Analytical Study on Wave Diffraction from a Vertical Circular Cylinder in Front of Orthogonal Vertical Walls

In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.     

The dimensions of sand ripples in full-scale oscillatory flows

New large-scale experiments have been carried out in two oscillatory flow tunnels to study ripple regime sand suspension and net sand transport processes in full-scale oscillatory flows. The paper focuses on ripple dimensions and the new data are combined with existing data to make a large dataset of ripple heights and lengths for flows with field-scale amplitudes and periods. A feature of the new experiments is a focus on the effect of flow irregularity. The combined dataset is analysed to examine the range of hydraulic conditions under which oscillatory flow ripples occur, to examine the effects of flow irregularity and ripple three-dimensionality on ripple dimensions and to test and improve existing methods for predicting ripple dimensions.The following are the main conclusions. (1) The highest velocities in a flow time-series play an important role in determining the type of bedform occurring in oscillatory flow. Bedform regime is well characterised by mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth peak velocities in the case of irregular flow. (2) For field-scale flows, sand size is the primary factor determining whether equilibrium ripples will be 2D or 3D. 2D ripples occur when the sand D₅₀ ≥ 0.30 mm and 3D ripples occur when D₅₀ ≤ 0.22 mm (except when the flow orbital diameter is low). (3) Ripple type (2D or 3D) is the same for regular and irregular flows and ripple dimensions produced by equivalent regular and irregular flows follow a similar functional dependence on mobility number, with mobility number based on maximum velocity in the case of regular flow and based on the mean of the highest one tenth velocities in the case of irregular flow. For much of the ripple regime, ripple dimensions have weak dependency on mobility number and ripple dimensions are similar for regular and irregular flows with the same flow orbital amplitude. However, differences in ripples produced by equivalent regular and irregular flows become significant at the high mobility end of the ripple regime. (4) Ripple dimensions predicted using the Wiberg and Harris formulae are in poor agreement with measured ripple dimensions from the large-scale experiments. Predictions based on the Mogridge et al. and the Nielsen formulae show better overall agreement with the data but also show systematic differences in cases of 3D ripples and ripples generated by irregular flows. (5) Based on the combined large-scale data, modifications to the Nielsen ripple dimension equations are proposed for the heights and lengths of 2D ripples. The same equations apply to regular and irregular flows, but with mobility number appropriately defined. 3D ripples are generally smaller than 2D ripples and estimates of 3D ripple height and length may be obtained by applying multipliers of 0.55 and 0.73 respectively to the 2D formulae. The proposed modified Nielsen formulae provide an improved fit to the large-scale data, accounting for flow irregularity and ripple three-dimensionality.     

Modelling linear wave transformation induced by dissipative structures—Random waves

The relevant theory is presented and numerical results are compared with the analytical solution for the interaction of non-breaking waves with an array of vertical porous circular cylinders on a horizontal bed. The extension to the cases of unidirectional and multidirectional waves is obtained by means of a transfer function. The influence of the mechanical properties of porous structures and wave irregularity on wave transformation is analysed. Results for unidirectional and multidirectional wave spectra are compared to those obtained for regular waves. The model presented reproduces well the analytical results and provides a tool for analysing several engineering problems.     

Observations of wave pump efficiency

Currently available data on wave pump efficiency is reviewed. The obtainable efficiency is an important consideration in the design of practical devices for the extraction of wave energy and the analysis of natural systems (e.g., coral flats and rip currents). We find that the peak efficiency is 0.5 for very steep (∼ 40–45°) ramps where the waves break over the top of the ramp. For flatter (< 30°) ramps, the breaking process is more gradual and the peak efficiency is less than 0.1. We have identified natural atoll lagoon systems where the flushing is wave driven and successfully modeled it as driven by a wave pump. The same is the case for rip currents. For both of these natural systems, the pump efficiency is around 0.035. In addition a numerical swash model is used to estimate wave pump efficiency and is seen to match the experimental results for natural systems or breaking wave scenario.     

Numerical prediction of MODUs drift during Hurricane Katrina

Severe hurricanes, such as Katrina, broke the mooring lines of a number of mobile offshore drilling units (MODU) deployed in the Gulf of Mexico and some of those MODUs went adrift. A drifting MODU may damage other critical elements of the offshore oil and gas infrastructure by colliding with floating or fixed production systems and transportation hubs, or by rupturing pipelines owing to their dragging anchors over the seabed. To avoid or mitigate the damage caused by a drifting MODU, it is desirable to understand the mechanics of the drift of a MODU under the impact of severe wind, wave and current and have the capability of predicting the trajectory of the drift. To explore the feasibility and accuracy of predicting the trajectory of a drifting MODU based on hindcast met-ocean conditions and limited knowledge of the condition of the drifting MODU, this study employed a simplified equation describing only the horizontal (surge, sway and yaw) motions of a MODU under the impact of steady wind, current and wave forces. The simplified hydrodynamic model neglects the first- and second-order oscillatory wave forces, unsteady wind forces (owing to wind gustiness), wave drift damping, and the effects of the body oscillation on the steady wind and current forces. It was assumed that the net effects of the oscillatory forces on the steady motion are insignificant. To verify the accuracy and feasibility of our simplified approach, the predicted drifting trajectories of two MODUs were compared with the corresponding measurements recorded by the global positioning system (GPS).     

2D Wave setup behind submerged breakwaters

In addition to reducing the incoming wave energy, submerged breakwaters also cause a setup of the sea level in the protected area, which is relevant to the whole shadow zone circulation, including alongshore currents and seaward flows through the gaps. This study examines such a leading hydraulic parameter under the simplified hypothesis of 2D motion and presents a prediction model that has been validated by a wide ensemble of experimental data. Starting from an approach originally proposed by Dalrymple and Dean [(1971). Piling-up behind low and submerged permeable breakwaters. Discussion note on Diskin et al. (1970). Journal of Waterways and Harbors Division WW2, 423–427], the model splits the rise of the mean water level into two contributions: one is due to the momentum flux release forced by wave breaking on the structure, and the other is associated with the mass transport process. For the first time, the case of random wave trains has been explicitly considered.     

The mid-depth circulation of the northwestern tropical Atlantic observed by floats

A comprehensive analysis of velocity data from subsurface floats in the northwestern tropical Atlantic at two depth layers is presented: one representing the Antarctic Intermediate Water (AAIW, pressure range 600–1050 dbar), the other the upper North Atlantic Deep Water (uNADW, pressure range 1200–2050 dbar). New data from three independent research programs are combined with previously available data to achieve blanket coverage in space for the AAIW layer, while coverage in the uNADW remains more intermittent. Results from the AAIW mainly confirm previous studies on the mean flow, namely the equatorial zonal and the boundary currents, but clarify details on pathways, mostly by virtue of the spatial data coverage that sets float observations apart from e.g. shipborne or mooring observations. Mean transports in each of five zonal equatorial current bands is found to be between 2.7 and 4.5 Sv. Pathways carrying AAIW northward beyond the North Brazil Undercurrent are clearly visible in the mean velocity field, in particular a northward transport of 3.7 Sv across 16°N between the Antilles islands and the Mid-Atlantic Ridge. New maps of Lagrangian eddy kinetic energy and integral time scales are presented to quantify mesoscale activity. For the uNADW, mean flow and mesoscale properties are discussed as data availability allows. Trajectories in the uNADW east of the Lesser Antilles reveal interactions between the Deep Western Boundary Current (DWBC) and the basin interior, which can explain recent hydrographic observations of changes in composition of DWBC water along its southward flow.     

Mesoscale surface circulation and variability of Southern Indian Ocean derived by combining satellite altimetry and drifter observations

High resoultion Eulerian mean velocity field has been derived by combining the satellite tracked surface drifter data with satellite altimetry and ocean surface winds. The drifter data used in this study includes Argos and surface drifter data from Global Drifter Program. Maps of Sea Level Anomaly(MSLA) weekly files with a resolution of(1/3)° in both Latitude and Longitude for the period 1993–2012 have been used. The Ekman current is computed using ocean surface mean wind fields from scatterometers onboard ERS 1/2,Quikscat and ASCAT. The derived mean velocity field exhibits the broad flow of Antarctic Circumpolar Current with speeds up to 0.6 m/s.Anomalous field is quite significant in the western part between 20° and 40°E and in the eastern part between 80°E and 100°E with velocity anomaly up to 0.3 m/s. The estimated mean flow pattern well agrees with the dynamic topography derived from in-situ observations. Also,the derived velocity field is consistent with the in-situ ADCP current measurements. Eddy kinetic energy illustrates an increasing trend during 1993–2008 and is in phase coherence with the Southern Annular Mode by three month lag. Periodic modulations are found in the eddy kinetic energy due the low frequency Antarctic Circumpolar Wave propagation.