对斜向波作用下带横隔板局部开孔沉箱防波堤的水平波浪力进行了理论研究。给出了开孔沉箱法向水平力和横隔板受力的理论计算方法,在极限情况下波浪力的计算结果与文献中的已有结果一致。利用数值算例分析了开孔沉箱总水平力的主要影响因素。开孔沉箱法向总水平力的减小主要集中于结构上半部分波浪影响范围以内。增加单个开孔沉箱的长度有利于减小结构所受总水平波浪力。当波浪入射角或沉箱前开孔墙孔隙影响系数幅值较大时,开孔沉箱横隔板上总水平力的最大值要超过相应的沉箱法向总水平力,此时要注意横隔板的强度问题。     

消浪室宽度对可渗明基床开孔沉箱消浪性能影响研究

开孔沉箱是将传统沉箱的前壁开孔,使沉箱前的入射波浪与反射波浪非同相位叠加,达到消能目的。消浪室是开孔沉箱的重要特征结构,其宽度对开孔沉箱的消浪性能具有重要影响。针对可渗明基床开孔沉箱,赋予消浪室宽度以较大的变化范围,开展专项物模试验,研究探讨了在规则波与不规则波作用下,相对消浪室宽度对可渗明基床开孔沉箱前波高反射系数的影响规律,发现反射系数随相对消浪室宽度的增加呈减小—增大—减小的振荡特性,这一发现有别于前人的研究成果,对工程中开孔沉箱消浪室结构的优化设计具有借鉴意义。同时,对试验工况进行数值模拟和解析计算,以物模试验值为标准,评价两种方法在研究相对消浪室宽度对开孔沉箱波高反射系数影响时的规律把握能力及计算精度,对工程中应用这两种方法给出相关建议。     

不规则波与开孔沉箱相互作用数值模拟

采用三步有限元法对N-S方程进行离散,同时借助CLEAR-VOF方法追踪流体自由表面,利用主动吸收式造波等手段改进了二维不规则波浪数值水槽,使得水槽中的波浪谱与目标靶谱吻合较好。进而建立了不规则波浪与开孔沉箱作用一种新的数值模式,分析研究不规则波作用下开孔沉箱的反射率,并与现有的物模结果和数模结果进行了对比,为不规则波与开孔沉箱作用问题的研究,探求了一种新的数值手段。     

有顶板开孔沉箱所受波浪力的数值分析

利用流体体积(VOF)方法并结合k-ε模型以及等温状态下的气体状态方程数值计算规则波对有顶板开孔沉箱的作用,将数值计算结果与物理模型试验数据分别对总水平力、前开孔板和后实体板的压力分布以及顶板总力等物理量进行对比,验证了所建立的数学模型和数值计算方法的有效性和可靠性,为分析有顶板开孔沉箱的波浪力提供了有效的计算方法.     

Laboratory experiments for wave motions and turbulence flows in front of a breakwater

In this paper, laboratory data for free surface displacements and velocity fields in front of a caisson breakwater covered with wave-dissipating blocks, together with wave pressures acting on the caisson, are presented and discussed. The core of the breakwater is made of a concrete caisson with a vertical front wall. The caisson is protected by a thick layer of tetrapods and is supported by a rubble mound. The breakwater is placed on the 1/25 impermeable slope. Two types of incident waves are used in the experiments: nonbreaking waves and spilling-type breaking waves. In the breaking wave case, the incident wave breaks offshore before it reaches the breakwater. The velocity data are obtained by using both the Laser Doppler Velocimeter (LDV) and the Electromagnetic Current Meter (EMCM). The raw data are analyzed using a numerical-filtering scheme so that turbulent fluctuations are separated from the phase-dependent wave motions. The vertical profiles of the time-averaged (over a wave period) turbulent velocity components at several vertical cross-sections in front of the breakwater are then analyzed. The spatial variations of the time-averaged turbulence velocity suggest that turbulence is generated inside the protective armor layer and transported into the flow region in front of the breakwater. The wave pressures on the vertical face and on the bottom of the caisson are also reported.     

Field evaluation of a microprocessor-based recording current meter modified for wave research

The need to estimate the resuspension and deposition of fine-grained sediments and their associated contaminant transport has, in shallow lakes and nearshore areas, called for the measurement of wave data as well as mean flows. Wave statistics recorded by a vector-average current meter over a two-week period are compared to independently measured wave data for a wave-dominated shallow lake at two depths. Wave orbital motions are within 3% of those determined by spectral analysis of frequently sampled currents. Wave propagation directions are within ±19° of spectrally determined directions and qualitatively similar to the fetch-weighted wind direction. Less satisfactory agreement was evident between the wave periods as determined by zero-crossings and the wave spectral peak periods. Reasonable wave periods could be inferred only when the r.m.s. orbital speed exceeded the mean speed. Another possible algorithm for evaluating wave period is tested and recommendations are made for improvements to the measurement system.     

斜向波作用下防波堤衔接段块体的稳定性和沉箱结构上波浪力试验研究

在斜向波浪作用下,防波堤结构衔接段会产生波能集中、壅水和漩涡等复杂的水动力情况,对该区域块体稳定性和沉箱结构产生极不利的影响,本文开展了三维整体波浪物理试验研究,以揭示不同角度斜向波与块体稳定性和沉箱结构受力敏感性的关系.同时将得到的试验结果与规范公式计算结果进行比较分析,得出两者之间的差异性.试验结果可为工程设计中结...