The water motions in a moonpool

Moonpools are vertical wells in a floating body, frequently found in drilling ships—to give passage to the drill pipe—and in diving support vessels—to launch diving bells and equipment through it. Observations showed that inside a moonpool considerable relative motions may occur, depending on the shape and depth of the moonpool and on the frequency range of the waves to which the ship is exposed.Recently, a research program has been carried out at the Netherlands Ship Model Basin in which the hydrodynamics with respect to a moonpool were investigated. A mathematical model describing the relative water motions inside a moonpool was developed, while also model tests were carried out to obtain empiric results with respect to the damping mechanisms and motion behaviour.     

On two-dimensional moonpool resonance for twin bodies in a two-layer fluid

This paper studies the moonpool resonance of two heaving rectangular bodies in a two-layer fluid. A mathematical model is proposed based on an eigenfunction matching approach. The motion of the two-dimensional bodies is assumed to be vertical and harmonic. Heave added mass and damping coefficients are computed to examine the hydrodynamic behavior of the twin bodies. The free surface and internal wave elevations are obtained near the resonant frequencies. The presented results and analyses reveal that there exist both Helmholtz and higher-order resonances in the two-layer fluid system, which is similar to the single-layer fluid case. It is also found that the resonances are closely associated with the free surface elevation inside moonpool gap, not the wave elevation at the interfacial surface. In addition, parametric studies have been performed to identify the dependencies of hydrodynamic behavior on geometry and density stratification.     

Coupling Response of Heave and Moonpool Water Motion of A Truss Spar Platform in Random Waves

This paper presents the heave responses and the moonpool water motions of a truss Spar platform with semi-closed moonpool in random waves. A 2-DOF(degree of freedom) coupling dynamical equations of the platform heave and vertical motions of the moonpool water are derived. The linear wave theory is used to simulate the random waves. The response statistical values and the power spectrums are calculated to analyze the mutual influences between the platform heave and the moonpool water motions for different opening ratios of the moonpool. The effect of coupling parameters on the platform heave and the moonpool water motions are analyzed. The results show that motions of the moonpool water significantly affected the platform heave when the characteristic wave period is far away from the natural period of the platform heave, and different moonpool opening ratios lead to different heave amplitudes of the platform. In the actual design, an optimized moonpool opening ratio can be designed to reduce heave motions of the platform.     

Magnitude and cross-shore distribution of bed return flow measured on natural beaches

Field measurements of cross-shore currents 0.25 m from the bed were made on two natural beaches under a range of incident wave conditions. The results indicated the presence of a relatively strong, offshore-directed mean current, both within and seaward of the surf zone. Typical velocities within the surf zone were of the order of 0.2–0.3 m/s. This bed return flow, or “undertow”, represents a mass conservation response, returning water seaward that was initially transported onshore in the upper water column, primarily above the trough of the incident waves. The measurements demonstrated that the bed return flow velocity increases with the incident wave height. In addition, the crossshore distribution of the bed return flow is characterised by a mid-surf zone maximum, which exhibits a strong decrease in velocity towards the shoreline and a more gradual decay in the offshore direction. Several bed return flow models based on mass continuity were formulated to predict the cross-shore distribution of the bed return flow under an irregular wave field and were compared with the field data. Best agreement was obtained using shallow water linear wave theory, after including the mass transport associated with unbroken waves. The contribution of the unbroken waves enables net offshore-directed bottom currents to persist outside the region of breaking waves, providing a mechanism, other than rip currents, to transport sediment offshore beyond the surf zone.     

Patterns of summer vertical and horizontal currents in coastal waters of the northern Gulf of Aqaba, Red Sea

This study was focused on analysis of the horizontal and vertical current components with correspondence to tide variation, heat flux, seiches and relative backscatter intensity in coastal waters of the northern Gulf of Aqaba during the summers of 2001–2004. Spectrum analysis has shown eight distinguishable peaks of the tide measurements. In addition to semidiurnal and diurnal barotropic tides, signal periods of 8.13, 5.89–6.32 and 4.06 h were related to shallow water compound and overtides of the principal solar and lunar constituent and to seiches (second and third mode) generated in the Red Sea, whereas seiches of the first mode might enhance the semidiurnal tide signal. The shortest periods of 1.02–1.05, 0.50 and 0.36 h were related to seiches (first, second and third mode, respectively) generated in the Gulf of Aqaba. The spectrum analysis and cross-correlation tests of the horizontal and vertical current components and relative backscatter intensity suggested that the vertical motion at the diurnal period was either due to migration of zooplankton or to water convection. Both of which were of the same order as vertical motion induced by horizontal motions of water particles projected parallel on the bottom gradient line. On the other hand, semidiurnal and diurnal periods detected in the vertical currents were caused by the strong signal in the cross-shore current component, first mode seiches generated from the Red Sea and tide. This could be considered as an indicator of the dominant force influencing the currents, such as winds, thermocline depth, seiches and tidal forcing. A permanent convection during summer is likely to occur in the shallow coastal waters due to relatively high inclined bottom, high evaporation and blowing of dry air, as well as the observed dominance of the downward vertical currents in coastal waters.     

The motion of a deep-sea remotely operated vehicle system: Part 1: Motion observations

Rapid and high-resolution motion and tension measurements were made of a caged deep-sea remotely operated vehicle (ROV) system. Simultaneous measurements were made of all six components of motion at the cage and ship A-frame and of the tension in the tether at the ship. Data were collected for cage depths of 0–1765 m. The most significant forcing was in the wave-frequency band (0.1–0.25 Hz) and accounted for over 90% of the variance of vertical acceleration. The vertical acceleration of the cage lagged the acceleration of the A-frame by up to 1.9 s and its variance was larger by up to a factor 2.2. For moderate displacements of the A-frame (≤2 m), the system is only weakly non-linear because the harmonics (3rd and 5th) of the vertical acceleration of the cage account for less than 2% of the total variance. The system is essentially one-dimensional because only the vertical motion of the cage and the vertical motion of the A-frame were coherent, while horizontal motions of the cage were weak and incoherent with any component of motion of the A-frame. The natural frequency of the system is 0.22 Hz at 1730 m, and we estimate that it is within the waveband for depths between 1450 m and the full operating depth of 5000 m.Large vertical excursions of the A-frame produce momentary slack in the tether near the cage. Retensioning results in snap loads with vertical accelerations of 0.5 gravity. Large rates of change of tension and vertical acceleration first occur at the cage during its downward motion and propagate to the surface with the characteristic speed (3870 m s⁻¹) of tensile waves for the tether. Six echoes are clearly detectable at both ends of the tether, and their pattern is extremely repeatable in different snap loads. Due to misalignment of the tether termination with the centres of mass and buoyancy, the cage pitches by up 14° during a snap. The resulting small radius of curvature poses the greatest stress on the tether.     

Numerical study of the motions and drift force of a floating OWC device

The motion and the drift force of a floating OWC (oscillating water column) wave energy device in regular waves are studied taking account of the oscillating surface-pressure due to the pressure drop across the duct of the air chamber. The potential problem inside the chamber is formulated by making use of the Green integral equation associated with the Rankine-type Green function while the outer problem with the Kelvin-type Green function. The added mass, wave damping and excitation coefficients as well as the motion and drift force of the OWC device are calculated for various values of parameter related to the pressure drop.     

The mixing and spreading phases of MEDOC. I

The processes which produce bottom water in the Mediterranean are studied. Observations show three phases. The first, called ‘preconditioning’, is not studied. The second ‘violent mixing’ phase occurs when the cold Mistral begins. Cooling at the surface leads to intense vertical mixing in a narrow chimney-like region. When the wind stops, the ‘sinking and spreading’ phase begins. Interleaving of water masses occurs; horizontal eddying on scales of 15 km is observed; and 600 m columns of water can be lifted up to 500 m.A two-dimensional model is used to explain the mixing phase. Non-penetrative vertical convection explains the observations well. Advection of water from outside the column is small, and slows down the descent of the outer parts of the column as observed. The column does not break up even when it reaches the bottom, or if the strong winds cease.The most efficient mechanism for the spreading phase is baroclinic instability. In conditions of vertical overturning there is a large amount of potential energy available to drive the instability. For an eddy viscosity of 50 m² s⁻¹, after 10 days sinking the growth time is 3–4 days and the eddies are mainly concentrated at the surface with a major axis length of about 15 km. These tend to stabilize the top few hundred meters of the column. Later, finite amplitude effects will produce slower perturbations in the rest of the column.     

Wave-induced motions of an air cushion structure in shallow water

Model tests were conducted on two 1:100 scaled models of a typical concrete gravity substructure at the University of Western Australia. The two models had dimensions 0.5 m length×0.5 m width with the first model being a sealed closed bottom box of height 0.1 m and the second model being an open bottom box with skirt length of 0.1 m. The mass of the air cushion model was changed to accommodate various water plug heights within the skirt chamber. Each model was floated at a constant draft of 0.1 m and tested in water depths ranging between 0.03 m (shallow) and 0.8 m (deep). The environment comprised regular waves with periods ranging between 0.6 and 3.5 s and amplitude of 0.08–0.02 m. To quantify the dynamic response the heave and pitch motions of each model were measured.A simplified theoretical solution based on long wavelength, linear wave assumptions was developed and applied to the geometries in consideration. Improvements to the theory are sought using the forcing function from a boundary element code, as well as utilizing added mass coefficients from free decay experiments. Results show that experimental trends compare reasonably well with analytical solution in particular for periods longer than the natural period. The results show that introducing air cushion support into a CGS increases the pitch response, while having little effect of the heave motion.     

A sulfur budget for the Black Sea anoxic zone

A budget for the sulfur cycle in the Black Sea is proposed which incorporates specific biogeochemical process rates. The average sulfide production in the water column is estimated to be 30–50 Tg yr⁻¹, occurring essentially in the layer between 500 and 2000 m. About 3.2–5.2 Tg sulfide yr⁻¹ form during sulfate reduction in surface sediments of the anoxic zone. Total sulfur burial in anoxic sediments of 1 Tg yr⁻¹ consists of 10–70% (ca. 40–50% is the average) water column formed (syngenetic) component, the rest being diagenetic pyrite. As a maximum, between 3 and 5 Tg yr⁻¹ contribute sulfide to the bottom water or diffuse downward in the sediment. About 20–50 Tg yr⁻¹ sulfide is oxidized mostly at the chemocline and about 10–20% of this amount (4.4–9.2 Tg yr⁻¹) below the chemocline by the oxygen of the Lower Bosphorus Current. A model simulating the vertical distribution of sulfide in the Black Sea water column shows net consumption in the upper layers down to ca. 500 m, essentially due to oxidation at the chemocline, and net production down to the bottom. On the basis of the calculated budget anoxic conditions in the Black Sea are sustained by the balance between sulfide production in the anoxic water column and oxidation at the chemocline. On average the residence time of sulfide in the anoxic zone is about 90–150 yr, comparable to the water exchange time between oxic and anoxic zones. Hydrophysical control on the sulfur cycle appears to be the main factor regulating the extent of anoxic conditions in the Black Sea water column, rather than rates of biogeochemical processes.     

Theoretical and experimental study on dynamic behavior of a damaged ship in waves

Most of the large scaled casualties are caused by loss of structural strength and stability due to the progressive flooding and the effect of waves and wind. To prevent foundering and structural failure, it is necessary to predict the motion of the damaged ship in waves.This paper describes the motion of damaged ship in waves resulting from a theoretical and experimental study. A time domain theoretical model, which can be applied to any type of ship or arrangement, for the prediction of damaged ship motion and accidental flooding has been developed considering the effects of flooding of compartments. To evaluate the accuracy of the model, model tests are carried out in ship motion basin for three different damaged conditions: engine room bottom damage, side shell damage and bow visor damage of Ro–Ro ship in regular and irregular waves with different wave heights and directions.     

Efficient primary energy conversion in irregular waves

This paper studies reactive control of wave-energy devices in irregular waves. Estimates of future velocity of the primary energy converter are based on a time history of past velocity measurements, and prediction of incident waves is not attempted. Time–domain computations for a single-degree-of-freedom oscillating water column in irregular waves reveal that control is not optimal; but would enhance efficiency at low peak frequencies where energy-rich swells predominate, and allow appreciably smaller devices to fulfill a given power requirement.     

A modified Euler–Lagrange transformation for particle orbits in nonlinear progressive waves

This paper presents a modified Euler–Lagrange transformation method to obtain the third-order trajectory solution in a Lagrangian form for the water particles in nonlinear water waves. We impose the assumption that the Lagrangian wave frequency is a function of wave steepness and an arbitrary vertical position for each water particle. Expanding the unknown function in a small perturbation parameter and using a successive expansion in a Taylor series for the water particle path and the period of a particle motion, the third-order asymptotic expressions for the Lagrangian particle trajectories, the mass transport velocity and the period of particle motion can be derived directly in Lagrangian form. The wave frequency and mean level of the particle motion in Lagrangian form differ from those of the Eulerian. Finally, the third-order asymptotic solution obtained is uniformly valid in contrast with early works containing resonant terms presented by Wiegel [1964. Oceanographical Engineering. Prentice-Hall, New Jersey, pp. 37–40] (Eqs. (B.1) and (B.1), (B.2) in Appendix B) or Chen et al.[2006. Theoretical analysis of surface waves shoaling and breaking on a sloping bottom. Part 2 nonlinear waves. Wave motion, 43, 356–369] based on a straightforward expansion for two-dimensional progressive waves.     

Some features of jump in water temperature in aSargassum forest

To clarify the influence of aSargassum forest on water temperature distributions observations were made inside and outside aSargassum forest off the Nagata Shore on the northern Saiki Bay open to the Bungo Channel on the Pacific side of Kyushu, Japan. About sixty thermistor probes were deployed at 0.5 m depth intervals from the bottom to the sea surface at seven stations spaced at 50–80 m distances along two transects: one inside the forest and the other outside. Water temperature was measured at five minutes intervals from 6 to 9 August 1987 with thermistor probes. The spatial standing crop distribution of theSargassum forest along the transects was investigated. A water temperature jump of about 2°C, recorded during the observation, is probably caused by an intrusion of a warm water mass from the central Bungo Channel to Saiki Bay. The water temperature jump under theSargassum forest on the rough bottom with stones occurred one to two hours behind that outside the forest (sandy bed) although the distance between the transects inside and outside the forest was only 50–80 m. It is suggested that theSargassum forest and the rough bottom would prevent intruding warm water from smoothly replacing cold water due to resistance of theSargassum species and the bottom to a current.     

Experimental study of turbulent oscillatory boundary layers in an oscillating water tunnel

A high-quality experimental study including a large number of tests which correspond to full-scale coastal boundary layer flows is conducted using an oscillating water tunnel for flow generations and a Particle Image Velocimetry system for velocity measurements. Tests are performed for sinusoidal, Stokes and forward-leaning waves over three fixed bottom roughness configurations, i.e. smooth, “sandpaper” and ceramic-marble bottoms. The experimental results suggest that the logarithmic profile can accurately represent the boundary layer flows in the very near-bottom region, so the log-profile fitting analysis can give highly accurate determinations of the theoretical bottom location and the bottom roughness. The first-harmonic velocities of both sinusoidal and nonlinear waves, as well as the second-harmonic velocities of nonlinear waves, exhibit similar patterns of vertical variation. Two dimensionless characteristic boundary layer thicknesses, the elevation of 1% velocity deficit and the elevation of maximum amplitude, are found to have power-law dependencies on the relative roughness for rough bottom tests. A weak boundary layer streaming embedded in nonlinear waves and a small but meaningful third-harmonic velocity embedded in sinusoidal waves are observed. They can be only explained by the effect of a time-varying turbulent eddy viscosity. The measured period-averaged vertical velocities suggest the presence of Prandtl's secondary flows of the second kind in the test channel. Among the three methods to infer bottom shear stress from velocity measurements, the Reynolds stress method underestimates shear stress due to missed turbulent eddies, and the momentum integral method also significantly underestimates bottom shear stress for rough bottom tests due to secondary flows, so only the log-profile fitting method is considered to yield the correct estimate. The obtained bottom shear stresses are analyzed to give the maximum and the first three harmonics, and the results are used to validate some existing theoretical models.     

Winter dynamics on the northern Portuguese shelf. Part 2: bottom boundary layers and sediment dispersal

The northern Portuguese shelf, between 41°N and 42°N, is characterised by the presence of a mid-shelf mud deposit, the Douro Mud Patch (DMP). Observations conducted between July 1996 and June 1999 under the framework of project OMEX II–II, are used to examine the impact of the dynamic processes in the lower water column, particularly on the DMP. The typical wave conditions observed during the winter maintain a highly energetic environment, capable of promoting the erosion of fine sediments at mid-shelf depths. However, the bottom nepheloid layers generated beneath these waves only extend a few meters above the bottom and are contained within rocky outcrops with similar heights that fringe the outer shelf. Each year there are about ten storms, mostly associated with southerly winds that create downwelling conditions over the shelf. The waves associated with these storms produce shear velocities over 3 cm/s at mid-shelf and bottom nepheloid layers which extend a few tens of meters above the bottom and spread offshore, over the outer shelf and upper slope. A rough estimate suggests that these events account for an offshore export of about 20×10⁶ kg of fine sediments each year (equivalent to 1–2% of sediments trapped at DMP).     

Investigation of the Energy Balance in the Water–Air Boundary Layer under the Conditions of Developing Wind Waves

We present the results of the analysis of the energy balance in a wind–water system under the conditions of developing waves. Our investigation is based on the use of the experimental data obtained in a water channel and taken from the literature. We propose an expression for the energy balance between the air flow and wavy water surface based on the data of simultaneous measurements of the vertical wind profiles and drift currents and the parameters of waves for various fetches and indifferent density stratification.     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

Wave reflection and transmission by curtainwall–pile breakwaters using circular piles

This paper presents a mathematical model which computes the hydrodynamic characteristics of a curtainwall–pile breakwater (CPB) using circular piles, by modifying the model developed for rectangular piles by Suh et al. [2006. Hydrodynamic characteristics of pile-supported vertical wall breakwaters. Journal of Waterway, Port, Coastal and Ocean Engineering 132(2), 83–96]. To examine the validity of the model, laboratory experiments have been conducted for CPB with various values of draft of curtain wall, spacing between piles, and wave height and period. Comparisons between measurement and prediction show that the mathematical model adequately reproduces most of the important features of the experimental results. The mathematical model based on linear wave theory tends to over-predict the reflection coefficient as the wave height increases. As the draft of the curtain wall increases and the porosity between piles decreases, the reflection and transmission coefficient increases and decreases, respectively, as expected. As the relative water depth increases, however, the effect of porosity disappears because the wave motion is minimal in the lower part of a water column for short waves.     

Wave power extraction from an oscillating water column along a straight coast

In order to study the effects of coastline on wave power absorption, we describe here a linearized theory of an oscillating water column (OWC) installed on a straight coast. The sea depth is assumed to be constant and the coast is a vertical cliff. The column is a vertical circular cylinder half embedded in the cliff and open on the seaside. Forced by incident waves from any direction, the water surface inside pushes the dry air above through a Wells turbine system to generate power. Carrying out the linearized theories of radiation and diffraction analytically, we calculate the coefficients of apparent mass and radiation damping, and the chamber pressure. Optimum absorption efficiency is examined under the constraint of constant chamber volume. Results are compared with a parallel study of an OWC installed either offshore or at the tip of a thin breakwater.