JONSWAP's parameters: Sorting out the inconsistencies

The original prognostic equations for the JONSWAP-spectrum contained inconsistencies. A subsequent paper (Hasselmann et al., 1976, J. phys. Oceanogr.6, 200–208) attempted to regularise the situation. This paper shows that there were still inconsistencies in the prognostic equations giving overestimations of the first moment of the spectrum and consequently the significant wave height. The prognostic equations are reworked systematically and results presented. It is shown that variable σ_a, σ_b and γ must be used to achieve consistent results     

Field measurements of wave overtopping at the rubble mound breakwater of Rome–Ostia yacht harbour

This paper describes a new station for full-scale measurement of wave overtopping at the Rome yacht harbour rubble mound breakwater in Ostia (Italy) and the results of the successful first measurement campaign carried out during the winter season 2003–2004. The equipment and the research activities were supported by the EU project CLASH, focusing on scale effects for wave overtopping at coastal structures. The site is characterized by a very small tidal range, a long shallow foreshore and depth-limited breaking waves which interact with a shallow sloping porous rock structure. Overtopping water is collected by a steel tank installed on the crown slab behind the parapet wall. The measurement of water level variation inside the tank by means of two pressure transducers allows the calculation of individual overtopping volumes. Incident waves, sea levels and wind are also measured. During seven independent storms, more than 400 individual overtopping events were recorded and about 86 h of valid data are available. This extensive dataset is presented, discussed and then used for comparison with two commonly used overtopping prediction formulae based on small-scale model tests showing their tendency to underestimate the prototype results. A strong correlation between the hourly mean overtopping discharge and corresponding maximum volume is also presented. The paper generally confirms the validity of the approach used in Troch et al. (2004) [Troch, P., Geeraets, J., Van de Walle, B., De Rouck, J., Van Damme, L., Allsop, W., Franco, L., 2004. Full-scale wave overtopping measurements on the Zeebrugge rubble mound breakwater. Coastal Engineering 51, 609–628] for field measurement of wave overtopping.     

The relationship between the amplitudinal characteristics of the high-frequency spectral components of wind-generated waves and the wind velocity over the sea

The relationship between the RMS amplitudes of the wind wave spectral components and the wind speed has been studied at ten frequencies in the band of 0.65–23 Hz. To measure the parameters of the high-frequenci waves, a resistance elevation wave gauge was operated, which was deployed in the Black See on an oceanographic platform near Katsively. The correlation between the wave amplitudes and the wind velocity at high frequencies of 5–23 Hz, corresponding to gravitation-capillary ripples, was found to reach a value of 0.8. At lower frequencies of 0.65–4.3 Hz, corresponding to short gravity waves, it dropped to 0.5–0.7. The response of spectral components to the wind speed variations in the gravity-capillary range is higher than in the range of short gravity waves. The results obtained differ from Phillips' idea about a saturated range for the frequency form of the spectrum of high-frequency gravity waves, since a linear dependence of the spectral amplitudes on the wind speed is established at a wind of force 1–8.Translated by Mikhail M. Trufanov.     

Nonlinear heave radiation forces on two-dimensional single and twin hulls

A study of nonlinear heave radiation of two-dimensional single and double hulls has been carried out in the time domain. The problem is analyzed by means of a fully nonlinear mathematical model, referred to as the mixed Eulerian–Lagrangian (MEL) model, which is based on an integral relation formulation coupled with time-integration of the nonlinear free-surface boundary conditions. The integral equation solver is based on a cubic-spline boundary-element scheme in which both potential and velocity continuity conditions can be enforced through the intersection points. The body undergoes periodic forced heave oscillation. By implementing effective wave-absorbing beaches at the two ends of the rectangular numerical tank, long-term steady-state force-histories could be achieved consistently in all computations.Results in terms of radiation forces for rectangular and triangular single- and twin-hull geometries are presented and discussed. Linear hydrodynamic forces in terms of added-mass and damping are validated for the rectangular hull. The Fourier-analyzed results reveal the extent of nonlinear (higher-order) components in the force-signals over different parameters which include the amplitudes of oscillation, hull-spacing for the twin-hulls and water depth.     

Experimental research on the statistical characteristics of radar signal spikes at small grazing angles

The results of research into the characteristics of spikes in a radar signal scattered by the sea surface at small grazing angles and horizontal polarization of radiation are reported. Studies were carried out at wind speeds of 4.4–10.3 m s^–1. It is shown that the experimental distribution of the amplitudes of the radar signal spikes is described well by an exponential function. The distribution of the amplitudes of spikes, normalized to their average value for the measurement cycle, is of universal character. It does not depend on the observational conditions. The relationship between the average level of signal and the wind speed agrees with the results of computation on the model suggested.Translated by Mikhail M. Trufanov.     

Application of desingularized approach to water wave propagation over three-dimensional topography

A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data.     

A prediction technique for the transverse vortex-induced oscillations of tensioned risers

In this paper, a model for the prediction of the vortex-induced transverse oscillations of tensioned risers is proposed.The model, based on the peak amplitudes of the oscillations recorded for cylindrical bodies in a uniform current, has been extended to multimodal oscillations in a sheared flow condition through a modal priority technique. The difference between this model and other similar ones lies in the following features:

the hydrodynamic damping, which has been introduced in a more general form without ‘a priori’ approximations;

the modal priority, which is based on the local amplitudes of the active vibration modes, rather than on their frequencies.

Some comparisons with experimental and numerical results available in the literature are presented and discussed.     

1997–1998 El Niño off Peru: A numerical study

An eddy-resolving numerical simulation for the Peru–Chile system between 1993 and 2000 is analyzed, mainly for the 1997–1998 El Niño. Atmospheric and lateral oceanic forcings are realistic and contain a wide range of scales from days to interannual. The solution is validated against altimetric observations and the few in situ observations available. The simulated 1997–1998 El Niño closely resembles the real 1997–1998 El Niño in its time sequence of events. The two well-marked, sea-level peaks in May–June and November–December 1997 are reproduced with amplitudes close to those observed. Other sub-periods of the El Niño seem to be captured adequately. Simple dynamical analyses are performed to explain the 1997–1998 evolution of the upwelling in the model. The intensity of the upwelling appears to be determined by an interplay between alongshore, poleward advection (related to coastal trapped waves) and wind intensity, but also by the cross-shore geostrophic flow and distribution of the water masses on a scale of 1000 km or more (involving Rossby waves westward propagation and advection from equatorial currents). In particular, the delay of upwelling recovery until fall 1998 (i.e., well after the second El Niño peak) is partly due to the persistent advection of offshore stratified water toward the coast of Peru. Altimetry data suggest that these interpretations of the numerical solution also apply to the real ocean.     

A nonlinear model of parametric rolling stabilization by anti-roll tanks

The present paper describes a mathematical model in which the fluid motion inside a U-tank is nonlinearly coupled to the heave, roll and pitch motions of the ship. The main purpose of the investigation is centred on the control of roll motion in the case of parametric resonance in longitudinal waves. A transom stern small vessel, known to be quite prone to parametric amplification, is employed in the study. Four tank designs are employed in order to study the influence of tank mass, tank natural frequency and tank internal damping on the control of parametric rolling at different head seas conditions. Additionally, the influence of the vertical position of the tank is also investigated. The main results are presented in the form of limits of stability, with encounter frequency and wave amplitudes as parameters. Distinct dynamical characteristics are discussed and conclusions are drawn on the relevant parameters for the efficient control of the roll amplifications in head seas.     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

Nonlinear modeling of liquid sloshing in a moving rectangular tank

A nonlinear liquid sloshing inside a partially filled rectangular tank has been investigated. The fluid is assumed to be homogeneous, isotropic, viscous, Newtonian and exhibit only limited compressibility. The tank is forced to move harmonically along a vertical curve with rolling motion to simulate the actual tank excitation. The volume of fluid technique is used to track the free surface. The model solves the complete Navier–Stokes equations in primitive variables by use of the finite difference approximations. At each time step, a donor–acceptor method is used to transport the volume of fluid function and hence the locations of the free surface. In order to assess the accuracy of the method used, computations are verified through convergence tests and compared with the theoretical solutions and experimental results.     

An effective wave-trapping system

This is a theoretical study of a breakwater-seawall wave-trapping system. The breakwater, being flexible, porous and thin beam-like, is held fixed in the sea bed and idealized as one-dimensional beam of uniform flexural rigidity and uniform mass per unit length. The seawall, being vertical, rigid and impermeable, is located behind the breakwater by a distance of L. The velocity potentials of the wave motion are coupled with the equation of motion of the breakwater. Analytical solutions in closed forms are obtained for the reflected and transmitted velocity potentials together with the displacement of the breakwater. The free-surface elevation, hydrodynamic forces acting on both the breakwater and the seawall are determined. It is found that the values of L, at which the minimum reflected-wave amplitudes reach, are in the range of λ to λ for breakwaters with different rigidity and permeability. It is shown that, when the spacing L maintains values in the range of λ to λ, the resultant amplitudes in both regions can be reduced to a favorable amount for any wave and structural parameters. It is also shown that the hydrodynamic forces on the breakwater decrease as the structural flexibility and porosity increase. However, with increases of the structural porosity and flexibility, the seawall experiences an increase of the hydrodynamic forces. Various results are presented in this paper to illustrate the effects of the structural and perous parameters together with the spacing on the response and efficiency of the breakwater-seawall wave-trapping system.     

Experimental study of the transformation of bound long waves over a mild slope with ambient currents

The effect of currents on the variation of cross-shore bound long waves forced by bichromatic waves over a plane slope was investigated in the laboratory. In still water the growth rate of the shoaling bound long waves over the slope is proportional to h^– 5/2 (h is still-water depth). It was found that the opposing current makes the amplitudes of the bound long waves greater than those of still water for all cases. However, the amplitudes of bound long waves in a following current are reduced in the weakly modulated cases but are enhanced in the fully modulated case.     

High-sediment tolerance in the reef coral Turbinaria mesenterina from the inner Great Barrier Reef lagoon (Australia)

Sedimentation is an important stressor on coral reefs subjected to run-off, dredging and resuspension events. Reefs with a history of high-sediment loads tend to be dominated by a few tolerant coral species. A key question is whether such species live close to their tolerance thresholds or near their niche optima. Here, we analyse experimentally the sediment tolerance of a spatially dominant coral, Turbinaria mesenterina (Dendrophylliidae), at nearshore reefs in the central Great Barrier Reef lagoon. Testing was conducted in a 5-week tank experiment under manipulated sediment loading and flow conditions. Physiological stress was assessed based on the behaviour of three key response variables: skeletal growth rate, energy reserves (lipid content) and photosynthetic performance. Because sediment effects are likely to vary between flow regimes, sediment and flow responses were tested using a full factorial design. Sediment loads greater than 110 mg cm⁻² had no effect on any of the physiological variables, regardless of flow (0.7–24 cm s⁻¹). Turbinaria mesenterina is thus tolerant to sediment loads an order of magnitude higher than most severe sediment conditions in situ. Likely mechanisms for such tolerance are that: (1) colonies covered in sediment (60–120 μm) in low-flow were able to clear themselves rapidly (within 4–5 h); and (2) sediment provides a source of food. These results suggest that intensified sediment regimes on coastal reefs may shift coral communities towards dominance by a few well-adapted species.     

Complete two-dimensional analysis of sea-wave-induced fully non-linear sloshing fluid in a rigid floating tank

A time-independent finite-difference method and a fifth-order Runge–Kutta–Felhberg scheme were used to analyze the dynamic responses of sea-wave-induced fully non-linear sloshing fluid in a floating tank. The interaction effect between the fully non-linear sloshing fluid and the floating tank associated with coupled surge, heave and pitch motions of the tank are analyzed for the first time in the present pilot study. For the analysis of fluid motion in the tank, the coordinate system is moving (translating and rotating) with tank motion. The time-dependent water surface of the sloshing fluid is transformed to a horizontal plane and the flow field is mapped on to a rectangular region. The Euler equations as well as the fully non-linear kinematic free surface condition were used in the analysis of the sloshing fluid. The strip theory for linearized harmonic sea-wave loading was adopted to evaluate the regular encounter wave force. In addition, the dynamic coefficients used in the dynamic equations of tank motion were also derived based on strip theory and a harmonic motion of the tank. The characteristics of free and forced tank motions with and without the sloshing effect are studied. By the damping effect, the response of free oscillation will damp out and that of forced oscillation will approach a steady state. Without sea-wave action, the contribution of the sloshing load would enlarge the angular response of tank motion as well as the rise of free surface and the sloshing effect will delay the damping effect on angular displacement. On the contrary, under sea-wave action, the sloshing effect will decrease the dynamic response of tank motion and rise of free surface. The interaction, sloshing and coupling effects are found to be significant and should be considered in the analysis and design of floating tanks.     

Wave propagation in a fully nonlinear numerical wave tank: A desingularized method

The problem of wave propagation in a fully nonlinear numerical wave tank is studied using desingularized boundary integral equation method coupled with mixed Eulerian–Lagrangian formulation. The present method is employed to solve the potential flow boundary value problem at each time step. The fourth-order predictor–corrector Adams–Bashforth–Moulton scheme is used for the time-stepping integration of the free surface boundary conditions. A damping layer near the end-wall of wave tank is added to absorb the outgoing waves with as little wave reflection back into the wave tank as possible. The saw-tooth instability is overcome via a five-point Chebyshev smoothing scheme. The model is applied to several wave propagations including solitary, irregular and random incident waves.     

Mesoscale eddies off Peru in altimeter records: Identification algorithms and eddy spatio-temporal patterns

Relatively little is known about coherent vortices in the eastern South-Pacific along the Peruvian coast, even with regard to basic facts about their frequency of occurrence, longevity and structure. This study addresses these issues with nearly 15 years of relatively high-resolution satellite altimetry measurements.We first compare two distinct automated methods for eddy identification. The objective validation protocol shows that the rarely-used geometrical or “winding-angle method”, based on the curvature of the streamline functions, is more accurate than the commonly-used “Okubo–Weiss algorithm”, which defines a vortex as a simple connected region with values of Okubo–Weiss parameter weaker than a given threshold.We then investigate vortices off Peru using more than 20,000 mesoscale eddies identified by the winding-angle method. Coherent eddies, characterized by a high ratio of vorticity to deformation rate, are typically formed along the coast and propagate westward at 3–6 cm s⁻¹. The vortices have a mean radius of 80 km, increasing northward, and are most frequently observed off of Chimbote (9°S) and south of San Juan (15°S). The mean eddy lifetime is about 1 month, but if eddies survive at least 2 months, the probability for surviving an additional week (or month) is constant at 90% (or 67%). Anticyclonic eddies tend to propagate northwestward whereas cyclonic vortices migrate southwestward. In general, cyclones and anticyclones are similar, except for eddies surviving at least 6 months. In this case, after a similar 3–4 months of radius and amplitude growth, amplitudes (or sizes) decay particularly rapidly for anticyclonic (or cyclonic) eddies. In terms of intensity, cyclonic eddies show a rapid decay during the first 3 months before arriving at a quasi-constant value, whereas anticyclones exhibit steady decline. Finally, eddy temporal variations were examined at seasonal and interannual scales in the “coastal” region favorable to the formation of energetic mesoscale structures. On seasonal scales, eddy activity is maximal in fall and minimum in spring. At interannual scales, the eddy activity index was maximal during the strong El Niño of 1997–1998 but another strong maximum of eddy activity also occurred late in 2004. These temporal variations are probably associated with the intensification of the upwelling thermal front and with the passage of coastal-trapped waves which generate baroclinic instabilities. Further investigation of the mechanisms involved on the eddy genesis is needed.     

A Gibbs–Pitzer function for high-salinity seawater thermodynamics

A high-salinity Gibbs function for seawater is derived from Pitzer equations of the sea salt components, in conjunction with the 2003 Gibbs function of seawater for low salinities. Various properties, computed from both formulations by thermodynamic rules, are compared with each other, and with high-salinity measurements. The new Gibbs–Pitzer function presented in this paper is valid in the range 0–110 g kg⁻¹ in absolute salinity, −7 to +25 °C in temperature, and 0–100 MPa in applied pressure. The formulation is expressed in the International Temperature Scale 1990 (ITS-90), and is consistent with the International Standard for Fluid Water (IAPWS-95), and with the 2005/2006 equations of state of ice Ih.     

A finite element model of interaction between viscous free surface waves and submerged cylinders

This paper describes the simulation of the flow of a viscous incompressible Newtonian liquid with a free surface. The Navier–Stokes equations are formulated using a streamline upwind Petrov–Galerkin scheme, and solved on a Q-tree-based finite element mesh that adapts to the moving free surface of the liquid. Special attention is given to fitting the mesh correctly to the free surface and solid wall boundaries. Fully non-linear free surface boundary conditions are implemented. Test cases include sloshing free surface motions in a rectangular tank and progressive waves over submerged cylinders.     

Eigensensitivity analysis of moisture-related buckling of marine composite panels

In this paper, an approximate closed-form solution is presented to compute the moisture-related buckling of symmetric angle-ply laminates. The environment corresponds to a steady state condition, which provides a uniform moisture distribution for the laminate. The laminate consists of four layers [θ/−θ]_s constructed of low, moderate and high stiffness ratio materials. Comparative results using the Rayleigh–Ritz method provides a means of assessing the accuracy of the expression. For certain laminate architectures, several modes must be computed to ascertain the lowest buckling mode, and once identified, provides an excellent approximation for the mode computed using the Rayleigh–Ritz method.