Amplitude decay and energy dissipation due to the interaction of internal solitary waves with a triangular obstacle in a two-layer fluid system: the blockage parameter

Experiments were carried out in a wave flume to examine the propagation of depression-type internal solitary waves (ISWs) over a submerged triangular-shaped obstacle. We observed the distortion and breaking of the ISW depression in a two-layer stratified fluid system as induced by the obstacle on the bottom. Physical factors, such as the amplitude of the wave, the thickness of the two layers, and the height of the submerged obstacle were utilized in our analysis of the wave–obstacle interaction. Wave breaking was determined in relation to input parameters arranged before the experimental runs. A classification scheme based on the blockage parameter ζ was proposed. The various degrees of ISW-obstacle interaction were visually classified with three schematic forms (ζ < 0.55 for a weak encounter; 0.55 < ζ < 0.7 for a moderate encounter; and 0.7 < ζ for wave breaking). Furthermore, the reflection and transmission coefficients were utilized to explore the resultant influence on changes in amplitude and energy of an ISW. The wave characteristics (e.g., amplitude-based wave reflection, energy-based reflection, amplitude-based transmission, and energy-based transmission) during the wave–obstacle interaction showed an approximately linear relation with the blockage parameter. Influenced by the submarine obstacle, the transmitted waves were found to always consist of a leading pulse (solitary wave) followed by a dispersive wave train. Moreover, due to bottom friction the energy budget of the leading pulse was reduced by a factor of at least 5% which could approach 50% in cases with strong breaking.     

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.     

纵向位移波穿过微极流体中微极弹性板的传播特性研究

基于微极流体理论和微极固体弹性理论,研究了纵向位移波通过微极流体中微极弹性板时的纵向位移波、耦合波一和耦合波二等三种微极弹性波的反射和透射特性。理论分析和数值计算结果表明:在一般情况下,各种反射和透射波的振幅比是入射波的入射角、频率和介质材料特性的函数;正入射时只有纵向位移波穿过固体板,而不存在其它波的传播;掠入射时仅有入射波沿界面传播而无反射、折射和透射现象发生。文章同时还讨论了反射、折射和透射系数随入射角的变化规律。     

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.     

Experimental investigation on the drag reducing efficiency of the outer-layer vertical blades

An experimental assessment has been made of the drag reducing efficiency of the outer-layer vertical blades, which were first devised by Hutchins and Choi (Proceedings of ASME FEDSM’02 2002 ASME Fluids Engineering Division Summer Meeting, Montreal) and Hutchins (An investigation of larger-scale coherent structures in fully developed turbulent boundary layers, Hutchins N (2003), PhD thesis, University of Nottingham). The reported drag reduction efficiency, which was as much as 30%, was quantified only in terms of the reduction in the local skin-friction coefficient. The assessment of the drag reducing efficiency did not take the side effects of the inclusion of the blades into considerations. Those effects are the increase in the wetted surface area and the flow disturbances due to the presence of the blades. In the present study, a series of drag force measurements in towing tank has been performed toward the assessments of the total drag reduction efficiency of the outer-layer vertical blades. It was found that for the case of h 4.0 × z 4.0 (h/δ = 1.04), the outer-layer vertical blades array achieved about 9.6% drag reduction without considering the increase in the wetted surface area. A proper scaling method to give collapsed plot of drag reduction efficiency C _F/C _F0 was attempted, but the correlation remained limited. Of the two scaling methods, the outer scaling is found to be relevant one.     

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.     

Structural safety assessment of a pontoon-type VLFS considering damage to the breakwater

 A structural safety assessment of a pontoon-type very large floating structure (VLFS) surrounded by a gravity-type breakwater was carried out for extreme wave conditions by considering the damage to the breakwater. Bending and shear collapses are considered to be a failure mode of the floating structure, while overturning damages the breakwater. The probability of the breakwater overturning, and the transmitted wave height before and after damage to the breakwater, are evaluated using design formulae for port and harbor facilities in Japan. The ultimate bending and shear strengths of the floating structure are calculated by the idealized structural unit method (ISUM) and FEM, respectively. The calculated failure probability for the floating structure is compared with the specified target safety level. It was found that the floating structure under consideration is most likely to fail by bending in transverse waves, and that the corresponding failure probability satisfies the target level. Received: September 12, 2002 / Accepted: October 4, 2002 Acknowledgment. The authors are grateful to Dr. Shigeo Ohmatsu, National Maritime Research Institute, Japan, for allowing us to use the program of hydroelastic response analysis. Address correspondence to: M. Fujikubo (e-mail: fujikubo@naoe.hiroshima-u.ac.jp) Updated from the Japanese original, which won the 2002 SNAJ prize (J Soc Arthit Jpn 2002;190:337–345)     

冰盖下两层流体水波与可渗透起伏海床的作用(英文)

The scattering problem involving water waves by small undulation on the porous ocean-bed in a two-layer fluid,is investigated within the framework of the two-dimensional linear water wave theory where the upper layer is covered by a thin uniform sheet of ice modeled as a thin elastic plate.In such a two-layer fluid there exist waves with two different modes,one with a lower wave number propagate along the ice-cover whilst those with a higher wave number propagate along the interface.An incident wave of a particular wave number gets reflected and transmitted over the bottom undulation into waves of both modes.Perturbation analysis in conjunction with the Fourier transform technique is used to derive the first-order corrections of reflection and transmission coefficients for both the modes due to incident waves of two different modes.One special type of bottom topography is considered as an example to evaluate the related coefficients in detail.These coefficients are depicted in graphical forms to demonstrate the transformation of wave energy between the two modes and also to illustrate the effects of the ice sheet and the porosity of the undulating bed.     

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.     

A comparative analysis of the European and North-American approaches to dealing with major oil spills

Background  

The question of what should be the right level of preparedness to react to a major oil spill (i.e. the EXXON VALDEZ spill, the ERIKA spill, and the PRESTIGE spill) is highly debated, especially in the aftermath of such spills. Little research, however, has been conducted with the aim to identify and compare governments’ best practices not only to fund preparedness measures but also to assess the countries’ ability to respond effectively to catastrophic oil spills. It is the author’s belief that important lessons can be learnt from a comparative analysis of countries’ best practices.     

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.     

斜向规则波与单列桩的相互作用

文章讨论了斜向入射波与桩列相互作用。根据流体通过孔隙结构传递波角小于入射波角以及压力和体积速度连续原理,利用波阻抗和桩列的流阻分析,导出反射系数、传递系数和波浪荷载的解析公式。公式内所有参数均是已知的。用文中公式预测结果与其他研究者的正向入射波试验数据对比,理论与试验很好地吻合。     

Elastic response characteristics of a very large floating structure in waves moored inside a reef

 This article describes the results of hydraulic model tests of the elastic response of a very large floating structure (VLFS) moored inside a reef in an isolated island. The distributions of strains and vertical displacements due to the elastic response of the VLFS were measured. The response characteristics were strongly affected by deformed nonlinear waves inside the reef. A two-step analytical method to compute the elastic response of a VLFS is proposed, and its validity is verified using the results of the hydraulic model tests. Received: May 2, 2002 / Accepted: March 17, 2003 RID="*" ID="*" Address correspondence to: S. Shiraishi (shiraishi@pari.go.jp) Acknowledgment. This study was supported by the Program for Promotions of Fundamental Transport Technology Research from the Corporation for Advanced Transport and Technology (CATT).     

Physical and biological correlates of virus dynamics in the southern Beaufort Sea and Amundsen Gulf

As part of the Canadian Arctic Shelf Exchange Study (CASES), we investigated the spatial and seasonal distributions of viruses in relation to biotic (bacteria, chlorophyll-a (chl a)) and abiotic variables (temperature, salinity and depth). Sampling occurred in the southern Beaufort Sea Shelf in the region of the Amundsen Gulf and Mackenzie Shelf, between November 2003 and August 2004. Bacterial and viral abundances estimated by epifluorescence microscopy (EFM) and flow cytometry (FC) were highly correlated (r² = 0.89 and r² = 0.87, respectively), although estimates by EFM were slightly higher (FC = 1.08 × EFM + 0.12 and FC = 1.07 × EFM + 0.43, respectively). Viral abundances ranged from 0.13 × 10⁶ to 23 × 10⁶ ml^− 1, and in surface waters were ~ 2-fold higher during the spring bloom in May and June and ~ 1.5-fold higher during July and August, relative to winter abundances. These increases were coincident with a ~ 6-fold increase in chl a during spring and a ~ 4-fold increase in bacteria during summer. Surface viral abundances near the Mackenzie River were ~ 2-fold higher than in the Mackenzie Shelf and Amundsen Gulf regions during the peak summer discharge, concomitant with a ~ 5.5-fold increase in chl a (up to 2.4 μg l^− 1) and a ~ 2-fold increase in bacterial abundance (up to 22 × 10⁵ ml^− 1). Using FC, two subgroups of viruses and heterotrophic bacteria were defined. A low SYBR-green fluorescence virus subgroup (V2) representing ~ 71% of the total viral abundance, was linked to the abundance of high nucleic acid fluorescence (HNA) bacteria (a proxy for bacterial activity), which represented 42 to 72% of the bacteria in surface layers. A high SYBR-green fluorescence viral subgroup (V1) was more related to high chl a concentrations that occurred in surface waters during spring and at stations near the Mackenzie River plume during the summer discharge. These results suggest that V1 infect phytoplankton, while most V2 are bacteriophages. On the Beaufort Sea shelf, viral abundance displayed seasonal and spatial variations in conjunction with chl a concentration, bacterial abundance and composition, temperature, salinity and depth. The highly dynamic nature of viral abundance and its correlation with increases in chl a concentration and bacterial abundance implies that viruses are important agents of microbial mortality in Arctic shelf waters.     

Evaluating transfer velocity-wind speed relationship using a long-term series of direct eddy correlation CO2 flux measurements

Long-term observations of the marine atmospheric boundary layer were performed by an eddy correlation system, which was set-up on a platform in the Baltic Sea. In this experiment the three-dimensional wind vector and the turbulent fluxes of momentum, sensible and latent heat and CO₂ were measured for one and a half years. Simultaneously the CO₂ partial pressure p_CO2 in surface water was measured by a submersible autonomous moored instrument for CO₂ at the platform in 7-m depth. The high-resolution eddy correlation measurements of the atmospheric CO₂ flux F_CO2, together with the measurements of the CO₂ partial pressure differences between air and sea Δp_CO2 led to a long-term data set which provided the possibility to investigate the parameterization of the CO₂ transfer velocity k as a function of 10-m wind speed u in a statistical manner. From half-hour mean CO₂ fluxes and CO₂ partial pressure differences, k was calculated using k = F_CO2 / (K₀Δp_CO2), with K₀ the CO₂ solubility. The half-hour mean data points, used for the determination of the k–u parameterization, show large scatter. However, assuming a linear, quadratic dependency the analysis yields: k₆₆₀ = 0.365u² + 0.46u (k at 20 °C and salinity 35 psu) with a correlation coefficient of r² = 0.81. The large scatter indicates that the kinetics of the air–sea CO₂ transfer velocity is not only a function of the wind speed alone, but might also be controlled by other environmental parameters and mechanisms, such as sea state and surface coverage with surfactants.     

透空式防坡堤周围的非线性波浪传播的数值模拟

对非线性波浪在透空式防波堤周围的波浪变形进行了数值模拟,在Boussinesq波浪方程中加入与透空建筑物有关的新耗散项,从而界定了透空建筑物引起的部分反射和透射,波浪折射—衍射的传播过程通过控制方程求解。波浪控制方程通过有限差分方法求解。模型应用于模拟波浪经过具有部分反射的群桩式透空结构,结果表明透空式防波堤可以有效地衰减波浪和作为重力式结构的一种替代方式。     

Sea ice and the onshore–offshore gradient in pre-winter zooplankton assemblages in southeastern Beaufort Sea

Zooplankton communities were studied in southeastern Beaufort Sea (Arctic Ocean) in September–October 2002. Cluster analysis and non-metric multidimensional scaling revealed three distinct mesozooplankton assemblages. A neritic assemblage occurred on the Mackenzie Shelf and in Franklin Bay, while distinct off-shelf assemblages prevailed in the Cape Bathurst Polynya and on the Beaufort Slope respectively. Over 95% of the mesozooplankton was comprised of eight copepod taxa. Pseudocalanus spp. contributed predominantly to the discrimination of the three assemblages and was the only significant indicator of the Shelf assemblage. Oithona similis, Oncaea borealis, Metridia longa and Calanus hyperboreus were indicators of the Polynya assemblage. Cyclopina sp. and Microcalanus pygmaeus were indicative of the overall off-shelf community (Polynya and Slope assemblages). The importance of omnivores and carnivores increased from the shelf to the polynya and the slope. Station depth and duration of reduced ice conditions during summer (< 50% ice concentration) underpinned the distribution of the assemblages (r² = 0.71 and 0.45 respectively). The abundance of Pseudocalanus spp. was independent of depth and increased with the duration of reduced ice conditions (r_s = 0.438). The abundance of Cyclopina sp., M. pygmaeus and other indicators of the offshore assemblages followed the opposite trend (r_s = − 0.467 and − 0.5 respectively). Under continued climate warming, a reduction of the ice cover will affect the biogeography of mesozooplankton on and around the Mackenzie Shelf, to the potential advantage of Pseudocalanus spp. and other calanoid herbivores.     

Changes in dissolved silicate loads to the Baltic Sea — The effects of lakes and reservoirs

We tested the hypothesis that dissolved silicate (DSi) yields [kg km^− 2 yr^− 1] of 82 major watersheds of the Baltic Sea can be expressed as a function of the hydraulic load (HL) as a measure of water residence time and the total organic carbon (TOC) concentration, both variables potentially increasing the DSi yield. Most boreal rivers fitted a linear regression model using HL as an independent variable to explain the DSi yield. Rivers with high HL, i.e., shortest residence times, showed highest DSi yields up to 2300 kg km^− 2 yr^− 1. This is most likely caused by an excess supply of DSi, i.e., the geochemical sources prevail over biological sinks in these boreal watersheds. The DSi yield for regulated and unregulated larger rivers of the boreal watersheds constituting about 40% of the total water discharge and of the total DSi load to the Baltic Sea, respectively, can be expressed as: DSi yield = 190 + 49.5 HL[m yr^− 1] + 0.346 TOC [µM] (R² = 0.80). Since both HL and TOC concentrations have decreased after damming, the DSi yields have decreased significantly in the regulated boreal watersheds, for the River Luleälven we estimated more than 30%. The larger eutrophic watersheds draining cultivated landscape of the southern catchment of the Baltic Sea and representing about 50% of the annual water discharge to the Baltic Sea, deviated from this pattern and showed lower DSi yields between 60–580 kg km^− 2 yr^− 1. DSi yields showed saturation curve like relationship to HL and it appears that DSi is retained in the watersheds efficiently through biogenic silica (BSi) production and subsequent sedimentation along the entire river network. The relationship between HL and DSi yields for all larger cultivated watersheds was best fitted by a Freundlich isotherm (DSi = 115.7HL¹⁰⁹; R² = 0.73), because once lake and reservoir area exceeds 10% of the watershed area, minimum DSi yields were reached. To estimate an uperturbed DSi yield for the larger eutrophic southeastern watersheds is still difficult, since no unperturbed watersheds for comparison were available. However, a rough estimate indicate that the DSi flux from the cultivated watersheds to the Baltic Sea is nowadays only half the uperturbed flux. Overall, the riverine DSi loads to the Baltic Sea might have dropped with 30–40% during the last century.     

Optimal ship tracking on a navigation route between two ports: a hydrodynamics approach

The optimal trajectory from Calcutta port to Mumbai port is charted for a tanker transshipping from the East coast to the West coast of India during rough weather. Rough weather is simulated over Indian seas using the state-of-the-art WAM numerical wave model (WAMDI Group in J Phys Oceanogr 18:1775–1810, 1988), assimilating satellite (IRS-P4) wind fields. These simulated wave fields and two-dimensional (2D) directional wave spectrum are an absolute representation of the irregular seaway. Hence, the same for the monsoon month of August 2000 formed the input basis for this study. Loss of ship speed due to the wave field (i.e., nonlinear motion of the tanker in waves) and associated sea-keeping characteristics in the seaway are estimated (Bhattacharya in Dynamics of marine vehicles, Wiley, New York, 1978). The approach adopted in this paper is unique in that it takes into account both voluntary and involuntary speed reductions of the ship. It helps in ship tracking by the optimum route using inverse velocity as the weight function for the path in an efficient way. Dijkstra’s algorithm [Numer Math 1(3):269–271, 1959] is applied in an iterative manner for determining the optimum track. The optimum track information has broad scope for use in modern shipping industry for obtaining safe and least-time routing by avoiding schedule delays with economic fuel consumption.