Statistical and dynamical analyses of propagation mechanisms of solitary internal waves in a two-layer stratification

The blocking effect of submarine ridges on the propagation of internal solitary waves (ISWs) over the topography of the seabed results in the fission of the solitary waves that accompany the generation of reflected and transmitted waves. In this study, multivariate analysis of variance (MANOVA) is used to investigate the inseparable relationship between the transmission and reflection. An examination of the error sums of squares and cross-products (SSCP) matrix and the correction matrix shows that the correlation between the transmission (at/ai) and reflection coefficients (ar/ai) is quite low (0.284). Moreover, from multivariate testing, including Pillai’s trace, Wilks’ lambda, Hotelling’s trace and Roy’s largest root, we conclude that the ridge height has a large effect (η = 0.456) on both the amplitude of the transmitted and reflected waves, as well as large (η = 0.411) and very large (η = 0.469) effects on the amplitudes of the transmitted and reflected waves, respectively. In conclusion, the results in the present study highlight the importance of the role played by ridge height in coherent ISW transmission and reflection during oceanic wave–ridge interactions.     

Hydrodynamic characteristics of slotted breakwaters under regular waves

The performance of a slotted breakwater consisting of one row of vertical slots was investigated theoretically and experimentally under normal regular waves. A simple theoretical model based on an eigenfunction was developed. The wave transmission, reflection, energy loss, and hydrodynamic force exerted on the breakwater were calculated for different values of the wave and structure parameters. The validity of the theoretical model was examined by comparing its results with theoretical and experimental results obtained from different studies. It was found that the transmission coefficient decreases with increasing dimensionless wavenumber (kh), increasing wave steepness (H _i/L), and decreasing breakwater porosity (ε). The reflection coefficient showed the opposite trend to the transmission coefficient. Also, about 20–50% of incident wave energy was lost due to the effect of the breakwater. In addition, the proposed theoretical model can be used for predicting the performance of slotted breakwaters and the hydrodynamic forces exerted on these structures using the friction coefficient f = 1.5.     

Hydrodynamic characteristics of double permeable breakwater under regular waves

The wave transmission, reflection, and energy dissipation of the double vertical wall with permeable lower part (horizontal slots) were experimentally and theoretically studied under normal regular waves. The effect of different wave and structural parameters on the hydrodynamic characteristics was investigated e.g. the wave length, the upper part drafts, the lower part porosities, and the space between the double walls. Also, the theoretical model based on an EigenFunction Expansion Method was developed to study the hydrodynamic breakwater performance. In order to examine the validity of the theoretical model, the theoretical results were compared with the present experimental results. Comparison between experiments and predictions showed that theoretical model provides a good estimate to the wave transmission, reflection, and energy dissipation coefficients when the friction factor f = 3. The hydrodynamic efficiency of the proposed breakwater is strongly affected by changing the following: (1) The two upper part drafts together, (2) The upper part draft of the first barrier, (3) The two lower part porosities together, (4) The lower part porosity of the first barrier.     

Characteristics of bubble plumes, bubble-plume bubbles and waves from wind-steepened wave breaking

Observations of breaking waves, associated bubble plumes and bubble-plume size distributions were used to explore the coupled evolution of wave-breaking, wave properties and bubble-plume characteristics. Experiments were made in a large, freshwater, wind-wave channel with mechanical wind-steepened waves and a wind speed of 13 m s^− 1. Bubble plumes exhibited a wide range of bubble distributions, physical extent and dynamics. A classification scheme was developed based on plume extent and “optical density” which is the ability of a plume to optically obscure the image of the background until maximum penetration of the plume. Plumes were classified as either dense (obscure) or diffuse (no-obscure). For each class, the plume bubble population size distribution, Φ(r,t), where r is the bubble radius and t the time, was determined. Dense plumes have a large radius peak in Φ and thus are enhanced in large bubbles. Diffuse plumes are well-described by a weakly size decreasing Φ(r,t) for r < 1000 μm and a more strongly size decreasing Φ(r,t) for r > 1000 μm.The bubble-plume formation rate, P, for each class, wave-breaking rate and wave characteristics were measured with respect to fetch. Wave-breaking rate and intensity are strongly fetch-dependent. In general, the trends in P and wave breaking are similar, reaching a maximum at the fetch of maximum wave breaking. The ratio of P for dense to diffuse plumes is even more sensitive to the occurrence of the most intense wave breaking, where dense plume formation is the greatest.Using P and the bubble size population distributions for each plume class, the global bubble-plume, injection size distribution, Ψ_i(r), was calculated. The volume injection rate for the study area was 640 cm³ s^− 1 divided approximately equally between bubbles smaller and larger than r  1700 μm.     

URANS and DES analysis for a Wigley hull at extreme drift angles

Vortical structures and associated instabilities for flows around the Wigley hull for a wide range of drift angles (10° ≤ α ≤ 60°) with free surface are identified and analyzed. Quantitative verification and validation are conducted on three systematically refined grids with comparison to the experimental data for α = 10°. Analysis of the flow pattern shows a strong correlation between the vortical structures and free-surface wave elevation. For α = 10° and 30°, the flows remain steady and vortices are generated at the keel and fore and aft perpendiculars of the hull. The strength and complexity of these vortices increase with increasing α. At α = 45°, flow becomes unsteady without any significant change in the main flow pattern. At α = 60°, a complex and unsteady flow field on the leeward side of the hull is formed with a large recirculation region from the aft to the fore end, which prevents the flow coming from below the keel from moving up and generating the keel vortices observed at lower drift angles. Karman-like and helical instabilities are analyzed. The effect of Froude number is more apparent for large than for small drift angles.     

Modelling of wave–current interactions at the mouths of the Danube

The target of the present study is the entrance to the Danube Delta in the Black Sea. The wave conditions in this coastal sector are usually significant from an energetic point of view and the relatively strong currents induced there by the outflow from the Danube lead to interactions between waves and currents. This process modifies considerably both the magnitude and direction waves, affecting also coastal navigation and sediment transport patterns. In order to assess the effects of the wave–current interactions, the simulating waves nearshore (SWAN) model was considered for developing a multilevel wave prediction system. Validations against measured data were carried out for each computational level. Five case studies corresponding to the most relevant patterns of the environmental matrix were analyzed. Finally, in order to assess the current effect for a longer timescale, an analysis concerning the variation of the main wave parameters was performed for a 3-month period considering some reference points. The results show that the currents produce considerable changes in the wave field, especially as regards the significant wave heights, mean wave directions and wavelengths. The Benjamin–Feir index was also estimated. The analysis of the variation induced by the current over this spectral shape parameter indicates that, in certain conditions, in the target area the wave heights cannot be considered Rayleigh distributed and freak waves may also occur.     

不同护面形式对潜堤透射系数的影响

针对实际工程中广泛应用的潜堤结构,采用物理模型试验的方法,对不规则波作用下不同护面形式对潜堤透射系数的影响进行了研究,讨论相对堤顶水深、相对堤顶宽度、深水波陡对潜堤透射系数的影响以及不同护面块体对消浪特性的影响。在前人研究成果的基础上,提出了改进的经验计算公式,为潜堤的工程设计提供理论参考。     

Strip method for a laterally drifting ship in waves

Lateral drift occurs due to the effects of wind forces, wave drifting forces, or both on ships sailing in actual seas. It is important therefore to investigate the influence of lateral drift on seakeeping performance for improved ship operation. The velocity potential was expanded as an asymptotic power series in terms of the lateral speed parameter, τ, defined as ω _e V ₀/g, where ω _e is the frequency of wave encounter; V ₀ denotes the lateral velocity, which is assumed to be sufficiently small; and g is the acceleration due to gravity. By combining this technique with the strip method, two sets of motion equations of all the hydrodynamic force coefficients for ship seakeeping were derived. The first set is for ships without lateral drift and is the same as the equations in the new strip method, and the second set is for the additional motions induced by lateral drift. It was found that all ship motion modes except surge are coupled when a ship drifts laterally in waves.     

Wave scattering by undulating bed topography in a two-layer ocean

The problem of wave scattering by undulating bed topography in a two-layer ocean is investigated on the basis of linear theory. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating at both the free surface of the upper layer and the interface between the two layers. Due to a wave train of a particular mode incident on an obstacle which is bottom-standing on the lower layer, reflected and transmitted waves of both modes are created by the obstacle. For small undulations on the bottom of the lower layer, a perturbation method is employed to obtain first-order reflection and transmission coefficients of both modes for incident wave trains of again both modes in terms of integrals involving the bed-shape function. For sinusoidal undulations, numerical results are presented graphically to illustrate the energy transfer between the waves of different modes by the undulating bed. U. BASU was born in 1949. She is a professor in the Department Applied Mathematics, Calcutta University, India. Her current research interests include water wave problems, continuum mechanics, etc.     

Seasonal phytoplankton responses to environmental factors in a shallow Mediterranean lagoon

Phytoplankton community structure was investigated in a 1-year study period from January to December 2006 in the Tunis North Lagoon (South Mediterranean). Twice a month, sampling was carried out from the whole water column. Phytoplankton species composition showed seasonal dynamics following the general environmental variable trends in the study area, with variation in species abundance levels within each season characterised by the presence of different phytoplankton communities. Analysis of environmental variables indicated that phytoplankton-dominant communities were associated with various water physicochemical characteristics, especially water temperature and salinity. Accordingly, significant correlation was recorded between water temperature and dinoflagellates (r = 0.35; p < 0.05) in summer and diatoms (r = 0.69; p < 0.05) in autumn, whereas euglenophytes, cyanophytes and chlorophytes were slightly correlated with temperature in autumn. Salinity was positively correlated with dichtyophytes (r = 0.41; p < 0.05) in winter and with diatoms (r = 0.65; p < 0.05) and euglenophytes (r = 0.57; p < 0.05) in autumn. On the other hand, relationships between high nitrogen nutrient concentration and phytoplankton concentration were recorded for diatoms (r = 0.43; p < 0.05 with NO₂; r = 0.49; p < 0.05 with NO₃) in winter. Silicate concentration supported proliferation of diatoms (r = 0.58; p < 0.05) in autumn in our study period. In contrast, increase of dinoflagellate concentration was associated with the decrease of these parameters in spring and summer.     

潜堤掩护水域波浪计算方法

采用波浪断面物理模型试验和数学模型耦合的方法,研究了抛石潜堤后方掩护水域的波浪计算方法。潜堤后方掩护水域波高由潜堤越浪后的再生波、潜堤间口门绕射波和小风区浪组成,其主要影响因素有潜堤结构形式、入射波浪要素、风区长度等。采用耦合模型,根据物理模型试验的结果,验证数模计算成果,考虑了越浪波高传递的沿程衰减,波浪相互作用时的能量损耗等因素,通过调整波浪破碎指标和波浪能量耗散参数,直接计算堤前设计波浪要素,计算结果更符合实际,为工程设计提供科学依据。     

Breaking wave at the bow of a fast displacement ship model

We investigated the flow structures under the bow wave generated by a fast displacement ship model (INSEAN model 2340) in the presence of wave breaking. The data acquired were also used for a detailed database for CFD validation. The mean and r.m.s. point-wise values of the wave height were measured by means of a finger probe. The intensity of the breaking wave was taken as the r.m.s value of the wave height. The mean velocity field under the free surface was measured at 0.15 L _PP and 0.2 L _PP downstream of the fore perpendicular by means of a 5-hole Pitot probe. Uncertainty assessment of the wave height and velocity field results was performed following the AIAA Standards S-071-1995. Preliminary CFD results from a RANSE code with a breaking model are shown in comparison with the measured data.     

新型透空板式防波堤消浪效果试验研究

为增大双层板式防波堤的波能耗散和防波堤结构的稳定,提出了的一种新型桩基双层板式防波堤,通过物理模型试验,对比分析了该防波堤结构（模型 c）与另两种结构型式的防波堤（模型 a、b）在不同的波浪参数下透射系数、反射系数的变化关系,探讨了新型桩基双层板式防波堤（模型 c）透射系数、反射系数随相对波高、相对水深及相对淹没深度的变化关系,分析了其波能损耗情况。结果表明,在试验范围内,对于长周期波,模型 c 比其他两种型式的防波堤消波效果好;当水深与模型顶平齐时新结构（模型 c）对波能的消耗大于淹没和出水两种情况,说明防波堤高程与水位平齐时其消波效果较好。     

Two-dimensional numerical simulation and experiment on strongly nonlinear wave–body interactions

A constrained interpolation profile (CIP)-based Cartesian grid method for strongly nonlinear wave–body interaction problems is presented and validated by a newly designed experiment, which is performed in a two-dimensional wave channel. In the experiment, a floating body that has a rectangular section shape is used. A superstructure is installed on the deck and a small floating-body freeboard is adopted in order to easily obtain water-on-deck phenomena. A forced oscillation test in heave and a wave–body interaction test are carried out. The numerical simulation is performed by the CIP-based Cartesian grid method, which is described in this paper. The CIP scheme is applied in the Cartesian grid-based flow solver. New improvements of the method include an interface-capturing method that applies the tangent of hyperbola for interface capturing (THINC) scheme and a virtual particle method for the floating body. The efficiency of the THINC scheme is shown by a dam-breaking computation. Numerical simulations on the experimental problem for both the forced oscillation test and the wave–body interaction test are carried out, and the results are compared to the measurements. All of the comparisons are reasonably good. It is shown, based on the numerical examples, that the present CIP-based Cartesian grid method is an accurate and efficient method for predicting strongly nonlinear wave–body interactions.     

Numerical simulation of interference effects for a high-speed catamaran

The simulations of the flow around a high-speed vessel in both catamaran and monohull configurations are carried out by the numerical solution of the Reynold averaged Navier–Stokes (RANS) equations. The goal of the analysis is the investigation of the interference phenomena between the two hulls, with focus on its dependence on the Reynolds number (Re). To this aim, numerical simulations are carried out for values of Re ranging from 10⁶ to 10⁸ for two different values of the Froude number (Fr = 0.30, 0.45). Wave patterns, wave profiles, limiting streamlines, surface pressure and velocity fields are analyzed; comparison is made between the catamaran and the monohull configurations. Dependence of the pressure and viscous resistance coefficients, as well as of the interference factor, on the Reynolds number is investigated. Verification and validation for both resistance coefficients and wave cuts is also performed.     

不同因素对潜堤波浪传播的影响

针对波浪穿过梯形潜堤时的波浪形态沿程变化问题,以梯形潜堤为研究对象,通过二维水槽试验,研究梯形潜堤上规则波的传播特征。以比波高为参数分析不同波浪要素(波高、周期和水深等)对波浪传播变形的影响。试验结果表明,其他条件不变时,入射波高越大、波浪周期越小、堤顶淹没水深越小时,波高在潜堤上方衰减越明显。在有足够水深,且波高较小时,波浪对潜堤均有良好的穿透性;波高较大时,波浪在潜堤上部发生破碎,波浪穿过潜堤后波高衰减,此时潜堤的消波作用明显;在波浪不发生破碎情况下,较长周期波浪在潜堤顶部比波高增大,且出现双峰值。     

浸没式穿孔板对超大型浮体的水弹性响应影响（英文）

Scattering of oblique flexural-gravity waves by a submerged porous plate in a finite water depth is investigated under the assumptions of linearized surface waves and small-amplitude structural response. The study is carried out using eigenfunction expansions and the corresponding orthogonal mode-coupling relations associated with flexural-gravity waves in uniform water depth. The characteristics of the roots of the complex dispersion relation are examined using the principle of counting argument and contour plot. Characteristics of the flexural-gravity waves are studied by assuming both the floating elastic plate and the submerged porous plate are infinitely extended in horizontal directions. The effectiveness of the submerged porous structure on the reflection, transmission, and dissipation coefficients is analyzed for various wave and structural parameters.     

Application of new parameterizations of gas transfer velocity and their impact on regional and global marine CO2 budgets

One of the dominant sources of uncertainty in the calculation of air–sea flux of carbon dioxide on a global scale originates from the various parameterizations of the gas transfer velocity, k, that are in use. Whilst it is undisputed that most of these parameterizations have shortcomings and neglect processes which influence air–sea gas exchange and do not scale with wind speed alone, there is no general agreement about their relative accuracy.The most widely used parameterizations are based on non-linear functions of wind speed and, to a lesser extent, on sea surface temperature and salinity. Processes such as surface film damping and whitecapping are known to have an effect on air–sea exchange. More recently published parameterizations use friction velocity, sea surface roughness, and significant wave height. These new parameters can account to some extent for processes such as film damping and whitecapping and could potentially explain the spread of wind-speed based transfer velocities published in the literature.We combine some of the principles of two recently published k parameterizations [Glover, D.M., Frew, N.M., McCue, S.J. and Bock, E.J., 2002. A multiyear time series of global gas transfer velocity from the TOPEX dual frequency, normalized radar backscatter algorithm. In: Donelan, M.A., Drennan, W.M., Saltzman, E.S., and Wanninkhof, R. (Eds.), Gas Transfer at Water Surfaces, Geophys. Monograph 127. AGU,Washington, DC, 325–331; Woolf, D.K., 2005. Parameterization of gas transfer velocities and sea-state dependent wave breaking. Tellus, 57B: 87–94] to calculate k as the sum of a linear function of total mean square slope of the sea surface and a wave breaking parameter. This separates contributions from direct and bubble-mediated gas transfer as suggested by Woolf [Woolf, D.K., 2005. Parameterization of gas transfer velocities and sea-state dependent wave breaking. Tellus, 57B: 87–94] and allows us to quantify contributions from these two processes independently.We then apply our parameterization to a monthly TOPEX altimeter gridded 1.5° × 1.5° data set and compare our results to transfer velocities calculated using the popular wind-based k parameterizations by Wanninkhof [Wanninkhof, R., 1992. Relationship between wind speed and gas exchange over the ocean. J. Geophys. Res., 97: 7373–7382.] and Wanninkhof and McGillis [Wanninkhof, R. and McGillis, W., 1999. A cubic relationship between air−sea CO2 exchange and wind speed. Geophys. Res. Lett., 26(13): 1889–1892]. We show that despite good agreement of the globally averaged transfer velocities, global and regional fluxes differ by up to 100%. These discrepancies are a result of different spatio-temporal distributions of the processes involved in the parameterizations of k, indicating the importance of wave field parameters and a need for further validation.     

不规则波作用下潜堤透射系数的计算方法及统计分布

通过物理模型试验的方法,研究了不规则波作用下抛石潜堤的透射系数及堤后稳定波高的统计分布。潜堤采用梯形断面形式。通过因次分析,得出影响潜堤透射系数的因子为相对浸没深度(a/H)、相对宽度(B/H)、波陡(H/L)、相对水深(d/H)。根据物理模型试验的结果,得出潜堤前后的稳定波高及潜堤透射系数与主要影响因子的变化规律。其中影响潜堤透射系数最主要的因子为相对浸没深度(a/H)、相对宽度(B/H)。借助MATLAB数学软件平台,将数据进行回归分析,得出不规则波作用下潜堤透射系数的经验公式。最后,得出不规则波作用下潜堤后稳定波高的统计分布。     

Effects of roughness on hydrodynamic characteristics of a submerged floating tunnel subject to steady currents

The effects of surface roughness as induced by marine fouling on the hydrodynamic forces on a submerged floating tunnel (SFT) are experimentally and numerically investigated in detail at Reynolds numbers Re = 8.125 × 10³–5.25 × 10⁴. A sensitivity analysis to different roughness parameters including roughness height, skewness, coverage ratio, and spatial arrangement is performed. In addition, an optimized parametric cross-section for an SFT is proposed, and the hydrodynamic performance of the parametric shape and circular SFT cross-section shape with roughness elements is compared. The pressure distribution along the SFT, flow separation and wake characteristics are analyzed to provide a systematic insight into the fundamental mechanism relating the roughness parameters and flow around an SFT. In order to better understand the nonlinear relationships among structural geometry, roughness parameters, flow states, and structural response, an artificial intelligence method using Random Forest (RF) for feature importance ranking is applied. The results show that with the parametric shape, the hydrodynamic forces on the fouled SFT can be effectively mitigated. The roughness height and coverage ratio affect the equivalent blockage and hence, change flow separation and recirculation length in the wake. Lower skewness of the roughness elements can increase the critical Re by changing the relative roughness parameter. Horizontal arrangement of the roughness elements on an SFT generally results in the largest hydrodynamic forces, compared to staggered and vertical distributions. Throughout the feature importance ranking, the flow regime is found to be the most important feature of the hydrodynamics of the SFT. In addition, the SFT cross-section shape and roughness coverage ratio play a dominant role.