Variation of the tidal properties around Gran Canaria

Analysis of water level and current meter series from different locations on the island shelf of Gran Canaria reveals strong variations in tidal properties. Semidiurnal sea level amplitudes agree with the results obtained from global tidal models for this region only on the northern coast of the island, while they decrease towards the southwest (10 cm difference for the M₂ constituent). Semidiurnal currents present maxima at the southeastern and northwestern extremities of the island (30–40 cm s⁻¹ for M₂) and minima in the north-northeast and southwest (3–6 cm s⁻¹ for M₂), showing simultaneous strong changes in the phase. Diurnal levels and currents display smaller variations than the semidiurnal band. The behaviour of semidiurnal constituents is studied with the help of analytical and numerical solutions, in which the incident wave is modelled by a barotropic M₂ Kelvin wave. The results show that the insular shelf could be a source of differences in level amplitudes around the island and could be also responsible for the enhancement of currents in the southeast and northwest. They also show that the variation of the current phases is due to the amplification of the standing character of the wave at the northeastern and southwestern parts of the shelf.     

波浪在三维圆形岛地形上的绕射研究

波浪在传播过程中遇到岛屿就会发生绕射。本文使用混合元方法对修正型缓坡方程进行了数值求解,并与KUO et al的解析解进行了比较验证。在此基础上研究了工程尺度背景下,波浪在三维圆形岛地形上的绕射,计算了不同入射波浪周期、浅滩形状参数和岛屿尺寸情况下,沿波浪传播方向断面上和岛屿岸线上的相对波高大小。计算结果表明：随着入射波周期的减小、浅滩形状参数的增大和岛屿尺寸的减小,圆形岛迎浪侧的相对波高振荡幅度、圆形岛背浪侧的相对波高大小以及岛屿岸线上的相对波高振幅和大小均随之增大。不同情况下,岛屿岸线上的相对波高最大值大多数发生在迎浪点,个别发生在迎浪点两侧20°~25°处;最小值发生在背浪点两侧30°附近。     

Effective fetch and non-linear four-wave interactions during wave growth in slanting fetch conditions

Wave growth in slanting fetch (with wind blowing obliquely off a coast) is investigated with 7 years worth of routine wave measurements in Lake IJssel in The Netherlands and with the SWAN wave model. Two aspects are considered in particular for this case: the validity of the concept of effective fetch and the role of the non-linear four-wave interactions. For slanting and parallel fetch conditions, we found some significant deviations from the effective fetch assumption, leading to 20–35% mismatch in either the peak period T_p or the significant wave height H_m0 respectively. However, the effect of discrepancies between various widely accepted wave growth formulas turned out to be even more important. The wave directions during slanting fetch are significantly ‘steered’ by the coastline, especially in the first kilometre(s) off the coast. The role of the non-linear four-wave interactions is investigated by running the SWAN (version 40.41) wave model with three different quadruplet formulations. Exact quadruplet methods (Xnl) yielded relatively strong wave steering, despite the four-wave interactions being relatively weak. Application of Xnl did not lead to better overall agreement with measurements — improvements for the mean wave period T_m01 were offset by some deterioration for the wave height H_m0.     

Global observations of nonlinear mesoscale eddies

Sixteen years of sea-surface height (SSH) fields constructed by merging the measurements from two simultaneously operating altimeters are analyzed to investigate mesoscale variability in the global ocean. The prevalence of coherent mesoscale features (referred to here as “eddies”) with radius scales of O(100 km) is readily apparent in these high-resolution SSH fields. An automated procedure for identifying and tracking mesoscale features based on their SSH signatures yields 35,891 eddies with lifetimes ?16 weeks. These long-lived eddies, comprising approximately 1.15 million individual eddy observations, have an average lifetime of 32 weeks and an average propagation distance of 550 km. Their mean amplitude and a speed-based radius scale as defined by the automated procedure are 8 cm and 90 km, respectively.The tracked eddies are found to originate nearly everywhere in the World Ocean, consistent with previous conclusions that virtually all of the World Ocean is baroclinically unstable. Overall, there is a slight preference for cyclonic eddies. However, there is a preference for the eddies with long lifetimes and large propagation distances to be anticyclonic. In the southern hemisphere, the distributions of the amplitudes and rotational speeds of eddies are more skewed toward large values for cyclonic eddies than for anticyclonic eddies. As a result, eddies with amplitudes >10 cm and rotational speeds >20 cm s⁻¹ are preferentially cyclonic in the southern hemisphere. By contrast, there is a slight preference for anticyclonic eddies for nearly all amplitudes and rotational speeds in the northern hemisphere.On average, there is no evidence of anisotropy of these eddies. Their average shape is well represented as Gaussian within the central 2/3 of the eddy, but the implied radius of maximum rotational speed is 64% smaller than the observed radius of maximum speed. In part because of this mismatch between the radii of maximum axial speed in the observations and the Gaussian approximation, a case is made that a quadratic function that is a very close approximation of the mode profile of the eddy (i.e., the most frequently occurring value at each radius) is a better representation of the composite shape of the eddies. This would imply that the relative vorticity is nearly constant within the interiors of most eddies, i.e., the fluid motion consists approximately of solid-body rotation.Perhaps the most significant conclusion of this study is that essentially all of the observed mesoscale features outside of the tropical band 20°S-20°N are nonlinear by the metric U/c, where U is the maximum circum-average geostrophic speed within the eddy interior and c is the translation speed of the eddy. A value of U/c > 1 implies that there is trapped fluid within the eddy interior. Many of the extratropical eddies are highly nonlinear, with 48% having U/c > 5 and 21% having U/c > 10. Even in the tropics, approximately 90% of the observed mesoscale features are nonlinear by this measure.Two other nondimensional parameters also indicate strong degrees of nonlinearity in the tracked eddies. The distributions of all three measures of nonlinearity are more skewed toward large values for cyclonic eddies than for anticyclonic eddies in the southern hemisphere extratropics but the opposite is found in the northern hemisphere extratropics. There is thus a preference for highly nonlinear extratropical eddies to be cyclonic in the southern hemisphere but anticyclonic in the northern hemisphere.Further evidence in support of the interpretation of the observed features as nonlinear eddies is the fact that they propagate nearly due west with small opposing meridional deflections of cyclones and anticyclones (poleward and equatorward, respectively) and with propagation speeds that are nearly equal to the long baroclinic Rossby wave phase speed. These characteristics are consistent with theoretical expectations for large, nonlinear eddies. While there is no apparent dependence of propagation speed on eddy polarity, the eddy speeds relative to the local long Rossby wave phase speeds are found to be about 20% faster in the southern hemisphere than in the northern hemisphere. The distributions of the propagation directions of cyclones and anticyclones are essentially the same, except mirrored about a central azimuth angle of about 1.5° equatorward. This small, but we believe statistically significant, equatorward rotation of the central azimuth may be evidence of the effects of ambient currents (meridional advection or the effects of vertical shear on the potential vorticity gradient vector) on the propagation directions of the eddies.While the results presented here are persuasive evidence that most of the observed westward-propagating SSH variability consists of isolated nonlinear mesoscale eddies, it is shown that the eddy propagation speeds are about 25% slower than the westward propagation speeds of features in the SSH field that have scales larger than those of the tracked eddies. This scale dependence of the propagation speed may be evidence for the existence of dispersion and the presence of features that obey linear Rossby wave dynamics and have larger scales and faster propagation speeds than the nonlinear eddies. The amplitudes of these larger-scale signals are evidently smaller than those of the mesoscale eddy field since they are not easily isolated from the energetic nonlinear eddies.     

A new predictive formula for inception of regular wave breaking

Efforts are made to enhance the predictive formula for the inception of wave breaking. To achieve success, the existing formulas are extensively reviewed. They are categorized into four types, i.e., the McCowan type, the Miche type, the Goda type and the Munk type. The inherent relations among the different types are then exploited. The differences among each formula within a group are also discussed. Four representative formulas from the different types are chosen to compare with the measured data for a total number of 1193 cases reported in literatures. It is shown that Goda's and Ostendorf and Madsen's formulas are advantageous in general among the selected ones. Goda's formula, however, is found to be inaccurate as the beach slope becomes steeper than 1/10. Ostendorf and Madsen's formula is fairly good even for cases of very steep slopes, but its accuracy for the cases of ordinary slopes is not as good as Goda's. A new predictive formula for the inception of wave breaking is proposed. The unique index, defined by ψ′_b = (1.21 − 3.30λ_b)(1.48 − 0.54γ_b)ψ_b, where ψ_b = gH_b/C_b², H_b is the breaking wave height, C_b is the breaking wave celerity, λ_b is the breaking wave steepness, γ_b is the relative breaking wave height, and g is the gravity acceleration, is introduced. The incipient condition of wave breaking is then given by ψ′_b = 0.69. This formula is a significant improvement to the existing ones in terms of the accuracy. In addition, it is a local relation. Further verification shows that the proposed formula performs similarly well when applied to the field and to the waves over permeable bed.     

Determination of residence time and mixing processes of the Ubatuba,Brazil, inner shelf waters using natural Ra isotopes

Coastal waters contain elevated dissolved activities of short-lived radium isotopes, ²²³Ra and ²²⁴Ra, having half-lives of 11.4 and 3.66 days, respectively. The input of these isotopes near the coast must be balanced by decay and mixing into the open ocean, where excess activities are zero. Since the decay rate is known, in the ideal case the mixing rate may be determined from the offshore distribution of these isotopes. This study found that samples collected in June 2000 followed the expected exponential decrease with distance offshore. We assign a dispersion coefficient of 28–39 m² s⁻¹ for this study. During January 2002 and November 2003, there was not a consistent decrease of activity with distance offshore. This is likely due to the ruggedness of the coastline, where many bays and small islands interrupt simple mixing patterns. To estimate exchange rates during 2002 and 2003, we used a model based on the decrease in the ²²⁴Ra/²²³Ra activity ratio (AR) with time for samples isolated from fresh inputs of Ra. This model yielded residence times of 1–2 weeks for samples collected within 20 km of the coast. We used this residence time to calculate the flux of ²²⁸Ra (half-life = 5.7 years) to the study area necessary to maintain the enrichment relative to ocean water. This enrichment is a factor of ten greater than the flux of ²²⁸Ra expected from submarine groundwater discharge (SGD) occurring within 50 m of shore.     

The effect of temporal wave averaging on the performance of an empirical shoreline evolution model

The effect of using time-averaged wave statistics in a simple empirical model for shoreline change is investigated. The model was first calibrated with a six-year time series of hourly wave conditions and weekly shoreline position at the Gold Coast, Australia. The model was then recalibrated with the hourly waves averaged over intervals up to 1 year. With wave averaging up to 2 days, model performance was approximately constant (squared correlation r² ~ 0.61–0.62), with only small changes in the values of empirical model parameters (e.g. the beach response coefficient c varied by less than 4%). With between 2 and 40 day averaging, individual storms are not resolved; model skill decreased only modestly (r² ~ 0.55), but c varied erratically by up to 40% of the original value. That is, optimal model coefficients depend on wave averaging, an undesirable result. With increased averaging (> 40 days) seasonal variability in the wave field is not resolved well and model skill declined markedly. Thus, temporal averaging of wave conditions increases numerical efficiency, but over-averaging degrades model performance and distorts best-fit values of model free parameters.     

Characteristic friction coefficient and scale effects in oscillatory porous flow

This work presents a simple method to evaluate the performance of a porous breakwater when it is impinged with normal incidence by a non-breaking monochromatic wave train. It is based on: 1) a potential flow model for wave interaction with permeable structures and 2) a set of experimental tests on a rectangular porous structure with uniform granular distribution. A characteristic friction diagram is obtained considering wave energy balance in a control volume, minimising the error between the numerical model and the experimental results for the wave transmission coefficient. Results show that, for large breakwater widths, the reflection process reaches a saturation regime before the waves exit the structure at a distance from the seaside between the interval 0.2 < x/L < 0.45. For larger breakwater widths, the reflection coefficient is almost constant (except for “resonant” conditions) and wave transmission decreases exponentially. Under such conditions, the wave propagation through the porous medium depends on the relative diameter D/L and the porosity of the material; the dependence on the relative breakwater width B/L and the ratio diameter wave height D/H is weak. This diagram intends to be useful for preliminary engineering studies of breakwater's efficiency and performance and as an adequate selection criteria of the experimental stone diameter to minimize scale effects in laboratory studies.     

The feeding and diet of the deep-sea shrimp Aristeus antennatus off the Balearic Islands (Western Mediterranean): Influence of environmental factors and relationship with the biological cycle

Spatio-temporal variation of feeding intensity and diet in the red shrimp Aristeus antennatus was studied at two locations around the island of Mallorca (Balearic Islands, Western Mediterraean) in August, September, and November 2003, and in February, April and June 2004 at depths between 550 and 750 m. The two areas, with different oceanographic conditions, were respectively located in the northwest (Sóller) and the south (Cabrera) of Mallorca. Off Sóller, feeding intensity of A. antennatus showed a significant increase from February to April and June 2004 in all the three size-classes studied (small shrimps: CL < 30 mm; medium: CL between 30 and 40 mm; large: CL ? 40 mm). Off Cabrera, the highest fullness was recorded in November 2003 among small and medium shrimp, while only large specimens showed patterns similar to that found off Sóller. Off Sóller, the diet of both small (CL < 34 mm) and large (CL ? 34 mm) A. antennatus was mainly influenced by season, with three dietary groups corresponding to August-September 2003, to November 2003/February 2004, and to hauls from April to June 2004. Off Cabrera, hauls (representing diets) were grouped by depth, never by season. The most remarkable seasonal shift in the diet of A. antennatus off Sóller was the increase of mesopelagic prey in April-June relative to other months. In all size categories there was an increase off Sóller in the energy intake of prey ingested from February to June 2004, an increase not found off Cabrera. Degree of digestion of mesopelagic prey indicated nocturnal feeding on mesopelagic fauna. These prey probably have a shallower depth distribution at night than found in our daylight sampling, and possible migratory movements among prey and A. antennatus at night would explain the lack of correlation between prey abundance in guts and in the environment found during daylight periods for most micronekton mesopelagic prey (euphausiids, myctophids and sergestids). Off Sóller, fullness and diet were significantly linked to temporal changes in water column productivity (e.g., Chl a readings, fluorescence) and to changes in the shrimp biology (lipid content of hepatopancreas, Gonado-somatic Index, GSI). Off Cabrera, we found a higher dependence of fullness and diet with T and S, both variables in turn related to depth. The increase of stomach fullness and dietary energy intake in pre-reproductive females from February to April-June 2004 found off Sóller, coupled with the consumption of mesopelagic prey, was parallel to a significant increase of the gonad weight (GSI, fecundity) in June. Most individuals attain gonad development in the period May-June, after two months of the peak of primary production at the surface. The strong link found between pelagic resources and reproductive processes in a deep-sea species such as the shrimp Aristeus antennatus, situated near the top of the trophic web, suggests a rapid energy flow via mesopelagic fauna between surface primary production and bathyal megabenthic communities at oligotrophic insular areas. In contrast to mainland areas off the Catalan coasts submitted to the influence of submarine canyons, around the island of Mallorca the empoverishment of benthos biomass may enhance consumption of micronektonic prey and a possible accumulation of pre-reproductive females of A. antennatus in areas (e.g., steep slopes and persistent frontal systems found off Sóller) with high zooplankton aggregations.     

Temporal variation in abundance and fecundity of the invading copepod Eurytemora americana in Bahía Blanca Estuary during an unusual year

Eurytemora americana has been only reported as invader in Bahía Blanca Estuary, Argentina within the South Hemisphere. There are a few experimental researches under laboratory conditions done with this species and its reproductive behaviour around the world is very scarce. Consequently, it is still not possible to completely understand its population dynamics. In the present study, E. americana reproductive temporal behaviour and relationships among abundance, female size, egg production and hatching success were examined in the Bahía Blanca Estuary, during 2007 pulse. In order to determine the potential relationships between these variables and the environmental variables, experimental incubations were conducted in the laboratory simulating natural conditions. Spearman’s rank correlation was used to analyze the relationships among all variables. Temporal change of biotic and environmental variables was corroborated by a Mann–Whitney/Kruskal–Wallis non-parametric tests, with significant differences (p ? 0.01) in all variables throughout the study. Abundance population results showed very high values in relation to those recorded in recent years in Bahía Blanca Estuary. This response could be due to the unusual combination of environmental factors (polar wave with temperatures ≤6 °C and a drought period with high salinities, 32.7–36.6) recorded during the studied winter period. Significant positive correlations between abundance and salinity (p < 0.01, n = 226), and hatching success (p < 0.01, n = 25) as well as a significant negative correlation between abundance and chlorophyll a (p < 0.01, n = 226) were found. Although E. americana shows a k-strategy within its annual pulse, it presented two markedly distinct behaviours depending on temporal environmental variability. From July to early september, when the estuary evidenced high salinity, low temperature and high food availability, E. Americana showed large females, large clutch size and high hatching success. When environmental conditions became unfavorable from September to October, small females, small clutch size and very low hatching success were observed. The latter is associated with diapause egg laying which ensures population recruitment. According to our findings the particular combination of low temperatures, high salinities and high available food (i.e. variables which each year modulate its pulse) during 2007 winter–spring, favored the great development of E. americana. This invading species in its opportunistic role has managed to exploit a vacant niche in the estuary, developing two different behaviours within the k-strategy depending on change in environmental conditions.     

Discussion of “Analytic solution of long wave propagation over a submerged hump” by Niu and Yu (2011)

Recently, Niu and Yu (2011) presented an analytical solution of the long wave refraction by a submerged circular hump. The geometry of the hump was assumed to be axi-symmetric and the water depth over the hump region was described by a positive constant plus a power function of the radial distance with an arbitrary value of the power exponent, i.e., h = h₁ + βr^s, where h₁ is the water depth at the crest of the hump. Their general hump is an extension of the paraboloidal hump (i.e., s = 2) studied by Zhang and Zhu (1994) and Zhu and Harun (2009). Because of this extension in the topography of the hump, the problem to seek a general analytical solution to the long-wave equation becomes much more complicated and the solution technique need to be more skillful, especially for the case with the exponent s being a rational, see Eq. (17) in Niu and Yu (2011).     

Contrasting oceanographic conditions and phytoplankton communities on the east and west coasts of Australia

The composition and dynamics of the phytoplankton communities and hydrographic factors that control them are described for eastern and western Australia with a focus on the Eastern Australian Current (EAC) and Leeuwin Current (LC) between 27.5° and 34.5°S latitude. A total of 1685 samples collected from 1996 to 2010 and analysed for pigments by high performance liquid chromatography (HPLC) showed the average TChla (monovinyl+divinyl chlorophyll a) concentration on the west coast to be 0.28±0.16 ??g L⁻¹ while it was 0.58±1.4 ??g L⁻¹ on the east coast. Both coasts showed significant decreases in the proportions of picoplankton and relatively more nanoplankton and microplankton with increasing latitude. On both coasts the phytoplankton biomass (by SeaWiFS) increased with the onset of winter. At higher latitudes (>27.5°S) the southeast coast developed a spring bloom (September) when the mean monthly, surface chlorophyll a (chla) concentration (by SeaWiFS) was 48% greater than on the south west coast. In this southern region (27.5-34.5°S) Synechococcus was the dominant taxon with 60% of the total biomass in the southeast (SE) and 43% in the southwest (SW). Both the SE and SW regions had similar proportions of haptophytes; ∼14% of the phytoplankton community. The SW coast had relatively more pelagophytes, prasinophytes, cryptophytes, chlorophytes and less bacillariophytes and dinophytes. These differences in phytoplankton biomass and community composition reflect the differences in seasonality of the 2 major boundary currents, the influence this has on the vertical stability of the water column and the average availability of nutrients in the euphotic zone. Seasonal variation in mixed layer depth and upwelling on the west coast appears to be suppressed by the Leeuwin Current. The long-term depth averaged (0-100 m) nitrate concentration on the west coast was only 14% of the average concentration on the east coast. Redfield ratios for NO₃:SiO₂:PO₄ were 6.5:11.9:1 on the east coast and 2.2:16.2:1 on the west coast. Thus new production (nitrate based) on the west coast was likely to be substantially more limited than on the eastcoast. Short term (hourly) rates of vertical mixing were greater on the east coast. The more stable water column on the west coast produced deeper subsurface chlorophyll a maxima with a 25% greater proportion of picoeukaryotes.     

Megacusps on rip channel bathymetry: Observations and modeling

The formation of beach megacusps along the shoreline of southern Monterey Bay, CA, is investigated using time-averaged video and simulated with XBeach, a recently developed coastal sediment transport model. Investigations focus on the hydrodynamic role played by the bay's ever-present rip channels. A review of four years of video and wave data from Sand City, CA, indicates that megacusps most often form shoreward of rip channels under larger waves (significant wave height (H_s) = 1.5–2.0 m). However, they also occasionally appear shoreward of shoals when waves are smaller (H_s ~ 1 m) and the mean water level is higher on the beach. After calibration to the Sand City site, XBeach is shown to hindcast measured shoreline change moderately well (skill = 0.41) but to overpredict the erosion of the swash region and beach face. Simulations with small to moderate waves (H_s = 0.5–1.2 m) suggest, similar to field data, that megacusps will form shoreward of either rip channels or shoals, depending on mean daily water level and pre-existing beach shape. A frequency-based analysis of sediment transport forcing is performed, decomposing transport processes to the mean, infragravity, and very-low-frequency (VLF) contributions for two highlighted cases. Results indicate that the mean flow plays the dominant role in both types of megacusp formation, but that VLF oscillations in sediment concentration and advective flow are also significant.     

Modeling the near-field effects of the worst-case tsunami in the Makran subduction zone

As a first step towards the development of inundation maps for the northwestern Indian Ocean, we simulated the near-field inundation of two large tsunami in the Makran subduction zone (MSZ). The tsunami scenarios were based on large historical earthquakes in the region. The first scenario included the rupture of about 500 km of the plate boundary in the eastern MSZ, featuring a moment magnitude of M_w 8.6. The second scenario involved the full rupture of the plate boundary resulting from a M_w 9 earthquake. For each scenario, the distribution of tsunami wave height along the coastlines of the region is presented. Also, detailed runup modeling was performed at four main coastal cities in the region for the second scenario. To investigate the possible effect of splay fault branching on tsunami wave height, a hypothetical splay fault was modeled which showed that it can locally increase the maximum wave height by a factor of 2. Our results showed that the two tsunami scenarios produce a runup height of 12-18 m and 24-30 m, respectively. For the second scenario, the modeled inundation distance was between 1 and 5 km.     

Influence of bathymetric fluctuations on coastal storm surge

Natural events constantly alter nearshore bathymetric properties. Hurricanes particularly affect bathymetry as they pass over a body of water. To compute an accurate forecast or recreate a hurricane's effects through hindcasting techniques, an operational bathymetry data set must be known in advance. However, obtaining and maintaining current and accurate bathymetric data can be costly and difficult to manage. In this paper we examine the extent to which variations in nearshore bathymetry affect the storm surge at the coast. A common question for wave and surge modeling is, “how good is the bathymetric data?” If we can allow for a range of fluctuations in the bathymetry without significantly adjusting the results of the surge predictions, we can potentially save months of field work and millions of dollars. A one-dimensional (1D) analytical solution for waves and water level is developed for initial testing. In the 1D case we find that as long as the amplitudes of the bathymetric fluctuations are less than 60% of the original depth, the surge at the coast is within ± 10% of the surge generated on the initial bottom slope. If the fluctuation produces a hole, a deepening of the local bathymetry, within 80% of the local water depth, the coastal storm surge calculated is still within 10% of the unperturbed value computed for bottom slopes shallower than 1:20. In addition, we find there is an optimum distance offshore for each sloped profile that corresponds to a depth between 25 and 40 m, beyond which the effects of bathymetric fluctuations begin to decrease. A coupled 2D modeling system is implemented to test our hypothesis along a realistic coastline. After selecting three study sites, we vary the bathymetry at the selected locations by ± 20%. Consistent with the 1D tests, the storm surge at the shoreline varies by less than 5%.     

Wave boundary layer over a stone-covered bed

This paper summarizes the results of an experimental investigation on wave boundary layers over a bed with large roughness, simulating stone/rock/armour block cover on the sea bottom. The roughness elements used in the experiments were stones the size of 1.4cm and 3.85cm in one group of experiments and regular ping-pong balls the size 3.6cm in the other. The orbital-motion-amplitude-to-roughness ratio at the bed was rather small, in the range a/k_s = 0.6–3. The mean and turbulence properties of the boundary-layer flow were measured. Various configurations of the roughness elements were used in the ping-pong ball experiments to study the influence of packing pattern, packing density, number of layers and surface roughness of the roughness elements. The results show that the friction factor seems to be not extremely sensitive to these factors. The results also show that the friction factor for small values of the parameter a/k_s does not seem to tend to a constant value as a/k_s → 0 (contrary to the suggestion made by some previous investigators). The present friction-factor data indicates that the friction factor constantly increases with decreasing a/k_s. An empirical expression is given for the friction factor for small values of a/k_s. The results further show that the phase lead of the bed friction velocity over the surface elevation does not seem to change radically with a/k_s, and found to be in the range 12°–23°. Furthermore the results show that the boundary-layer turbulence also is not extremely sensitive to the packing pattern, the packing density, the number of layers and the surface roughness of the roughness elements. There exists a steady streaming near the bed in the direction of wave propagation, in agreement with the existing work. The present data indicate that the steady streaming is markedly smaller in the case where the ping-pong balls are aligned at 45° to the wave direction than in the case with 90° alignment. Likewise, it is found that the steady streaming is relatively smaller in the case of the one-layer ping-pong-ball roughness than in the case of the two-layer situation.     

Wave driven alongshore sediment transport and stability of the Dutch coastline

The wave-driven alongshore sediment transport is commonly supposed to smooth out the irregularities on the coastline. However, it has been shown that waves approaching the coast with a high angle with respect the shore-normal can reverse that tendency and cause the rectilinear coast to be unstable [Ashton, A., Murray, A.B., Arnault, O., 2001. Formation of coastline features by large-scale instabilities induced by high-angle waves. Nature 414, 296–300; Falqués, A., Calvete, D., 2005. Large scale dynamics of sandy coastlines. Diffusivity and instability. J. Geophys. Res. 110, doi:10.1029/2004JC002587]. The extended one-line coastline model presented in the latter paper is here applied to investigate the stability of the Dutch coast. The main aim is testing the hypothesis that the shoreline sand waves observed along this coast could be generated by such an instability. It is found that the Dutch coast has potential for instability. This is most prominent on the Holland coast, followed by the Delta coast and is very weak on the Wadden coast. Whether the instability actually occurs or not depends on the cross-shore bathymetric profile of the shoreline waves. Under the sensible assumption that the bathymetric perturbation is just a shift of the equilibrium beach profile, the Dutch coast is stable. In this case, the mean annual coastline diffusivity is evaluated and it is found to be typically about 0.010–0.015 m² s^− 1, that is, roughly smaller by a factor 2 than that predicted by the traditional one-line model. However, the Dutch coast may be unstable with respect to coastline waves with a maximum bathymetric signal at a few hundred meters from the coast. This is shown in one case where the shoals associated with the sand wave are inside the surf zone during moderate storm waves. Thus the sand waves could result from the cross-shore redistribution of the sand associated with an alongshore series of shoals and bed depressions generated by the alongshore transport in the surf zone. While the generation or not of such shoreline waves by this instability strongly depends on their profile, its propagation once they have been created is less sensitive and is well reproduced by the present model. It is explained why the propagation is to the NE along the Delta and Wadden coasts, why it is faster on the latter and why on the Holland coast there is no clear propagation direction.     

A numerical model for combined refraction-diffraction of short waves on an island

A combined wave refraction-diffraction numerical model was developed to predict wave conditions around an arbitrary island. The methodology was based on the mild-slope equation, solved using a finite difference scheme with a marching procedure. The new model reduced the computer's memory demand considerably in comparison with finite-element, parabolic, error vector propagation and other finite difference approaches, and could therefore predict wave conditions for a large coastal area under given offshore boundary-wave conditions. Laboratory data on wave conditions under submerged circular and elliptical shoal conditions were selected to validate the numerical results. Good agreement was observed in all cases. Wave characteristics around an island were predicted using this model with the given deep-water wave condition. The model can predict wave conditions for any island with a mild-slope coastline.     

Spatial variability of epifaunal communities from artificial habitat: Shipwrecks in the Southern Bight of the North Sea

We investigated the cover, community structure and abiotic environment of nine shipwrecks lying at increasing distance from the Belgian coast. Results indicated that all shipwrecks were strongly dominated by cnidarians in terms of biomass and by amphipods in terms of abundances. Based on their epifaunal composition, three groups of shipwrecks could be determined. Metridium senile dominated a species poor community of the coastal sites. On the same sites, a Tubularia larynx community with a more species-rich assemblage was also developing. The T. larynx community had a lower biomass value (102 g AFDW m⁻²) and significantly lower species richness compared to the other sites. The coastal sites were characterized by periodic salinity decreases, large seasonal temperature fluctuation, high total suspended matter load and reduced current velocity. Channel water masses influence the offshore sites causing a more stable temperature and salinity environment, less turbid waters and high current speed. Tubularia indivisa dominated this community, with an average biomass of 229 g AFDW m⁻². Intermediate sites were also dominated by T. indivisa, but a higher biomass (424 g AFDW m⁻²) was observed. They showed intermediate results for the abiotic parameters and fast current velocities. Hypotheses for the observed variation in community structures are discussed in the light of the abiotic characterization of the shipwrecks.