Added masses for circular cylinders near or penetrating fluid boundaries—review, extension and application to water-entry, -exit and slamming

The members of many offshore structures and pipelines are circular cylinders which are often near to or penetrating the fluid boundaries, i.e. the sea bed, other solid boundary or free surface. It seems appropriate therefore to collect together some known analytical results concerning the cylinder added masses in such cases, the free surface (z = 0) condition being simplified. Comparison with simple experiments indicates that for horizontal motions, φ/z = 0z = 0 is appropriate while for vertical motions φ = 0 on z = 0 is appropriate. The effects caused by the variation in the added mass with cylinder submergence in both modes are important for a wide range of practical situations. For high speed entry (slamming) of the cylinder the effect of free surface rise is significant.     

Research on the hydrodynamic characteristics of heave plate structure with different form edges of a spar platform

The hydrodynamic characteristics of heave plates with different form edges of Truss Spar Platform are studied in this paper.Numerical simulations are carried out for the plate forced oscillation by the dynamic mesh method and user defined functions of FLUENT.The added mass coefficient and the damping coefficient of heave plate with tapering condition and the chamfer condition are calculated.The results show that,in a certain range,the hydrodynamic performance of heave plate after being tapered is better.     

孤立波与升沉水平板相互作用数值模拟研究

合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。     

On the planing of a flat plate at high Froude numbers in a two-dimensional case

We seek the solution of the planing of a flat plate at high Froude numbers by a perturbation procedure. The angle of attack of the plate is assumed to vary with the speed of the plate in the present study. A harmonic function K is introduced for the solution of the first-order disturbance potential which becomes the Green function in the limiting case when the Froude number tends to infinity. We get the solution of the first-order potential from Green's theorem applied to K and the first-order potential. Then we obtain the asymptotic solutions of the angle of attack α, lift L and drag D as follows:

where α1. Here W, L_W, and U are the weight of the plate per unit width, wetted length, and speed of the plate, respectively.     

Age,growth and natural mortality of blue jack mackerel Trachurus picturatus (Carangidae) from the Canary Islands,Spain (NW Africa)

Status assessment of exploited fish populations is a general requirement to ensure sustainability of fisheries in both global and local contexts. The blue jack mackerel Trachurus picturatus (Bowdich, 1825) remains unassessed in a data-limited fishery in the eastern central Atlantic, within the waters of the Canary Islands (Spain) off the coast of northwest Africa. This is the most southwestern targeted fishery in the species’ distributional range. To obtain basic life-history information, a total of 2 472 specimens were analysed, ranging from 10.2 to 31.9 cm total length, from samples collected monthly between March 2005 and March 2006. Length–weight relationships (a = 0.0023; b = 3.418; R ² = 0.97) showed no significant difference between sexes. Deposition periodicity and coherence of the ageing criteria were verified by analysis of the monthly evolution of the otolith edge. Ages were estimated by counting annual growth rings on whole otoliths, with these fish ranging from age 0 to 6 years. The von Bertalanffy growth model, which was used to estimate growth parameters from both direct readings and back-calculated length-at-age data, gave good statistical fits. The parameters from the direct readings were: L∞ = 34.9 cm; k = 0.214 y^–1; t ₀ = ?2.545 y (R ² = 0.84), and the natural mortality rates estimated from empirical methods varied between 0.20 and 0.55 y^–1.     

The study of wave pressure and uplift force on a submerged plate

Boundary element method (BEM) is used to study wave pressure acting on a vertical quay, as well as the uplift forces on a submerged plate. The plate, placed in front of the quay, is bored with holes. The results are then compared with the case of a plate without any perforation.The results showed that: for q/h = 0.45, where q is the depth of submergence of the plate and h is water depth, wave pressure acting on the vertical quay is very similar for plates with or without borings. However, with q/h = 0.20, wave pressure on the quay is changed according to wave periods, widths of the plate, the distance of the plate away from the quay, as well as the ratio of the holes to the plates. Uplift forces exerted on the plate are indeed smaller for plates with borings than without, and decrease with increasing porous ratio. Furthermore, the uplift forces will be the same for the same porous ratios, regardless of these ratios being caused by a single or a double perforation.     

Infra-gravity wave generation by the shoaling wave groups over beaches

A physical parameter, μb, which was used to meet the forcing of primary short waves to be off-resonant before wave breaking, has been considered as an applicable parameter in the infra-gravity wave generation. Since a series of modulating wave groups for different wave conditions are performed to proceed with the resonant mechanism of infra-gravity waves prior to wave breaking, the amplitude growth of incident bound long wave is assumed to be simply controlled by the normalized bed slope, βb. The results appear a large dependence of the growth rate, α, of incident bound long wave, separated by the three-array method, on the normalized bed slope, βb. High spatial resolution of wave records enables identification of the cross-correlation between squared short-wave envelopes and infra-gravity waves. The cross-shore structure of infra-gravity waves over beaches presents the mechanics of incident bound- and outgoing free long waves with the formation of free standing long waves in the nearshore region. The wave run-up and amplification of infra-gravity waves in the swash zone appear that the additional long waves generated by the breaking process would modify the cross-shore structure of free standing long waves. Finally, this paper would further discuss the contribution of long wave breaking and bottom friction to the energy dissipation of infra-gravity waves based on different slope conditions.     

Modified eigenfunction expansion methods for interaction of water waves with a semi-infinite elastic plate

The eigenfunction expansion method (will be referred to as error function method in this paper) of analysing reflection and transmission of ocean waves at a semi-infinite thin elastic plate [J Geophys Res 95 (1990) 11629; Phil Trans R Soc Lond A 347 (1994) 185] is modified and extended to cases with simply supported and built-in edges. The form of the error function in the eigenfunction expansion method of Fox and Squire [J Geophys Res 95 (1990) 11629] has been modified based on a dimensional analysis and also extended to plates with either a simply supported or a built-in edge. The modified error function does not include the so-called Lagrange multipliers used in the original method and therefore the modified solution is independent of the selection of the Lagrange multipliers. It is demonstrated that the modified error function method satisfies the relation of energy conservation very well for the three edge conditions examined. The relation of energy conservation for plates is derived for elastic plates with simply supported and built-in edges and it is found that the relation of energy conservation for a free edge is also held for simply supported and built-in edges.In addition, a minor modification has also been made to the eigenfunction method (will be called inner product method in this study) of Sahoo et al. [Proceedings of 10th International Offshore and Polar Engineering Conference 3 (2000) 594]. It will be shown that the modified inner product method becomes mathematically well defined. The modified coefficient matrixes for different edge conditions are diagonal and thus the linear simultaneous equations can be solved very easily. It is also demonstrated with examples that the extended error function method and the modified inner product method give identical results.     

Modified McCormicks model for equilibrium shorelines behind a detached breakwater

Experimental data of equilibrium shorelines behind a detached breakwater obtained by previous investigators were collected and re-reviewed to investigate the major parameters affecting the shoreline shapes. The result shows that the equilibrium shorelines depend not only on the breakwater length B and the distance of the breakwater from the initial shoreline S, but also on the incident wave steepness H₀/L₀, beach slope S_b and the sand size D₅₀. Most of equilibrium shorelines behind a detached breakwater could be approximately described by a couple of elliptic curves as proposed by McCormick (Ports, Coastal & Ocean Engineering ASCE 119, 1993, p. 657). However, after re-examination, this paper shows that the dimensionless semiminor axis b/S and the dimensionless distance G/b in the McCormick’s elliptic-curve model should be modified, as compared with the available experimental data. The modified expressions of b/S and G/b were proposed, and the performances of the modified expressions were also detaily examined in this paper.     

A numerical experiment of the M2 tide in the Yellow sea

Semi-diurnal tides in the Yellow Sea are calculated by integrating the shallow water wave equations with frictional and inertial terms.It is found that the results depend on the bottom friction. In the frictionless case the tidal range is unstably amplified because of the occurrence of resonance of the semi-diurnal tidal component in Inchon Bay. When the bottom friction is in the form of the square of velocity, the results agree fairly well with the observations.The following results are obtained. First, the tidal range is larger at the coast of the Korean Peninsula than at the China Coast. Second, resonance of the semi-diurnal tide occurs in Inchon Bay. Third, bottom friction is very important in the shallow ocean,i.e., when the bottom friction become large, the phase lag is retarded and the tidal range decreases.The amplitude and the phase lag calculated in this study agree well with the observations in the case of _b =_b ² V¦V¦, _b ²=0.0026, especially in the coast of the Korean Peninsula.     

Anisotropic Drained Deformation Behavior and Shear Strength of Natural Soft Marine Clay

The deformation behavior and shear strength of soft marine clays subjected to wave or traffic loads are different from that in triaxial loading due to the changes of major principal stress direction β and intermediate principal stress coefficient b. To investigate the anisotropy affected by β and b in natural soft marine clay, a series of drained tests were conducted by hollow cylinder apparatus. The principal stress direction relative to vertical direction were maintained constant under an increasing shear stress, with fixed intermediate principal stress coefficient b. The influence of the b and β on anisotropy of typically Wenzhou intact clay is discussed. It was found that octahedral stress–strain relationships expressed anisotropy with different b and β. The friction angle and deviator stress ratio with different b and β were presented to provide guidance for engineering projects in the coastal zone.     

Dynamic instability of laminated sandwich plates subjected to in-plane partial edge loading

The dynamic instability of laminated sandwich plates subjected to in-plane partial edge loading is studied for the first time using an efficient finite element plate model. The plate model is based on a refined higher order shear deformation plate theory, where the transverse shear stresses are continuous at the layer interfaces with stress free conditions at plate top and bottom surfaces. Interestingly the plate model having all these refined features requires unknowns at the reference plane only. However, this theory requires C¹ continuity of transverse displacement, which is difficult to satisfy arbitrarily in any existing finite element. To deal with this, a new triangular element developed by the authors is used in the present paper.     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.     

Carbon flux in the northwest Mediterranean estimated from microbial production

Spring profiles of microbial production derived from the dark incorporation of tritiated leucine and tritiated thymidine in the northwest Mediterranean show an exponential decline with depth. Assuming this to represent a steady-state balance between microbial respiration and the downward flux of carbon, the downward flux is estimated as (1−/)p/b, where p is the microbial production, their gross growth efficiency and b the coefficient of exponential decline with depth. Summer profiles, ranging over about 3° of latitude and 4° of longitude, were well fitted by a two-component exponential decline, suggesting two distinct microbial substrates. Values of b for the more rapidly declining component varied between 0.01 and 0.06 m⁻¹ according to location. In the case of the slower component, b was estimated as 0.002 m⁻¹, and did not vary significantly over the region. Estimated fluxes of carbon at the surface are 123–335 mg m⁻² d⁻¹ for the fast and 95 mg m⁻² d⁻¹ for the slow component. Below about 200 m, carbon flux is dominated by the slow component. Flux estimates are compatible with flux estimates from sediment traps in the same region. The observed changes between the spring and summer profiles, combined with the horizontal homogeneity of the summer profiles below 200 m, are consistent with a downward transport of about 5–10 m d^–1, implying a significant dispersive component to the observed fluxes.     

Vibrations of a rectangular orthotropic plate with a free edge: a comparison of analytical and numerical results

Transverse vibrations of a rectangular orthotropic plate with a free edge while the others are supported according to four different combinations of boundary conditions are considered in the present paper. The presence of a concentrated mass is also taken into account. In view of the difficulty of satisfying exactly the natural boundary conditions at the free edge, the fundamental frequency of vibration is determined by means of the optimized Rayleigh-Ritz method and a pseudo-Fourier expansion which contains, in its argument, the optimization parameters γ_i. The results are in excellent agreement with those obtained by means of a finite element algorithmic procedure.     

Determination of Henry's law constants for hexachlorocyclohexanes in distilled water and artificial seawater as a function of temperature

Henry's law constants were determined for α- and γ-hexachlorocyclohexane (HCH) as a function of temperature (0.5–45°C) in artificial seawater (SW; 30‰) and distilled water (DW) using the gas stripping method. Water samples (1–5 ml) were withdrawn from the stripping vessel during the stripping process (30–360 h), solvent extracted and analyzed by gas chromatography—electron-capture detection. The effect of bubbling depth was checked to ensure that bubbles leaving the system were at equilibrium with HCHs in the aqueous phase. Henry's law constants determined at 35 and 45°C in SW were significantly higher (P≤ 0.05) than in DW for both α- and γ-HCH, but not at lower temperatures. The slopes (m) and intercepts (b) of log H vs. 1 / T plots were: α-HCH (DW, 0.5–45°C); m = −2810 ± 110, B = 9.31 ± 0.38; α-HCH (SW, 0.5–23°C); M = −2969 ± 218, B = 9.88 ± 0.76; γ-HCH (DW, 0.5–45°C); M = −2382 ± 160, B = 7.54 ± 0.54; γ-HCH (SW, 0.5–23°C); M = −2703 ± 276, B = 8.68 ± 0.96. Henry's law constants determined in this study compared well with those calculated from reported vapor pressure and solubility data.     

Stratification background conditions for development of double-diffusion processes in the North Pacific

Based on mean multiyear temperature and salinity data structural zones and layers are isolated. Within their limits there are favourable conditions for the development of processes such as layer convection and salt fingers. It is shown that distribution of their parameters is conditioned by location of intermediate water mass boundaries and front interfaces. Stability of the density ratio valueR for various areas is revealed. The obtained results are in good agreement with STD=sounding data. Compared are profiles ofR and local estimates of heat and salt fluxes for various structural zones.UDK 551.465.15     

Planing and impacting plate forces at large trim angles

Added mass theory has been shown to give excellent agreement with experimental measurements on planing surfaces at normal planing angles [e.g. Payne, P.R. (1982, Ocean Engng9, 515–545; 1988, Design of High-Speed Boats, Volume 1: Planning. Fishergate. Inc., Annapolis, Maryland)] and to agree exactly with more complex conformal transformations where such a comparison is possible. But at large trim angles, it predicts non-transient pressures that are greater than the free-stream dynamic pressure and so cannot be correct. In this paper, I suggest that the reason is because, unlike a body or a wing in an infinite fluid, a planing plate only has fluid on one side—the “high pressure” side. So the fluid in contact with the plate travels more slowly as the plate trim angle (and therefore static pressure) increases. This results in lower added mass forces than Munk, M. (1924) The Aerodynamic Forces on Airship Hulls (NACA TR-184) and Jones, R. T. (1946) Properties of Low-Aspect-Ratio Pointed Wings at Speeds Below and Above the Speed of Sound (NACA TR-835) originally calculated for wings and other bodies in an infinite fluid.For simplicity of presentation, I have initially considered the example of a triangular (vertex forward) planning plate. This makes the integration of elemental force very simple and so the various points are made without much trouble. But the penalty is that there seem to be no experimental data for such a configuration; at least none that I have been able to discover. But at least the equations obtained in the limits of zero and infinite aspect ratio, small trim angles (τ) and τ = 90° all agree with established concepts and the variation of normal force with trim angle looks like what we would expect from our knowledge of how delta wings behave in air.I then employed the new equation to calculate the force on a rectangular planing surface at a trim angle τ, having a constant horizontal velocity u_o and a vertical impact velocity of ż. This happens to have been explored experimentally by Smiley, R. F. [(1951) An Experimental Study of Water Pressure-Distributions During Landings and Planing of a Heavily Loaded Rectangular Flat Plate Model (NACA TM 2453)] up to trim angles of τ = 45°, and so a comparison between theory and experiment is possible. The results of this comparison are encouraging, as is also a comparison with the large trim angle planing plate measurements of Shuford, C. L. [(1958) A Theoretical and Experimental Study of Planing Surfaces Including Effects of Cross Section and Plan Form (NACA Report)].As two practical applications, I first employed the new equations to calculate the “design pressures” needed to size the plating of a transom bow on a high-speed “Wavestrider” hull. The resulting pressures were significantly different to those obtained using semi-empirical design rules in the literature. Then I used the theory to critically review data obtained from tank tests of a SES bow section during water impact to identify how the “real world” of resilient deck plating diverged from the “model world” of extreme structural rigidity.