Instability and evolution of nonlinearly interacting water waves

We consider the modulational instability of nonlinearly interacting two-dimensional waves in deep water, which are described by a pair of two-dimensional coupled nonlinear Schrodinger equations. We derive a nonlinear dispersion relation. The latter is numerically analyzed to obtain the regions and the associated growth rates of the modulational instability. Furthermore, we follow the long term evolution of the latter by means of computer simulations of the governing nonlinear equations and demonstrate the formation of localized coherent wave envelopes. Our results should be useful for understanding the formation and nonlinear propagation characteristics of large-amplitude freak waves in deep water.

Under-water scene investigation using ground penetrating radar (GPR) in the search for a sunken jet ski, Northern Ireland

A search for a submerged jet ski and the lost limb of its driver involved in a collision with a speedboat was made in a shallow lake in Northern Ireland. The location of both was crucial to establishing events at the time of the accident. Local intelligence suggested both objects were likely to be partially-buried by lacustrine silt. To avoid sediment churning, this required non-invasive, completely non-destructive assessment and mapping of the scene. A MALA RAMAC ground-penetrating radar system (GPR) mounted on floats for surveying from walkways and jetties or placed in a small rubber dinghy for offshore profiling was used. A grid was established and each line surveyed with 100, 200 and 400MHz antennae. In waters over 6m deep GPR data showed the form of the lake floor but excessive ringing occurred in the data. In waters less than 6m deep ringing diminished on both 100 and 200MHz data, the latter displaying the best trade-off between depth penetration and horizontal object resolution. 400MHz data failed to be of use in waters over 2m deep and at these depths showed only limited improvement of image quality compared to 200MHz data. Surface objects such as a wooden walkway caused interference on 200 and 400MHz data when antennae were oriented both normal and parallel to survey direction; this may be a function of the low attenuation of radar waves in freshwater, allowing excellent lateral and vertical radar wave penetration. On 200MHz data the damaged jet-ski was clearly imaged in a location that contradicted the speedboat driver's account of the accident.

A Description of the Stationary Wave Pattern of a Marine Craft in Shallow and Intermediate Water Depths

A stationary phase model is used to study supercritical waves generated by high speed ferries. Some general relationships in terms of wave angle, propagation direction, dispersion relationship and depth wavelength relationship are explored and discussed. In particular, it is shown that the wave pattern generated by high speed craft at supercritical speeds depends mainly on the relationship of water depth and ship speed and that the wave patterns are similar in terms of location of crests and troughs for a given depth Froude number. In addition it is found that the far field wave pattern can be described adequately using a single moving point source. The theoretical model compares well with towing tank measurements and full scale data over a range of parameters and hull shapes. The paper also demonstrates that the far field wave pattern at supercritical speeds should be non-dimensionalised by water depth and not hull length unlike it is usually done for subcritical speeds.

The hydrodynamics of small seabed mounted bottom hinged wave energy converters in shallow water:PhD thesis

This thesis investigates the hydrodynamics of a small, seabed mounted, bottom hinged, wave energy converter in shallow water. The Oscillating Wave Surge Converter is a pitching flap-type device which is located in 10-15m of water to take advantage of the amplification of horizontal water particle motion in shallow water. A conceptual model of the hydrodynamics of the device has been formulated and shows that, as the motion of the flap is highly constrained, the magnitude of the force applied to the flap by the wave is strongly linked to the power absorption.

An extensive set of experiments has been carried out in the wave tank at Queen’s University at both 40th and 20th scales. The experiments have included testing in realistic sea states to estimate device performance as well as fundamental tests using small amplitude monochromatic waves to determine the force applied to the flap by the waves. The results from the physical modelling programme have been used in conjunction with numerical data from WAMIT to validate the conceptual model.

The work finds that tuning the OWSC to the incident wave periods is problematic and only results in a marginal increase in power capture. It is also found that the addition of larger diameter rounds to the edges of the flap reduces viscous losses and has a greater effect on the performance of the device than tuning. As wave force is the primary driver of device performance it is shown that the flap should fill the water column and should pierce the water surface to reduce losses due to wave overtopping.

With the water depth fixed at approximately 10m it is shown that the width of the flap has the greatest impact on the magnitude of wave force, and thus device performance. An 18m wide flap is shown to have twice the absorption efficiency of a 6m wide flap and captures 6 times the power. However, the increase in power capture with device width is not limitless and a 24m wide flap is found to be affected by two-dimensional hydrodynamics which reduces its performance per unit width, especially in sea states with short periods. It is also shown that as the width increases the performance gains associated with the addition of the end effectors reduces. Furthermore, it is shown that as the flap width increases the natural pitching period of the flap increases, thus detuning the flap further from the wave periods of interest for wave energy conversion.

The effect of waves approaching the flap from an oblique angle is also investigated and the power capture is found to decrease with the cosine squared of the encounter angle. The characteristic of the damping applied by the power take off system is found to have a significant effect on the power capture of the device, with constant damping producing between 20% and 30% less power than quadratic damping. Furthermore, it is found that applying a higher level of damping, or a damping bias, to the flap as it pitches towards the beach increases the power capture by 10%.

A further set of experiments has been undertaken in a case study used to predict the power capture of a prototype of the OWSC concept. The device, called the Oyster Demonstrator, has been developed by Aquamarine Power Ltd. and is to be installed at the European Marine Energy Centre, Scotland, in 2009.

The work concludes that OWSC is a viable wave energy converter and absorption efficiencies of up 75% have been measured. It is found that to maximise power absorption the flap should be approximately 20m wide with large diameter rounded edges, having its pivot close to the seabed and its top edge piercing the water surface.

The influence of water motion on the growth rate of the kelp Laminaria hyperborea

The kelp Laminaria hyperborea is a dominant component of the subtidal nearshore ecosystem and is subjected to a heterogeneous wave and current climate. Water motion is known to influence physiological processes in macroalgae such as photosynthesis and nutrient uptake attributed to mass-transfer limitation. The study attempts to establish the effect of water motion on the growth rates of blades and elongation rates of the stipes of L. hyperborea at adjacent wave-exposed and wave-sheltered locations over a 12month period from field observations. The observations were supported by detailed physical and chemical measurements (light, temperature, seawater nutrient concentrations and hydrodynamics) and of tissue carbon and nitrogen concentrations together with δ¹³carbon. Despite a 30% difference in the root mean square of the velocity (Vel_rms) between the two survey locations, there was no evidence to suggest that water motion had any direct influence on the growth rates of either the blades or elongation of stipes of L. hyperborea. No significant differences were observed between either environmental or plant physiological variables between the sheltered and exposed locations. Using an integral velocity parameter (Vel_rms) the present study also highlighted the importance of the tidally induced current component of water flow in the subtidal zone. 

Time-lapse monitoring of climate effects on earthworks using surface waves

The UK’s transportation network is supported by critical geotechnical assets (cuttings/embankments/dams) that require sustainable, cost-effective management, while maintaining an appropriate service level to meet social, economic, and environmental needs. Recent effects of extreme weather on these geotechnical assets have highlighted their vulnerability to climate variations. We have assessed the potential of surface wave data to portray the climate-related variations in mechanical properties of a clay-filled railway embankment. Seismic data were acquired bimonthly from July 2013 to November 2014 along the crest of a heritage railway embankment in southwest England. For each acquisition, the collected data were first processed to obtain a set of Rayleigh-wave dispersion and attenuation curves, referenced to the same spatial locations. These data were then analyzed to identify a coherent trend in their spatial and temporal variability. The relevance of the observed temporal variations was also verified with respect to the experimental data uncertainties. Finally, the surface wave dispersion data sets were inverted to reconstruct a time-lapse model of S-wave velocity for the embankment structure, using a least-squares laterally constrained inversion scheme. A key point of the inversion process was constituted by the estimation of a suitable initial model and the selection of adequate levels of spatial regularization. The initial model and the strength of spatial smoothing were then kept constant throughout the processing of all available data sets to ensure homogeneity of the procedure and comparability among the obtained VS sections. A continuous and coherent temporal pattern of surface wave data, and consequently of the reconstructed VS models, was identified. This pattern is related to the seasonal distribution of precipitation and soil water content measured on site.