A novel technique in analyzing non-linear wave-wave interaction

During wave growth non-linear wave–wave interactions cause transfer of some wave energy from lower to higher wave periods as the spectrum grows. Wavelet bicoherence, which is a new technique in the analysis of wind–wave and wave–wave interactions, is used to analyze non-linear wave–wave interactions. A selected record of wind wave that contains the maximum wave height observed during 6 h of wave generation is divided into five segments and wavelet bicoherence is computed for the whole record, and for all divided segments. The study shows that the non-linear wave–wave interaction occurs at different bicoherence levels and these levels are different from one segment to another due to the non-stationarity feature of the examined data set.     

Experimental study on mechanism of sea-dike failure due to wave overtopping

This work, which was largely a fruit of China's national marine hazard mitigation service, explicitly reveals the major mechanism of sea-dike failure during wave overtopping. A large group of wave-flume experiments were conducted for sea dikes with varying geometric characteristics and pavement types. The erosion and slide of the landward slope due to the combined effect of normal hit and great shear from overtopping flows was identified the major trigger of the destabilization of sea dikes. Once the intermittent hydrodynamic load and swash caused any deformation (bump or dent) of the pavement layer, pavement fractions (slabs or rubble) on the slope started to be initiated and removed by the water. The erosion of the landward slope was then gradually aggravated followed by entire failure within a couple of minutes. Hence, the competent velocity would be helpful evaluate the failure risk if as well accounted in standards or criteria. However, the dike top was measured experiencing the largest hydrodynamic pressure with a certain cap while the force on the wall increased rapidly as the overtopping intensity approached the dike-failure threshold. The faster increase of the force on the wall than on the landward slope yielded the sequencing of loads reaching hypothetic limits before failure as: dike top – top-mounted wall – landward slope. Therefore, beside the slide failure, the fatigue damage due to the instantaneous hydrodynamic impact might be another mechanism of the dike failure, which did not appear in the experiment but should be kept in mind. Instead of the widely adopted tolerable overtopping rate, a 0.117–0.424 m³/(m s) range of overtopping discharge and a 10 m/s overtopping velocity for the failure risk of typical sea dikes along China's coastlines were suggested, which enables the possible failure risk prediction through empirical calculations. The failure overtopping rate was identified strongly dependent on the pavement material, the landward slope and the dike-mounted wall but showed little variation with the width of the dike top. The flat concrete pavement and gentle landward slopes are suggested for the dike design and construction. For given configurations and hydrodynamic conditions in the experiment, the dike without the wall experienced less overtopping volume than those with the 1-m top-mounted wall. Meanwhile, the remove of the wall increased the failure overtopping rate, which means a certain increase of the failure criterion. Thus, care must be taken to conclude that the dike-mounted wall seems not an entirely appropriate reinforcement for the stability and safety of coastal protections. This should be further checked and discussed by researchers and engineers in the future.     

An energy-controlling boundary condition for partial wave reflections in the mild slope equation

An energy-controlling technique to actively manage the reflective property of waves from solid boundary is presented. As linear waves propagate through an energy-controlling area, a reduction in wave heights occurs due to energy dissipation, which can be placed under direct control through the imaginary part of the wavenumber and phase velocity. Based on this relationship, the present study investigates a new method to control reflected waves with desired heights in the mild slope equation model. The method is validated through numerical tests for various reflection coefficients and the results confirm the promising use of energy-controlling boundary condition for partial wave reflections.     

Experimental and numerical investigations on the intact and damage survivability of a floating–moored oscillating water column device

This paper investigates the intact and damage survivability of a floating–moored Oscillating Water Column (OWC) device using physical model experiments and Computational Fluid Dynamics (CFD) simulations. Different extreme wave conditions have been tested using irregular and regular wave conditions. The device was moored to the tank floor via four vertical taut lines and the effect of the mooring line pre–tension on the device response was studied. It was found that the instantaneous position of the floating device was a key factor in the survivability analysis such that a certain irregular wave train that might not include the largest wave could induce the maximum response. Reducing the pre–tension minimized the maximum surge, but significantly increased the maximum tension due to mooring slack events causing snatch loads. A design regular wave with a period equal to the peak period and a height of 1.9–2.0 times the significant wave height could reasonably predict the same maximum line tension as the irregular sea state, but a smaller wave height was required to achieve the maximum surge. A single failure in the mooring system increased the maximum tension by 1.55 times the intact tension. For a damaged mooring system, using the same design regular wave condition derived from the survivability analysis with an intact mooring system could result in overestimating the maximum tension by more than 20% in comparison to the tension from the irregular sea state, but a smaller regular wave height or a different regular wave condition representing another sea state could lead to the same maximum tension. This highlighted the importance of investigating survival conditions with a damaged mooring system instead of simply using the same conditions derived for the intact mooring system.     

Large-scale experiments on beach profile evolution and surf and swash zone sediment transport induced by long waves,wave groups and random waves

New large-scale laboratory data are presented on the influence of long waves, bichromatic wave groups and random waves on sediment transport in the surf and swash zones. Physical model testing was performed in the large-scale CIEM wave flume at UPC, Barcelona, as part of the SUSCO (swash zone response under grouping storm conditions) experiment in the Hydralab III program (Vicinanza et al., 2010). Fourteen different wave conditions were used, encompassing monochromatic waves, bichromatic wave groups and random waves. The experiments were designed specifically to compare variations in beach profile evolution between monochromatic waves and unsteady waves with the same mean energy flux. Each test commenced with approximately the same initial profile. The monochromatic conditions were perturbed with free long waves, and then subsequently substituted with bichromatic wave groups with different bandwidth and with random waves with varying groupiness. Beach profile measurements were made at half-hourly and hourly intervals, from which net cross-shore transport rates were calculated for the different wave conditions. Pairs of experiments with slightly different bandwidth or wave grouping show very similar net cross-shore sediment transport patterns, giving high confidence to the data set. Consistent with recent small-scale experiments, the data clearly show that in comparison to monochromatic conditions the bichromatic wave groups reduce onshore transport during accretive conditions and increase offshore transport during erosive conditions. The random waves have a similar influence to the bichromatic wave groups, promoting offshore transport, in comparison to the monochromatic conditions. The data also indicate that the free long waves promote onshore transport, but the conclusions are more tentative as a result of a few errors in the test schedule and modifications to the setup which reduced testing time. The experiments suggest that the inclusion of long wave and wave group sediment transport is important for improved near-shore morphological modeling of cross-shore beach profile evolution, and they provide a very comprehensive and controlled series of tests for evaluating numerical models. It is suggested that the large change in the beach response between monochromatic conditions and wave group conditions is a result of the increased significant and maximum wave heights in the wave groups, as much as the presence of the forced and free long waves induced by the groupiness. The equilibrium state model concept can provide a heuristic explanation of the influence of the wave groups on the bulk beach profile response if their effective relative fall velocity is larger than that of monochromatic waves with the same incident energy flux.     

Measured and modeled wave overtopping on a natural beach

The rate of wave overtopping of a barrier beach is measured and modeled. Unique rate of wave overtopping field data are obtained from the measure of the Carmel River, California, lagoon filling during a time when the lagoon is closed-off with no river inflow. Volume changes are based on measured lagoon height changes applied to a measured hypsometric curve. Wave heights and periods are obtained from directional wave spectra data in 15 m fronting the beach. Beach morphology was measured by GPS walking surveys. Three empirical overtopping models by Van der Meer and Janssen (1995), Hedges and Reis (1998) and Pullen et al. (2007) with differing parameterizations on wave height, period and beach slope and calibrated using extensive laboratory data obtained over plane, impermeable beaches are applied in a quasi-2D manner and compared with the field observations. Three overtopping events are considered when morphology data were available less than 2 weeks prior to the event. The models are tuned to fit the data using a reduction factor to account for beach permeability, berm characteristics, non-normal wave incidence and surface roughness influence. In addition, the run-up model by Stockdon et al. (2006) based on field data is examined and found to underestimate run-up as the calculated values were too small to predict any of the observed overtopping. The three overtopping models performed similarly well with values of 0.72–0.87 for the two narrow-banded wave cases, with an average reduction factor of 0.78. The European model (Pullen et. al., 2007) performed best overall and in particular for the case of the broad-banded, double peaked wave spectrum.     

TOPEX Constrained Solution of Mean Sea Surface by Joint Processing of TOPEX,ERS-1 and GEOSAT Altimetric Measurements

We present an improved crossover adjustment procedure to determine mean sea surface height using TOPEX, 35-day repeat phase ERS-1, Geosat, and 168-day repeat phase ERS-1 satellite altimeter data. The mean sea surface frame defined by the TOPEX data is imposed as certain constraints in our crossover adjustment procedure rather than held fixed as in some other procedures. The new procedure is discussed in detail. Equations are developed to incorporate the a priori information of Topex data as well as other satellite altimeter data. The numerical computation result shows that the rms crossover discrepancies are reduced by an order of 1 cm when the Topex data is not fixed. Furthermore, the computed mean sea surface is less noisy and more realistic than that computed by the traditional procedure.     

Sea Level Variations and Geomorphological Changes in the Coastal Belt of Pakistan

The UNEP in its regional seas program in 1989 has included Pakistan in a group of countries which are vulnerable to the impact of rising sea level. If the present trend of sea level rise (SLR) at Karachi continues, in the next 50 years the sea level rise along the Pakistan Coast will be 50 mm (5 cm). Since the rising rates of sea level at Karachi are within the global range of 1-2 mm/year, the trends may be treated as eustatic SLR. Historical air temperature and sea surface temperature (SST) data of Karachi also show an increasing pattern and an increasing trend of about 0.67°C has been registered in the air temperature over the last 35 years, whereas the mean SST in the coastal waters of Karachi has also registered an increasing trend of about 0.3°C in a decade. Sindh coastal zone is more vulnerable to sea level rise than Baluchistan coast, as uplifting of the coast by about 1-2 mm/year due to subduction of Indian Ocean plate is a characteristic of Baluchistan coast. Within the Indus deltaic creek system, the area nearby Karachi is more vulnerable to coastal erosion and accretion than the other deltaic region, mainly due to human activities together with natural phenomena such as wave action, strong tidal currents, and rise in sea level. Therefore, The present article deals mainly with the study of dynamical processes such as erosion and accretion associated with sea level variations along the Karachi coast and surrounding Indus deltaic coastline. The probable beach erosion in a decade along the sandy beaches of Karachi has been estimated. The estimates show that 1.1 mm/year rise in sea level causes a horizontal beach loss of 110 mm per year. Therefore, coast eroded with rise in sea level at Karachi and surrounding sandy beaches would be 1.1 m during a period of next 10 years. The northwestern part of Indus delta, especially the Gizri and Phitti creeks and surrounding islands, are most unstable. Historical satellite images are used to analyze the complex pattern of sediment movements, the change in shape of coastline, and associated erosion and accretion patterns in Bundal and Buddo Islands. The significant changes in land erosion and accretion areas at Bundal and Buddo Islands are evident and appear prominently in the images. A very high rate of accretion of sediments in the northwestern part of Buddo Island has been noticed. In the southwest monsoon season the wave breaking direction in both these islands is such that the movement of littoral drift is towards west. Erosion is also taking place in the northeastern and southern part of Bundal Island. The erosion in the south is probably due to strong wave activities and in the northeast is due to strong tidal currents and seawater intrusion. Accretion takes place at the northwest and western parts of Bundal Island. By using the slope of Indus delta, sea encroachment and the land area inundation with rising sea level of 1 m and 2 m have also been estimated.     

Assessment of SARAL/AltiKa Wave Height Measurements Relative to Buoy,Jason-2, and Cryosat-2 Data

SARAL/AltiKa GDR-T are analyzed to assess the quality of the significant wave height (SWH) measurements. SARAL along-track SWH plots reveal cases of erroneous data, more or less isolated, not detected by the quality flags. The anomalies are often correlated with strong attenuation of the Ka-band backscatter coefficient, sensitive to clouds and rain. A quality test based on the 1 Hz standard deviation is proposed to detect such anomalies. From buoy comparison, it is shown that SARAL SWH is more accurate than Jason-2, particularly at low SWH, and globally does not require any correction. Results are better with open ocean than with coastal buoys. The scatter and the number of outliers are much larger for coastal buoys. SARAL is then compared with Jason-2 and Cryosat-2. The altimeter data are extracted from the global altimeter SWH Ifremer data base, including specific corrections to calibrate the various altimeters. The comparison confirms the high quality of SARAL SWH. The 1 Hz standard deviation is much less than for Jason-2 and Cryosat-2, particularly at low SWH. Furthermore, results show that the corrections applied to Jason-2 and to Cryosat-2, in the data base, are efficient, improving the global agreement between the three altimeters.