Haeundae Beach in Korea: Seasonal-to-decadal wave statistics and impulsive beach responses to typhoons

Haeundae Beach represents Korean pocket beaches that are currently erosional and dominated by summertime typhoons. The decadal wave characteristics 9 km offshore of Haeundae Beach were analyzed using the WAM model that was validated through the 2007 wave observations. The wave statistics modelled for 1979–2007 indicates that the seasonal mean significant wave height (H _s ) is highest (0.6–0.7 m) in summer due to typhoons, in contrast to the lowest (around 0.5 m) autumn analog. The wave direction is also pronouncedly seasonal with the principal bearings of SSW and NE in the summer and winter seasons, respectively. The WAM results additionally show that the H _s has gradually increased over the region of Haeundae Beach since 1993. Beach profiling during June–November 2014 shows the opposite processes of the typhoon and fair-weather on beach sands. During a typhoon, foreshore sands were eroded and then accumulated as sand bars on the surf zone. In the subsequent fair-weather, the sand bars moved back to the beach resulting in the surf-zone erosion and foreshore accretion. A total of 5 cycles of these beach-wide sand movements yielded a net retreat (up to 20 m) of the shoreline associated with large foreshore erosion. However, the surf zone only slightly accumulated as a result of the sand cycles. This was attributed to the sand escape offshore from the westernmost tip of the beach. The present study may provide an important clue to understanding the erosional processes in Haeundae Beach.     

Infra-gravity wave generation by the shoaling wave groups over beaches

A physical parameter, μb, which was used to meet the forcing of primary short waves to be off-resonant before wave breaking, has been considered as an applicable parameter in the infra-gravity wave generation. Since a series of modulating wave groups for different wave conditions are performed to proceed with the resonant mechanism of infra-gravity waves prior to wave breaking, the amplitude growth of incident bound long wave is assumed to be simply controlled by the normalized bed slope, βb. The results appear a large dependence of the growth rate, α, of incident bound long wave, separated by the three-array method, on the normalized bed slope, βb. High spatial resolution of wave records enables identification of the cross-correlation between squared short-wave envelopes and infra-gravity waves. The cross-shore structure of infra-gravity waves over beaches presents the mechanics of incident bound- and outgoing free long waves with the formation of free standing long waves in the nearshore region. The wave run-up and amplification of infra-gravity waves in the swash zone appear that the additional long waves generated by the breaking process would modify the cross-shore structure of free standing long waves. Finally, this paper would further discuss the contribution of long wave breaking and bottom friction to the energy dissipation of infra-gravity waves based on different slope conditions.     

Some properties of surf-beats

Long ocean waves with periods of several minutes (surf-beats) were observed at a marine observation tower. We have analysed time series data of an envelope of incident swell, long period current velocity and surface elevation fluctuations. Current velocity was measued by an electromagnetic flow meter. Surf-beats amplitudeH ^(l) is shown to be proportional to 3/2 power of incident swell amplitudeH ^(s), and decreases with increase of depthh in proportional toh ^–1/2 such thatH ^(l) H ^(s) (H ^(s)/h)^1/2. Frequency energy density functionP _LL (f) of surface elevation had two dominant peaks whose frequencies were highly stable through the entire observational period. Cross-spectral analysis suggested that those peaks correspond to traveling edge waves caused by the excess momentum and mass flux in the surf zone. The forced long ocean waves predicted byLonguet-Higgins andStewart (1964) was ditected. Phase-shift and wave height of the wave with respect to those of incident swell envelope are shown to be in remarkable agreement with the predictions. However the forced long wave is only a minor component in the total energy of surf-beats. Current fields are shown to be largely composed of non-surface modes.     

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.     

Landward migration of inner bars

A field investigation was carried out to collect data of inner bar migration. Profiles were measured once or twice a week for a two-year period at Naka Beach, Ibaraki Prefecture, Japan. It was found that the onshore migration of inner bars could be described by two dimensionless quantities as: $\text{5D}\text{(H}{}_{\mathrm{<mtext>b</mtext>}}\text{)}{}_{\mathrm{<mtext>max</mtext>}}\text{<}\text{(H}{}_{\mathrm{<mtext>b</mtext>}}\text{)}{}_{\mathrm{<mtext>max</mtext>}}\text{gT}{}^2{}_{\mathrm{<mtext>max</mtext>}}\text{<}\text{20D}\text{(H}{}_{\mathrm{<mtext>b</mtext>}}\text{)}{}_{\mathrm{<mtext>max</mtext>}}$ where (H_b)_max is the maximum value of daily average breaker height during one interval between surveys, T_max is the average wave period of the day giving (H_b)_max, D is the mean size of the beach sediment, and g is the acceleration due to gravity. Analyses based on surfzone sediment dynamics yields $\text{v}\text{?}\text{(}\text{wD}\text{b}\text{)}\text{= 2 × 10}{}^{\mathrm{?11}}\text{(}\text{(}\text{H}\text{?}{}_{\mathrm{<mtext>b</mtext>}}\text{D}\text{)}{}^3$, where $\text{v}\text{?}$ is the average speed of onshore bar-migration, b is the bar height, $\text{H}\text{?}{}_{\mathrm{<mtext>b</mtext>}}$ is the average breaker height, and w is the fall velocity of the beach sediment. Nomographs for the speed of landward migrating bars are also presented.     

Waves,long waves and nearshore morphology

Recent field measurements on beaches of different slopes have established that wave motion at periods substantially longer than the incident waves dominates the velocity field close to the shore. Analysis of a number of extensive data sets shows that much of this long wave motion is in the form of progessive edge waves, though forced wave motion, standing edge waves and free waves propagating away from the shore may also contribute to the energy.Theoretically, the drift velocities in bottom boundary layers due to edge waves show spatial patterns of convergence and divergence which may move sediment to form either regular crescentic or cuspate features when only one edge wave mode dominates, or a bewildering array of bars, bumps and holes when several phase-locked modes exist together.Convincing field demonstration of the link between nearshore topography and edge waves only exists for the special case of small-scale beach cusps on steep beaches, formed by edge waves at the subharmonic (twice the period) of the incident waves. At longer periods the link is proving more difficult to establish, due to the longer time-scales of topographic changes, the interaction between pre-existing topography and the water motion, and the observation of broad-banded edge wave motion which is not readily linked to topography with a well-defined scale.These ideas are, however, central to the study of nearshore processes, as most of the plausible alternate hypotheses do not seem to lead to quantitative predictions. Clearly, further theoretical and observational work is essential.     

Extreme value statistics for wave run-up on a natural beach

Statistics of wave run-up maxima have been calculated for 149 35-minutes data runs from a natural beach. During the experiment incident wave height varied from 0.4 to 4.0 m, incident wave period from 6 to 16 s, and beach face slope from 0.07 to 0.20. Four extreme statistics were calculated; the maximum run-up height during each run, the 2% exceedence level of shoreline elevation, the 2% exceedence height for individual run-up peaks, and the 2% exceedence level for swash height as determined by the zero-upcrossing method. These statistics were best parameterized when normalized by the incident significant wave height and plotted against the Iribarren number, ξ = β/(H/L₀)^1/2. The swash data (with set-up removed) showed less scatter than total run-up (with set-up included). For Iribarren number greater than 1.5 the run-up was dominated by the incident frequencies, for lower Iribarren number longer period motions dominated the swash. A reasonable value of wave steepness for a fully developed storm sea is 0.025 so that a storm Iribarren number can be estimated as 6.3 times the beach slope. Using this and an offshore design wave height, the included graphs may provide guidance in determining a design run-up height.     

An experimental study on geometric characteristics of beach erosion profiles

The beach profile and sediment transport are very important factors in the design of coastal structures, and the beach profile is mainly affected by a number of parameters, such as wave height and period, beach slope, and the material properties of the bed. In this study, considering wave height (H₀=6.5, 11.5, 16, 20, 23, 26 and 30 cm), wave period (T=1.46 and 2.03 s), beach slope (m=1/10 and 1/15) and mean sediment diameter (d₅₀=0.18, 0.26, 0.33 and 0.40 mm), an experimental investigation of coastal erosion profile (storm profile) was carried out in a wave flume using regular waves, and geometric characteristics of erosion profile were determined by the resultant erosion profile. Dimensional and non-dimensional equations were obtained by using linear and non-linear regression methods through the experimental data and were compared with previously developed equations in the literature. The results have shown that the experimental data fitted well to the proposed equations with respect to the previously developed equations.     

Geological control of beach morphodynamic state

The concept of beach morphodynamic states has achieved widespread acceptance in the coastal geological literature since its inception in the mid-1980s and expansion in the 1990s. Much of the pioneering work was undertaken in Australia under a range of environmental conditions in microtidal environments and a close empirical relationship between beach 3-dimensional morphology and the Dean's parameter (H_b/W_sT) was established. Subsequently, the Relative Tidal Range parameter (H_b/TR) was extended to beaches of all tidal ranges.In this paper, observations are presented from 25 beaches around the north coast of Ireland. These beaches exist on an environmental gradient that encompasses marked tidal and wave energy variability (micro to macrotidal and low to high wave energy). Each beach was visually categorised into one of several established beach states described in the literature, on the basis of field observations. For each beach, the RTR and Dean's parameter were calculated for the immediately antecedent period and used to predict the beach state using published relationships. Observed and predicted beach states were then compared.Comparison of observed and predicted beach states showed that while beaches with observed dissipative morphology typically matched the expected criteria, most other beach states did not. Lack of agreement between predicted and observed beach states has been reported elsewhere and attributed to failings in the RTR and Dean's parameter. In addition, this study identifies geological factors as important constraints on actual beach state. In the majority of beaches studied, inherited geological factors appear to be more important determinants of beach morphology than contemporary dynamics.     

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.     

Prediction of geometrical properties of perfect breaking waves on composite breakwaters

Breaking wave loads on coastal structures depend primarily on the type of wave breaking at the instant of impact. When a wave breaks on a vertical wall with an almost vertical front face called the “perfect breaking”, the greatest impact forces are produced. The correct prediction of impact forces from perfect breaking of waves on seawalls and breakwaters is closely dependent on the accurate determination of their configurations at breaking. The present study is concerned with the determination of the geometrical properties of perfect breaking waves on composite-type breakwaters by employing artificial neural networks. Using a set of laboratory data, the breaker crest height, h_b, breaker height, H_b, and water depth in front of the wall, d_w, from perfect breaking of waves on composite breakwaters are predicted using the artificial neural network technique and the results are compared with those obtained from linear and multi-linear regression models. The comparisons of the predicted results from the present models with measured data show that the h_b, H_b and d_w values, which represent the geometry of waves breaking directly on composite breakwaters, can be predicted more accurately by artificial neural networks compared to linear and multi-linear regressions.     

Measuring run-up on a natural beach

Field experiments have been performed to evaluate and intercompare two techniques for measuring run-up on natural beaches, resistance wires and films. Simultaneous deployment of wire sensors shows a low error (< 5%) in electronics gain, but a strong sensitivity to the elevation of the wires above the beach face. On a low slope (β ～ 0.02) beach, with incident wind waves of moderate height (H ～ 1 m), differences of only a few cm in the wire elevation cause variance differences as large as 25%, in otherwise identical sensors. Replicate digitizations of the same run-up film show variance differences as large as 20%, with an average deviation from the mean variance of 8%.Use of the film and resistance wire sensors on the same run-up field showed small differences in the mean swash elevation (i.e., set-up), but an 83% difference in swash variance. Much further work is needed to determine the dependence of sensor differences on beach slope, porosity, camera elevation and other factors.     

Spectral characteristics of random wave run-up

The time series of shoreline variations (run-up variations) due to random waves have been measured on uniform sloping beaches with slopes ranging from $\text{1}\text{5}$ to $\text{1}\text{30}$ and the energy spectra of the variations (run-up spectra) have been examined. The main characteristics of run-up spectra obtained from the experimental results are as follows: (1) a phenomenon of energy saturation is seen in a high frequency region; and (2) the spectral energy densities are independent of offshore incident wave energy. In the saturation region, the run-up spectra show f⁻⁴ dependence and tan ⁴θ dependence (f: frequency, tanθ: beach slope). Only in a low frequency region, the energy densities increase with increasing incident wave energy. In addition to the experimental study, it is shown by numerical simulations that if run-up variations are formed by parabolas induced by bores running up and down on the beach surface, the spectra of the variations show f⁻⁴ dependence, and the low frequency run-up energy densities increase with increasing running-up velocities of bores.     

Wave damping over artificial Posidonia oceanica meadow: A large-scale experimental study

An experimental study, conducted in the large wave flume of CIEM in Barcelona, is presented to evaluate the effects of Posidonia oceanica meadows on the wave height damping and on the wave induced velocities. The experiments were performed for irregular waves from intermediate to shallow waters with the dispersion parameter h/λ ranging from 0.09 to 0.29. Various configurations of the artificial P. oceanica meadow were tested for two stem density patterns (360 and 180 stems/m²) and for plant's height ranging from 1/3 to 1/2 of the water depth.The results for wave height attenuation are in good agreement with the analytical expressions found in literature, based on the assumption that the energy loss over the vegetated field is due to the drag forces. Based on this hypothesis, an empirical relationship for the drag coefficient related to the Reynolds number, Re, is proposed. The Reynolds number, calculated using the artificial P. oceanica leaf width as the length scale and the maximum orbital velocity over the meadow edge as the characteristic velocity scale, ranges from 1000 to 3500 and the drag coefficient C_d ranges from 0.75 to 2.0.The calculated wave heights, using the analytical expression from literature and the proposed relationship for the estimation of C_d, are in satisfactory agreement with those measured. Wave orbital velocities are shown to be significantly attenuated inside the meadow and just above the flume bed as indicated by the calculation of an attenuation parameter. Near the meadow edge, energy transfer is found in spectral wave velocities from the longer to the shorter wave period components. From the analysis it is shown that the submerged vegetation attenuates mostly longer waves.     

Trade-wind waves and mud dynamics on the French Guiana coast,South America: Input from ERA-40 wave data and field investigations

The South American coast between Brazil and Venezuela is affected by longshore migrating mud banks derived from the fine-grained Amazon sediment discharge. Onshore mud migration prevails over shallow ‘bank’ areas alternating alongshore with deeper ‘inter-bank’ areas. The transport on the inner shelf, and attachment to the shoreline, of this migrating mud has been attributed mainly to wind waves. However, the lack of in situ data on waves hampers understanding of the relationship between waves and mud dynamics. A 44-yr record (1960–2004) of the ERA-40 wave dataset generated by the European Centre for Medium-Range Weather Forecasts (ECMWF) was used, in conjunction with field investigations in French Guiana, to define both event-scale and longer-term patterns of mud mobilisation induced by waves. The ratio H₀³ / T², combining wave height H and period T, and the angle of wave incidence α, were singled out as the most relevant parameters for describing wave forcing. Typical ‘bank’ and ‘inter-bank’ profiles and corresponding mud densities, and a 3-month record of changes in the thickness of the fluid mud layer in an estuarine navigation channel were monitored by echo-sounding from October 2002 to January 2003. An 80-day record of bed-level changes in the intertidal zone was obtained from August to November 2004 using a pressure transducer. The results on the wave regime of French Guiana confirm a distinctly seasonal pattern, and highlight an increase in H₀³ / T² over the 44-yr period related to an increase in trade-wind velocities determined from corresponding trends in Atlantic wind pseudo-stress off the South American coast. Wave forcing over bank areas leads to the liquefaction of a 1–3 m-thick layer of mud that is transported onshore (and alongshore by the longshore component of wave energy). The episodic nature of high wave energy events generally results in the formation of mud bar features from the shoreward mobilisation of gel-like fluid mud. The effect of waves on mud is particularly marked following long periods of low energy, and especially at the onset of the high wave energy season (October to May), when even moderate wave energy events can lead to significant mobilisation of mud.Significant phases of increased wave energy are attended by higher long-term (annual) rates of longshore mud bank migration but the correlation is rather poor between the wave forcing parameter H₀³ / T² and migration rates because stronger wave forcing is generally associated with low angles of wave incidence. This suggests a complementary role of other hydrodynamic mechanisms, such as geostrophic and tidal currents, in longshore mud bank migration.     

Analysis of temporal and spatial characteristics of waves in the Indian Ocean based on ERA-40 wave reanalysis

Based on the 45-year (09/1957-08/2008) European Centre for Medium-Range Weather Forecasts (ECMWF) Reanalysis (ERA-40) wave reanalysis dataset, this study analyzes interannual and interdecadal variabilities and intraseasonal oscillations of sea surface wind speed (WS), wind sea wave height (H^w), swell wave height (H^s) and significant wave height (H_s) in the Roaring Forties and tropical waters of the Indian Ocean, to determine swell propagation characteristics. The results show: (1) monthly variabilities of H^s in the Roaring Forties are in good agreement with those in tropical waters of the Indian Ocean; swell plays a dominant role in mixed waves throughout most of the Indian Ocean; and WS, H^w, H^s, and H_s exhibit a significant increasing trend over the 45-year study period. (2) H^s in the Roaring Forties and tropical waters of the Indian Ocean share a common period of 9.8–10.4 years on an interdecadal scale; and WS and H^s in the Roaring Forties and H^s in the tropical waters of the Indian Ocean share a common period of approximately 8 days (weekly oscillation) on an intraseasonal scale. (3) Swell of the Roaring Forties needs approximately 30 h to fully respond to the wind in this region. Approximately 84 h are required for H^s to propagate from the Roaring Forties to the tropical waters of the south Indian Ocean, while it takes approximately 132–138 h for H^s to propagate from the Roaring Forties to the tropical waters of the north Indian Ocean.     

Modified McCormicks model for equilibrium shorelines behind a detached breakwater

Experimental data of equilibrium shorelines behind a detached breakwater obtained by previous investigators were collected and re-reviewed to investigate the major parameters affecting the shoreline shapes. The result shows that the equilibrium shorelines depend not only on the breakwater length B and the distance of the breakwater from the initial shoreline S, but also on the incident wave steepness H₀/L₀, beach slope S_b and the sand size D₅₀. Most of equilibrium shorelines behind a detached breakwater could be approximately described by a couple of elliptic curves as proposed by McCormick (Ports, Coastal & Ocean Engineering ASCE 119, 1993, p. 657). However, after re-examination, this paper shows that the dimensionless semiminor axis b/S and the dimensionless distance G/b in the McCormick’s elliptic-curve model should be modified, as compared with the available experimental data. The modified expressions of b/S and G/b were proposed, and the performances of the modified expressions were also detaily examined in this paper.     

Effect of bed roughness on turbulent boundary layer and net sediment transport under asymmetric waves

This paper presents an investigation of the roughness effects in the turbulent boundary layer for asymmetric waves by using the baseline (BSL) k–ω model. This model is validated by a set of the experimental data with different wave non-linearity index, N_i (namely, N_i = 0.67, N_i = 0.60 and N_i = 0.58). It is further used to simulate asymmetric wave velocity flows with several values of the roughness parameter (a_m/k_s) which increase gradually, namely from a_m/k_s = 35 to a_m/k_s = 963. The effect of the roughness tends to increase the turbulent kinetic energy and to decrease the mean velocity distribution in the inner boundary layer, whereas in the outer boundary layer, the roughness alters the turbulent kinetic energy and the mean velocity distribution is relatively unaffected. A new simple calculation method of bottom shear stress based on incorporating velocity and acceleration terms is proposed and applied into the calculation of the rate of bed-load transport induced by asymmetric waves. And further, the effect of bed roughness on the bottom shear stress and bed-load sediment transport under asymmetric waves is examined with the turbulent model, the newly proposed method, and the existing calculation method. It is found that the higher roughness elements increase the magnitude of bottom shear stress along a wave cycle and consequently, the potential net sediment transport rate. Moreover, the wave non-linearity also shows a big impact on the bottom shear stress and the net sediment transport.     

Shoreline response to a single shore-parallel submerged breakwater

Submerged breakwaters (SBWs) are becoming a popular option for coastal protection, mainly due to their low aesthetic impact on the natural environment. However, SBWs have rarely been employed for coastal protection in the past and therefore, their efficacy remains largely unknown. The main objective of the present study was to investigate the structural and environmental conditions that govern the mode of shoreline response (i.e shoreline erosion vs shoreline accretion) to SBWs. The relative importance of the key structural and environmental parameters governing the response mode to a single shore parallel SBW is investigated through a combination of theoretical analysis and numerical modelling. Using physical considerations, a theoretical response-function model is derived under several simplifying assumptions including parallel depth contours, linear wave theory, shore normal waves, and no wave–current interaction. Numerical modelling is undertaken with the Mike21 model suite to simulate the depth averaged velocity fields (without morphological updating) due to waves acting on a single shore-parallel SBW located on a schematised beach with parallel depth contours. In total 92 coupled wave–current simulations were undertaken. The results indicate that the mode of shoreline response to the SBW can be expressed in terms of the two non-dimensional parameters h_B/H₀ and (s_B/h_B)^3/2(L_B/h_B)²(A³/h_B)^1/2 (variables defined in the text).