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.     

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.     

Theoretical and experimental investigation of a vertical wall response to wave impact

The laboratory and field experiments so far have shown that when a wave breaks directly on a vertical faced coastal structure, the resulting impact pressures may become very severe in magnitude and short in duration. Some experimental evidence in the literature suggests that the structural response to the extremely high magnitude impact forces is only limited. This study is mainly concerned with the comparison of the theoretical and experimental results of a vertical wall response under the wave impact loading. In the dynamic analysis of the wall the classical elastic plate theory is used and the numerical results for the dynamic values of the transverse displacement are obtained by employing the method of finite elements. In the theoretical analyses the experimental pressure histories are used and the theoretical wall deflection histories are compared with the experimental results. The computational and experimental deflection histories exhibit similar patterns. The theoretical maximum wall deflections are mostly found to be slightly smaller than the experimental values.     

Forced transverse vibrations of a simply supported rectangular orthotropic plate in the case where the force acts over a plate subdomain

The present study deals with the exact solution of the title problem in the case where a uniformly distributed p₀ cos ωt-type force acts over a rectangular portion of the plate. The problem is of interest in naval and ocean engineering systems where a motor or an engine mounted on a plate or slab induces a dynamic excitation over a finite area. Mechanical designers commonly consider the problem from the point of view of a concentrated dynamic or static force. On the other hand, modelling the structural system as an orthotropic element is of considerable interest in ocean and naval design in view of the ever-increasing use of composite materials and also of the anisotropic characteristics often induced by metallurgical processes.     

Wave interaction with ‘’-type breakwaters

The wave transmission, reflection and energy dissipation characteristics of ‘’-type breakwaters were studied using physical models. Regular and random waves in a wide range of wave heights and periods and a constant water depth were used. Five different depths of immersion (two emerged, one surface flushing and two submerged conditions) of this breakwater were selected. The coefficient of transmission, K_t, and coefficient of reflection, K_r, were obtained from the measurements, and the coefficient of energy loss, K_l was calculated using the law of balance of energy. It was found that the wave transmission is significantly reduced with increased relative water depth, d/L, whether the vertical barrier of the breakwater is surface piercing or submerged, where ‘d’ is the water depth and ‘L’ is the wave length. The wave reflection decreases and energy loss increases with increased wave steepness, especially when the top tip of the vertical barrier of this breakwater is kept at still water level (SWL). For any incident wave climate (moderate or storm waves), the wave transmission consistently decreases and the reflection increases with increased relative depth of immersion, Δ/d from −0.142 to 0.142. K_t values less than 0.3 can be easily obtained for the case of Δ/d=+0.071 and 0.142, where Δ is the height of exposure (+ve) or depth of immersion (−ve) of the top tip of the vertical barrier. This breakwater is capable of dissipating wave energy to an extent of 50–80%. The overall performance of this breakwater was found to be better in the random wave fields than in the regular waves. A comparison of the hydrodynamic performance of ‘’-type and ‘T’-type shows that ‘T’-type breakwater is better than ‘’-type by about 20–30% under identical conditions.     

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.     

马尼拉俯冲带潜在地震海啸对华南沿海的影响

马尼拉俯冲带潜在地震海啸对我国南部沿海城市构成巨大威胁,利用情景式数值模拟技术重构灾害过程并评估危险等级有助于理解南海海啸传播规律并指导预警预报和防灾减灾工作。根据美国太平洋海洋环境研究中心(Pacific Marine Environmental Laboratory, PMEL)发布的马尼拉俯冲带断层参数设计M_w 7.5、M_w 8.1和M_w 8.5三个震级下共19个震源,应用非静压海啸数值模型(Non-hydrostatic Evolution of Ocean WAVE, NEOWAVE)模拟各震源激发海啸在南海海盆的传播过程,通过最大波辐和测点时间序列发现海啸波能量传输分布并评估代表区域危险等级。研究表明, M_w 7.5级地震海啸对我国南部沿海的影响较低,波幅一般不超过30 cm; M_w 8.1级地震海啸对华南沿海主要造成太平洋海啸预警中心定义的Ⅱ或Ⅲ级海啸危险等级,海啸影响范围和能量分布特征由震源位置决定; M_w 8.5级地震海啸主要对中国沿海构...     

Steepness and asymmetry of extreme waves and the highest waves in deep water

Traditional wave steepness s=H/L does not define steep asymmetric waves in a random sea uniquey. Three additional parameters characterising single zero-downcross waves in a time series are crest front steepness, vertical asymmetry factor and horizontal asymmetry factor. Results for steepness and asymmetry from zero-downcross analysis of wave data obtained from full scale measurements in deep water on the Norwegian continental shelf in 58 time series are presented. The analysis demonstrates clearly the asymmetry of both “extreme waves” and the highest waves. The period and height of the highest waves are also given together with their correlation to spectral parameters. The measured maximum wave heights are also compared with predicted values of maximum wave heights showing good agreement.     

Experimental study on the performance of twin plate breakwater

The wave transmission characteristics and wave induced pressures on twin plate breakwater are investigated experimentally in regular and random waves.A total of twenty pressure transducers are fixed on four surfaces of twin plate to measure the wave induced dynamic pressures.The spatial distribution of dynamic wave pressure is given along the surface of the twin plate.The uplift wave force obtained by integrating the hydrodynamic pressure along the structure is presented.Discussed are the influence of different incident wave parameters including the relative plate width B /L,relative wave height /i H a and relative submergence depth s /a on the non-dimensional dynamic wave pressures and total wave forces.From the investigation,it is found that the optimum transmission coefficient,t K occurs around B /L 0.41 ~ 0.43,and the twin plate breakwater is more effective in different water depths.The maximum of pressure ratio decreases from 1.8 to 1.1 when the relative submergence depth of top plate is increased from 0.8to +0.8.     

Nocdap results: On the relationship of extreme waves and currents for design of offshore structures

Simultaneous wind, wave, and current data during 21 storms spanning four winters at Tromsøflaket (230 m depth) were analysed to determine joint probabilities of occurrence. Waves were measured with a Waverider Buoy, winds with a recording anemometer onboard a vessel and currents at up to five depths with Aandera RCM-4 current meters. Measured currents were filtered to separate tidal currents from residual currents. In most of the statistical analyses, the actual current profiles were replaced with a simplified “equivalent” profile (constant above 50 m depth) whose magnitude was chosen to give the same drag load on a single pile as the actual profile when both profiles were combined with wave orbital velocities. The data suggest that the equivalent current is weakly correlated with the wave height. Within the range of the data analysed, an in-line equivalent residual current of 30 cm sec⁻¹ is adequate for design drag force calculations.The data presented here are used to illustrate a procedure for data analysis and are not suitable for use as design criteria.     

Wave interaction with twin plate wave barrier

The wave transmission and reflection characteristics and wave induced pressures on single surface plate and twin plate barriers were investigated experimentally for a wide range of wave heights and periods in regular and random waves. Seven different spacing between the plates were tested. It is found in general, hydrodynamically the twin plate is better than the single surface plate to reduce the wave transmission and increase the wave reflection. It is found that the transmission coefficient of twin plate reduced from 0.8 to 0.3 when the relative plate width is increased from 0.18 to 0.84. Transmission coefficient of twin plate barrier shows oscillating behavior, when relative plate width is increased due to blocking and pumping effect. The reflection coefficient increased from 0.25 to 0.65, when the relative width of the plate is increased from 0.18 to 0.84. The increase in spacing between the plates was also found to increase the reflection coefficient. The transmission coefficient, K_t for 98% probability of non-exceedence was found to be minimum and is about 0.60 when the relative spacing between the plate is about 0.12, compared to K_t=0.76 for single surface plate. The reflection coefficient for 98% probability of non-exceedence was found to exceed 0.66 for single surface plate, whereas it is 0.73 for twin plate with relative spacing of about 0.40. From the investigation with wide range of input parameters, it is found that the twin plate barrier needs to be designed for highest 98% pressure ratio of 2.0, which is equal to the static pressure induced by the design incident wave height.     

Recent developments in “added-mass” planing theory

The results of several recent isolated investigations in planing theory are consolidated in this paper, together with new insights generated by a recent numerical solution of the vertically impacting wedge problem by Zhao and Faltinsen [(1992), Water entry of two-dimensional bodies. J. Fluid Mech. 246, 593–612]. As a result, in contrast to some earlier studies, it is found that the “wetted width” associated with the added mass is not that of the intersection of the wedge with the undisturbed water surface, but the wetted width of the splashed-up water, as originally proposed by Wagner [(1932), Uber Stoss-und Gleitvorgange an der Oberflache von Flussig-Keiten, Zeitschrift für Angewandte Mathematik und Mechanik, Band 12, Heft 4 (August)]. However, the splash-up ratio is not the value of (π/2–1) which he proposed, but a value which decreases with increasing deadrise, originally proposed in the late-1940s by Pierson (“Pierson's hypothesis” in the paper). For 30° deadrise, for example, Pierson's splash-up ratio is two-thirds that of Wagner's.The new equations are employed to determine the increase in the “added mass” of prismatic hull sections due to chine immersion, using experimental data. If m_o^′ is the added amss of the hull section whose chines are just wetted, Payne [(1988), Design of High-speed Boats. Volume 1: Planing. Fishergate, Inc., Annapolis, Maryland, U.S.A.] postulated that the increase in added mass due to a chine submergence (z_c) would be

where b is the chine beam and k is a constant which Payne [(1988), Design of High-speed Boats. Volume 1: Planing. Fishergate, Inc., Annapolis, Maryland, U.S.A.] gave as .The present analysis includes the “one-sided flow” correction introduced in Payne [(1990), Planing and impacting forces at large trim angels. Ocean Engng 17, 201–234]. Partly for that reason and partly because of the more precise analysis of the experimental data, the present paper revises the value to k = 2 for wetted length to beam ratios normally employed. For deadrise angles in excess of 40° and wetted keel to beam ratios in excess of 2.0, there is some evidence that k < 2.0.The revised theoretical formulation is compared with eight different sets of experimental data for flat plate and prismatic hull forms and is found to be in excellent agreement when the speed is high enough for “dynamic suction” (a loss of buoyancy at low speeds and low wetted lenghts) to be unimportant. This is true for “chines-dry” operation with deadrise angles up to 50° and chines-wet operation at length to beam ratios far in excess of the most extreme conventional practice.The research involved in performing this analysis led to the realization that different towing tanks measure different wetted chine lengths for the same hulls and test conditions. Some consistently measure more splash-up than “theory” (based on Pierson's splash-up hypothesis) predicts and others measure somewhat less than the theory. Some examples are given in Appendix B. The reason for this is not understood.     

Wave reflection characteristics of plane, dentated and serrated seawalls

The hydrodynamic performance of vertical and sloped plane, dentated and serrated seawalls were investigated using physical model studies. Regular and random waves of wide range of heights and periods were used. Tests were carried out for different inclinations of the seawall (i.e. θ=30, 40, 50, 60 and 90°) and for a constant water depth of 0.7 m. The wave reflection was measured to assess the dissipation character of the seawalls. It was observed that the serrated seawall was superior to the plane and dentated seawall in reducing the wave reflection. Even for the vertical case, the coefficient of reflection due to regular waves for dentated seawall ranged from 0.6–0.99 and for the vertical serrated seawall it was 0.45–0.98, whereas for the vertical plane wall, it was almost 1.0. It was found that the characteristic dimension of the seawall (i.e. L/W) and the relative water depth (i.e. d/L) were better influencing parameters compared to the conventionally used surf similarity parameter ‘ξ’ (ξ=tan θ/(H_i/L)^0.5) in predicting the reflection from the dentated and serrated seawall, where L is the local wave length, W the width of the dent along the length of the seawall slope, d the water depth at the toe and H_i is the incident wave height. A similar trend was observed for the random waves too. The reduction in the wave reflection due to random waves for the dentated seawall as compared to the plane seawall was about 18% and for the serrated seawall, it was 20%. It was observed that the reflection due to random waves was lesser for all the three different walls than the regular waves, due to the mutual interaction of random waves. Multiple regression analysis on the measured data points was carried out and predictive equations for the reflection coefficient were obtained for both regular and random waves. This study will be useful in the design of energy dissipating type vertical quay walls in ports and harbours, sloped seawalls for shore protection from erosion and sloped caisson as breakwaters. Comparison of predictive formulae with the experimental results revealed that the prediction methods were good enough for practical purposes.     

Estimates of Energy Dissipation Rates in the Three-Dimensional Deep Ocean Internal Wave Field

Using the “Eikonal Approach” (Henyey et al., 1986), we estimate energy dissipation rates in the three-dimensional Garrett-Munk internal wave field. The total energy dissipation rate within the undisturbed GM internal wave field is found to be 4.34 × 10⁻⁹ W kg⁻¹. This corresponds to a diapycnal diffusivity of about 0.3 × 10⁻⁴ m²s⁻¹, which is less than the value 10⁻⁴ m²s⁻¹ required to sustain the global ocean overturning circulation. Only when the high vertical wavenumber, near-inertial current shear is enhanced can diapycnal diffusivity reach ∼10⁻⁴ m²s⁻¹. It follows that the energy supplied at low vertical wavenumbers and low frequencies is efficiently transferred to high vertical wavenumbers and near-inertial frequencies in the mixing hotspots in the real ocean.     

Time series of carbonate system variables off Otaru coast in Hokkaido, Japan

We report several biogeochemical parameters (dissolved inorganic carbon (DIC), total alkalinity (TA), dissolved oxygen (DO), phosphate (PO₄), nitrate + nitrite (NO₃ + NO₂), silicate (Si(OH)₄)) in a region off Otaru coast in Hokkaido, Japan on a “weekly” basis during the period of April 2002–May 2003. To better understand the long-term temporal variations of the main factors affecting CO₂ flux in this coastal region and its role as a sink/source of atmospheric CO₂, we constructed an algorithm of DIC and TA using other hydrographic properties. We estimated the CO₂ flux across the air–sea interface by using the classical bulk method. During 1998–2003 in our study region, the estimated fCO_2sea ranged about 185–335 μatm. The maximum of fCO_2sea in the summer was primarily due to the change of water temperature. The minimum of fCO_2sea in the early spring can be explained not only by the change of water temperature but also the change of nutrients and chlorophyll-a. To clarify the factors affecting fCO_2sea (water temperature, salinity, and biological activity), we carried out a sensitivity analysis of these effects on the variation of fCO_2sea. In spring, the biological effect had the largest effect for the minimum of fCO_2sea (40%). In summer, the water temperature effect had the largest effect for the maximum of fCO_2sea (25%). In fall, the water temperature effect had the largest effect for the minimum of fCO_2sea (53%). In winter, the biological effect had the largest effect for the minimum of fCO_2sea (35%).We found that our study region was a sink region of CO₂ throughout a year (−0.78 mol/m²/yr). Furthermore, we estimated that the increase of fCO_2sea was about 0.56 μatm/yr under equilibrium with the atmospheric CO₂ content for the period 1998–2003, with the temporal changes in the variables (T, S, PO₄) on fCO_2sea, thus as the maximum trend of each variable on fCO_2sea was 0.22 μatm/yr, and the trend of residual fCO₂ including gas exchange was 0.34 μatm/yr. This result suggests that interaction among variables would affect gas exchange between air and sea effects on fCO_2sea. We conclude that this study region as a representative coastal region of marginal seas of the North Pacific is special because it was measured, but there is no particular significance in comparison to any other area.     

Numerical modeling of wave runup and forces on an idealized beachfront house

In this paper, a numerical wave model based on the incompressible Reynolds-averaged Navier–Stokes (RANS) and k–ε equations is used to estimate the impact of a solitary wave on an idealized beachfront house located at different elevations on a plane beach. The locations of the free surface are reconstructed by volume of fluid (VOF) method. The model is satisfactorily tested against the experimental data of wave runup, and the analytical solution of wave forces on vertical walls. The time histories of wave profiles, forces, and overturning moments on the idealized house are demonstrated and analyzed. The variations of wave forces and overturning moments with the elevation of the idealized beachfront house are also investigated.     

A comparison of two spectral wave models in the Southern California Bight

Two models, a spectral refraction model (Longuet-Higgins) and a parabolic equation method (PEM) refraction-diffraction model (Kirby), are used to simulate the propagation of surface gravity waves across the Southern California Bight. The Bight contains numerous offshore islands and shoals and is significantly larger (≈ 300 km by 300 km) than regions typically studied with these models. The effects of complex bathymetry on the transformation of incident wave directional spectra, S₀(f,θ₀), which are very narrow in both frequency and direction are difficult to model accurately. As S₀(f,θ₀) becomes broader in both dimensions, agreement between the models improves and the spectra predicted at coastal sites become less sensitive to errors in the bathymetry grid, to tidal changes in the mean water depth, and to uncertainty in S₀(f,θ₀) itself. The smoothing associated with even relatively narrow (0.01 Hz-5° bandwidth) S₀(f,θ₀) is usually sufficient to bring the model predictions of shallow water energy into at least qualitative agreement. However, neither model is accurate at highly sheltered sites. The importance of diffraction degrades the predictions of the refraction model, and a positive bias [O (10%) of the deep ocean energy] in the refraction-diffraction model estimates, believed to stem from numerical “noise” (Kirby), may be comparable to the low wave energy. The best agreement between the predicted spectra generally occurs at moderately exposed locations in deeper waters within the Bight, away from shallow water diffractive effects and in the far-field of the islands. In these cases, the differences between the models are small, comparable to the errors caused by tidal fluctuations in water depth as waves propagate across the Bight. The accuracy of predicted energies at these sites is likely to be limited by the uncertainty in specifying S₀(f,θ₀).     

Ecological and biological strategies of Etropus crossotus and Citharichthys spilopterus (Pleuronectiformes:Paralichthyidae) related to the estuarine plume, Southern Gulf of Mexico

Differences in the biological and ecological strategies of two tropical flatfishes, Etropus crossotus (fringed flounder) and Citharichthys spilopterus (bay whiff) are discussed. The comparative analysis was based on the seasonal distribution of relative abundance of the two species and flatfish movements utilizing estuarine plume influenced areas as part of their life cycles. Growth parameters of the von Bertalanffy equation and recruitment were estimated (FISAT software) to compare life cycle patterns. The recruitment patterns illustrate the key difference between “estuarine-dependent” and “estuarine-related” nekton strategies. Both species have a short life cycle with a continuous recruitment activity. E. crossotus is an estuarine-related species, with two recruitment pulses (winter frontal season), in the estuarine plume on the shelf. C. spilopterus is an estuarine-dependent species, with a main recruitment pulse during the rainy season in the estuarine plume, and a residual secondary pulse inside the adjacent estuarine system (Terminos Lagoon). The results show that the ecological success of these tropical coastal marine flatfish, with similar biological patterns, is based upon the sequential use (in time and space) of estuarine plume influenced habitats, suggesting that fish migration to shallow waters is related to food availability changes as a strategy towards optimum recruitment.     

Present-day stress and pore pressure fields in the Cuu Long and Nam Con Son Basins, offshore Vietnam

Knowledge of the in situ, or contemporary stress field is vital for planning optimum orientations of deviated and horizontal wells, reservoir characterization and a better understanding of geodynamic processes and their effects on basin evolution.This study provides the first documented analysis of in situ stress and pore pressure fields in the sedimentary formations of the Cuu Long and Nam Con Son Basins, offshore Vietnam, based on data from petroleum exploration and production wells.In the Cuu Long Basin, the maximum horizontal stress is mainly oriented in NNW–SSE to N–S in the northern part and central high. In the Nam Con Son Basin, the maximum horizontal stress is mainly oriented in NE–SW in the northern part and to N–S in the central part of the basin.The magnitude of the vertical stress has a gradient of approximately 22.2 MPa/km at 3500 m depth. Minimum horizontal stress magnitude is approximately 61% of the vertical stress magnitude in normally pressured sequences.The effect of pore pressure change on horizontal stress magnitudes was estimated from pore pressure and fracture tests data in depleted zone caused by fluid production, and an average pore pressure–stress coupling ratio (ΔS_h/ΔP_p) obtained was 0.66. The minimum horizontal stress magnitude approaches the vertical stress magnitude in overpressured zones of the Nam Con Son Basin, suggesting that an isotropic or strike-slip faulting stress regime may exist in the deeper overpressured sequences.