Deep-water Waves Research Articles

Wave Runup Over Steep Rocky Cliffs

AbstractWave runup is known to depend on offshore wave conditions and coastal morphology. While most field studies on wave runup have focused on low‐to‐mild‐sloping sandy beaches, runup measurements on steep and irregular rocky cliff profiles are still very scarce. Here we investigate the physical processes controlling wave runup in such environments and the range of applicability of empirical runup formula. This study focuses on the steep rocky cliffs (0.1 < tanβ < 0.4) of Banneg Island, a small island located in the Molène archipelago, Brittany, France, occasionally flooded during extreme water level events. A statistical parameter for extreme runup is derived from the measurements of pressure sensors deployed in the intertidal zone. Deep water wave parameters are used to force a high‐resolution wave model, and nearshore wave parameters and high‐resolution topographic data are analyzed concurrently with runup time series in order to assess the dependence of the runup on hydrodynamic conditions and morphological parameters. The wave runup is shown to be strongly related to the square root of the offshore significant wave height times the offshore wavelength. The measurements also reveal the depth dependence of the runup, which is mainly attributed to the curvature of the foreshore profile. In comparison to empirical relation obtained for a mild‐sloping beach, the present data show a significant reduction in normalized wave runup, that is attributed to enhanced bottom friction over the rocky bottom.

Near and far-field hazards of asteroid impacts in oceans

Hazards resulting from asteroid ocean impacts were modelled using hydrocode simulations to examine the near-field effects including the initial formation and subsequent long range propagation of tsunami waves that can transport potentially damaging energy far from the impact site.Three-dimensional simulations of oblique impacts into deep water, with trajectory angles ranging from 27° to 60° above the horizontal, were performed with the Los Alamos Rage hydrocode. The simulations include atmospheric effects such as ablation and airbursts. These oblique impact simulations are performed in order to help determine whether there are additional dangers due to the obliquity of impact not covered by previous studies. The energy transferred to both the air blast wave and the water are calculated as well as the amount of sea water lofted into the upper atmosphere. Water crater sizes and subsequent surface elevation profiles, surface pressures, and depth-averaged mass fluxes within the water are prepared for use in far-field propagation studies. Like previous three-dimensional simulations, these simulations show that except at exceedingly shallow entry angles below those simulated here the resulting waves are roughly circular and that the initial waves and central jet oscillation are highly turbulent and dissipate a lot of the energy.Two-dimensional axisymmetric simulations of long range propagation of impact tsunami were performed using the Lawrence Livermore ALE3D hydrocode on the NASA Pleiades supercomputer. These simulations showed that impacts under 1 gigaton TNT equivalent into the deep ocean basins will create deep-water waves that undergo dispersion, whereas impacts onto continental shelves will create shallow-water waves that do not suffer dispersion. The simulations also showed that on the order of 1% of the kinetic energy of the impact is converted into the tsunami wave. This is an order of magnitude less than previous semi-empirical estimates of ∼15% based on explosion test data and laboratory scale impacts.

Free Surface Reconstruction for Phase Accurate Irregular Wave Generation

The experimental wave paddle signal is unknown to the numerical modellers in many cases. This makes it quite challenging to numerically reproduce the time history of free surface elevation for irregular waves. In the present work, a numerical investigation is performed using a computational fluid dynamics (CFD) based model to validate and investigate a non-iterative free surface reconstruction technique for irregular waves. In the current approach, the free surface is reconstructed by spectrally composing the irregular wave train as a summation of the harmonic components coupled with the Dirichlet inlet boundary condition. The verification is performed by comparing the numerically reconstructed free surface elevation with theoretical input waves. The applicability of the present approach to generate irregular waves by reconstructing the free surface is investigated for different coastal and marine engineering problems. A numerical analysis is performed to validate the free surface reconstruction approach to generate breaking irregular waves over a submerged bar. The wave amplitudes, wave frequencies and wave phases are modelled with good accuracy in the time-domain during the higher-order energy transfers and complex processes like wave shoaling, wave breaking and wave decomposition. The present approach to generate irregular waves is also employed to model steep irregular waves in deep water. The free surface reconstruction method is able to simulate the irregular free surface profiles in deep water with low root mean square errors and high correlation coefficients. Furthermore, the irregular wave forces on a monopile are investigated in the time-domain. The amplitudes and phases of the force signal under irregular waves generated by using the current technique are modelled accurately in the time-domain. The proposed approach to numerically reproduce the free surface elevation in the time-domain provides promising and accurate results for all the benchmark cases.

Experimental investigation of nonlinear internal waves in deep water with miscible fluids

Laboratory experimental results are presented for nonlinear internal solitary waves (ISW) propagation in ‘deep water’ configuration with miscible fluids. The results are validated against direct numerical simulations and traveling wave exact solutions where the effect of the diffused interface is taken into account. The waves are generated by means of a dam break and their evolution is recorded with laser-induced fluorescence and particle image velocimetry. In particular, data collected in a frame moving with the waves are presented here for the first time. Our results are representative of geophysical applications in the deep ocean where weakly nonlinear theories fail to capture the characteristics of large amplitude ISWs from field observations.

Recent Sedimentation of a Mesotidal Wave-Dominated River Mouth: Lach Van, Vietnam

ABSTRACT Chien, N.Q. and Tung, T.T., 2018. Recent sedimentation of a mesotidal wave-dominated river mouth: Lach Van, Vietnam. In: Almar, R.; Almeida, L.P.; Viet, N.T., and Sall, M. (eds.), Tropical Coastal and Estuarine Dynamics. Journal of Coastal Research, Special Issue No. 81, pp. 50–56. Coconut Creek (Florida), ISSN 0749-0208 The sedimentation of a wave-dominated river mouth in Tonkin Gulf, Vietnam, has been investigated for the time period 2005–2017. Deepwater wave statistics and the potential longshore sediment transport (LST) has been determined, which shows a net LST rate of ~105 m3/yr southward. A one-line model is used to estimate the change in local coastline; the model is verified against shoreline position data obtained from satellite images. It is apparent that the accretion occurs on both sides of the river mouth with a rate of ~10 m/yr. Coastline evolution trend is then predicted for the aforementioned time period, and results show evidences that accretion is intensifying in recent years, ...

High frequency resonant response of a monopile in irregular deep water waves

Experiments with a weakly damped monopile, either fixed or free to oscillate, exposed to irregular waves in deep water, obtain the wave-exciting moment and motion response. The nonlinearity and peak wavenumber cover the ranges: $\unicode[STIX]{x1D716}_{P}\sim 0.10{-}0.14$ and $k_{P}r\sim 0.09{-}0.14$ where $\unicode[STIX]{x1D716}_{P}=0.5H_{S}k_{P}$ is an estimate of the spectral wave slope, $H_{S}$ the significant wave height, $k_{P}$ the peak wavenumber and $r$ the cylinder radius. The response and its statistics, expressed in terms of the exceedance probability, are discussed as a function of the resonance frequency, $\unicode[STIX]{x1D714}_{0}$ in the range $\unicode[STIX]{x1D714}_{0}\sim 3{-}5$ times the spectral peak frequency, $\unicode[STIX]{x1D714}_{P}$. For small wave slope, long waves and $\unicode[STIX]{x1D714}_{0}/\unicode[STIX]{x1D714}_{P}=3$, the nonlinear response deviates only very little from its linear counterpart. However, the nonlinearity becomes important for increasing wave slope, wavenumber and resonance frequency ratio. The extreme response events are found in a region where the Keulegan–Carpenter number exceeds $KC>5$, indicating the importance of possible flow separation effects. A similar region is also covered by a Froude number exceeding $Fr>0.4$, pointing to surface gravity wave effects at the scale of the cylinder diameter. Regarding contributions to the higher harmonic forces, different wave load mechanisms are identified, including: (i) wave-exciting inertia forces, a function of the fluid acceleration; (ii) wave slamming due to both non-breaking and breaking wave events; (iii) a secondary load cycle; and (iv) possible drag forces, a function of the fluid velocity. Also, history effects due to the inertia of the moving pile, contribute to the large response events. The ensemble means of the third, fourth and fifth harmonic wave-exciting force components extracted from the irregular wave results are compared to the third harmonic FNV (Faltinsen, Newman and Vinje) theory as well as other available experiments and calculations. The present irregular wave measurements generalize results obtained in deep water regular waves.

Integral and Asymptotic Properties of Solitary Waves in Deep Water

AbstractWe consider two‐ and three‐dimensional gravity and gravity‐capillary solitary water waves in infinite depth. Assuming algebraic decay rates for the free surface and velocity potential, we show that the velocity potential necessarily behaves like a dipole at infinity and obtain a related asymptotic formula for the free surface. We then prove an identity relating the “dipole moment” to the kinetic energy. This implies that the leading‐order terms in the asymptotics are nonvanishing and in particular that the angular momentum is infinite. Lastly we prove that the “excess mass” vanishes. © 2018 the Authors. Communications on Pure and Applied Mathematics is published by the Courant Institute of Mathematical Sciences and Wiley Periodicals, Inc.

On the phase dependence of the soliton collisions in the Dyachenko–Zakharov envelope equation

Abstract. We study soliton collisions in the Dyachenko–Zakharov equation for the envelope of gravity waves in deep water. The numerical simulations of the soliton interactions revealed several fundamentally different effects when compared to analytical two-soliton solutions of the nonlinear Schrodinger equation. The relative phase of the solitons is shown to be the key parameter determining the dynamics of the interaction. We find that the maximum of the wave field can significantly exceed the sum of the soliton amplitudes. The solitons lose up to a few percent of their energy during the collisions due to radiation of incoherent waves and in addition exchange energy with each other. The level of the energy loss increases with certain synchronization of soliton phases. Each of the solitons can gain or lose the energy after collision, resulting in increase or decrease in the amplitude. The magnitude of the space shifts that solitons acquire after collisions depends on the relative phase and can be either positive or negative.

Laboratory study of the effect of vertically varying vegetation density on waves, currents and wave-current interactions

Under the influence of vegetation, waves, currents, turbulence as well as sediment processes are all changed, which significantly affect aquatic environment. Vegetation appears spatially heterogeneous in terms of vegetation density in most natural wetlands. However, how vertical heterogeneity of vegetation canopy affects turbulence under waves and currents is still not well understood. In this paper, the effects of different vegetation densities (i.e. sparse, dense and vertically-varying density) on vegetation-induced wave attenuation, mean flow adjustment as well as turbulence are studied through laboratory experiments. For regular waves, higher vegetation density results in smaller wave transmission coefficients and local wave heights. The difference between the effects of vertically uniform and varying vegetation density on wave height decay is significant for deep water waves and insignificant for intermediate water waves. The vertically varying vegetation density slightly changes the wave-averaged velocity distribution, producing reverse flows within the canopy. Turbulence intensity decreases more significantly with increasing water depth in the case with vertically varying vegetation density. For unidirectional flow, the vertically varying vegetation density increases the vertical gradient of mean streamwise velocity compared with the emergent uniform vegetation. The time series of u oscillates relatively stronger near bottom, and causes higher TKE, which is different with that in oscillatory flow. Compared with the submerged uniform vegetation, the vertical variation of mean velocity affected by vegetation with vertically varying density is smaller in both pure current and wave-current flow. Affected by dense submerged vegetation, the mean velocity of combined wave-current flow is significantly lower than that of pure current, while it is reduced near the bottom and increased in the upper layer comparing with that of pure current under the influence of sparse submerged vegetation. TKE values in wave-current flow is promoted in the upper layer with coexisting waves in the case of submerged uniform vegetation, while it is barely affected near the bed. In the case with vertically varying vegetation density, TKE values in the wave-current flow are slightly decreased than that in the pure current condition, especially near the bottom.

Coastal erosion in the south-eastern Mediterranean: case of beaches in North Tunisia

This research is conducted as part of a Spanish International Cooperation Agency project with the aim to investigate the sustainable protection of Tunisian coastal zones, as in the case of Beni Khiar and Dar Chaabane coasts (Hammamet Gulf) separated by Oued El Kebir river. The sedimentary dynamic of these beaches is studied in order to identify the main causes responsible for their erosion by the use of different approaches of in situ measurements and numerical methods. Geophysical surveys and sedimentary analyses have demonstrated that sediments are finer and less carbonated from Beni Khiar to Dar Chaabane. Then, the shoreline mapping of several missions of aerial photos has illustrated a mean shoreline retreat between 3 and 4 m/year. In terms of sand volume, a sediment loss more than 30,000 m3/year at Dar Chaabane has been observed since the hill lake structures were built within Oued El Kebir river in 1996. Finally, modelled hydrodynamic and sedimentary patterns have illustrated the refraction of waves in deep water close to shoals and a high-energy concentration along Dar Chaabane coast. The sediment transport direction is mainly of NE-SW induced by ESE-SE wave-driven alongshore current. Results provided by these approaches have shown the importance of Oued El Kebir sediment yield in supplying the neighbouring beaches. Changes in sedimentary dynamics are affected by the modification of hydrodynamic patters caused by the presence of hydrological dams and the implementations of hotels close to the shoreline. This finding underlines the key role of Oued El Kebir fluvial activity in controlling the equilibrium of beaches and their sensitivity to coastal managements induced by man activities, as in the case of the most Mediterranean beaches.

A note on the secondary load cycle for a monopile in irregular deep water waves

Laboratory experiments with a bottom hinged surface-piercing cylinder, exposed to irregular deep water waves, are used to investigate high-frequency forcing. The focus is on the secondary load cycle, a strongly nonlinear phenomenon regarding the wave load on a vertical cylinder, first identified by Grue et al. (1993 Preprint Series. Mechanics and Applied Mathematics, pp. 1–30. University of Oslo, available at http://urn.nb.no/URN:NBN:no-52740; 1994 Ninth International Workshop on Water Waves and Floating Bodies (ed. M. Ohkusu), pp. 77–81, available at http://iwwwfb.org). For a total of 2166 single wave events, the force above $3\unicode[STIX]{x1D714}$ (where $\unicode[STIX]{x1D714}$ is the governing wave frequency) is used to identify and split the strongly nonlinear forces into two peaks: a high-frequency peak closely correlated in time with the wave crest when the total load is positive and a high-frequency peak defining the secondary load cycle which occurs close in time to the wave zero downcrossing when the total load is negative. The two peaks are studied by regression analysis as a function of either the Keulegan–Carpenter number ($KC$) or the Froude number ($Fr$). Regarding the secondary load cycle, the best correlation is found with $Fr$. The speed of the travelling edge of the undisturbed wave approximates the fluid velocity. A threshold value separating between small and large forces is found for $KC\sim 4$–5, indicating effects of flow separation. Alternatively, the threshold occurs for $Fr\sim 0.3$–0.4, indicating local wave effects at the scale of the cylinder diameter. The findings suggest that both effects are present and important.

Fully nonlinear capillary–gravity solitary waves under a tangential electric field, Part II: Dynamics

The stability and dynamics of two-dimensional fully nonlinear capillary–gravity solitary waves are studied when a uniform electric field is applied in the direction parallel to the undisturbed free surface of a dielectric fluid. For simplicity, we assume that the permittivity of the gas above the fluid is much smaller, therefore the two-layer problem can be reduced to be a one-layer one. The existence of fully localized solitary waves in deep water has been thoroughly studied in our previous work (Tao and Guo, 2014) via weakly nonlinear normal form analysis and fully nonlinear numerical computation. In the present paper, the stability and dynamics of the obtained solitary waves are investigated based on the time-dependent conformal map technique. Similar to the nonelectric capillary–gravity solitary waves, all depression waves, together with elevation waves featuring two big troughs connected by a small dimple, are found to be stable. Furthermore, head-on and overtaking collisions between stable solitary waves are studied via a numerical time integration.

Material Transport under a Wave Train in Interaction with Constant Wind: A Eulerian RANS Approach Combined with a Lagrangian Particle Dispersion Model

The interaction of a developed train of gravity deep water waves with suddenly applied winds is investigated in this manuscript. The direction of the wind is the same as that of the wave train (i.e., following) and its imposed surface shear stress is constant and steady. The focus of this study is on a micro-scale water wave field where the time scale is on the order of ten wave periods and the length scale is on the order of ten wave lengths. Accurate 2D Reynolds-averaged Navier–Stokes (RANS) multi-phase simulations of Navier–Stokes equations are performed in a Eulerian framework to capture the flow features, induced by the wave field and the surface wind. The sufficiently large spatial domain in the horizontal direction, combined with the sufficiently long simulation time, permits the development of surface currents and the consequent formation of a near-surface shear layer. The interaction of surface currents with the wave orbital velocity field results in the generation of spilling breaking waves. Downstream of the domain, vertical turbulent structures are observed as the result of such breaking waves. Lagrangian particle tracking is performed, using the RANS simulation velocity and eddy diffusivity data. A second order random acceleration particle tracking method is applied with the vitally important spatial gradients of the eddy diffusivity (Journal of Marine Science and Engineering, 2018, 6, 10.3390/jmse6010007.) also included in calculations. The spatial gradients of the eddy diffusivity were proved to be a key factor in material transport simulations. Our particle tracking results exhibit strong vertical mixing downstream of the domain and by means of visualizing the spiral trajectory of neutrally buoyant particles. Such enhanced vertical mixing (caused by horizontal winds) is the result of the strong near-surface advection (induced by currents) and the turbulence (induced by breaking waves). The objectives of this paper are twofold. Firstly, a numerical approach to simulate wind breaking waves is proposed based on: using K − ϵ RANS model to capture turbulence features, employing the Volume of Fluid Method (VOF) to model the free surface flow, and applying a constant shear stress body force at the interfacial cells to simulate the wind force. Such treatment of the winds eliminates the need for fully resolving the air phase. The computed eddy viscosity profiles are in good agreement with the experimental profiles reported in the literature ( ν t = − κ u * z , Journal of Physical Oceanography, 1977, 7, pp. 248–255; Journal of Physical Oceanography, 1984, 14, pp. 855–863). Secondly, effects of the horizontally applied wind on the vertical mixing and eddy viscosity profiles on the water column are studied. It is observed that, away from the surface and outside the shear layer, the negative horizontal gradient of eddy diffusivity (induced by the dampening effect of breaking surface waves), combined with the downwards advection velocities (induced by breaking waves), results in an enhanced vertical mixing and reduced horizontal drift of transported material.

On the incomplete recurrence of modulationally unstable deep-water surface gravity waves

The issue of a recurrence of modulationally unstable water wave trains within the framework of the fully nonlinear potential Euler equations is addressed. It is examined, in particular, if a modulation, which appears from nowhere (i.e., is infinitesimal initially) and generates a rogue wave, can disappear with no trace. If so, this wave solution would be a breather solution of the primitive hydrodynamic equations. It is shown with the help of the fully nonlinear numerical simulation that when a rogue wave emerges from a uniform Stokes wave train, it excites other waves which have different lengths. This process prevents the complete recurrence and, eventually, results in a quasi-periodic breathing of the wave envelope. Meanwhile the discovered effects are rather small in magnitude, and the period of the modulation breathing may be thousands of the dominant wave periods. Thus, the obtained solution may be called a quasi-breather of the Euler equations.

Design, analysis and verification of a volume-of-fluid model with interface-capturing scheme

The Volume-of-Fluid (VoF) model with interface-capturing scheme, available in many commercial and open-source CFD packages, may be widely used for simulations of free-surface hydrodynamics but is certainly not used without difficulties. While practitioners have come to expect conservation of mass and momentum, unconditional stability, second-order of accuracy and good iterative convergence, none of these qualities are evident when a free surface gets involved. In this paper, we investigate how these qualities are affected by the discontinuous nature of the volume fraction, which requires specialized numerical techniques for advection, for the interpolation of material properties, for the hydrostatic balance and for the pressure-weighted interpolation used in finite-volume methods with co-located variables. We find that conservation properties and good iterative convergence can still be attained, but not second-order of accuracy and unconditional stability. Code verification is presented to substantiate these findings, with cases ranging from one to three dimensions, from uniform to locally refined grids and from the stand-alone volume fraction equation to the complete set of mass, momentum and volume fraction equations. For the latter, a novel manufactured solution based on a sinusoidal wave in deep water is introduced. These tests permit not only to quantitatively assess the results for comparison with theoretical predictions but also ensure that our findings are characteristic of the VoF method and not of a particular implementation.

Kinematics and dynamics of green water on a fixed platform in a large wave basin in focusing wave and random wave conditions

Green water kinematics and dynamics due to wave impingements on a simplified geometry, fixed platform were experimentally investigated in a large, deep-water wave basin. Both plane focusing waves and random waves were employed in the generation of green water. The focusing wave condition was designed to create two consecutive plunging breaking waves with one impinging on the frontal vertical wall of the fixed platform, referred as wall impingement, and the other directly impinging on the deck surface, referred as deck impingement. The random wave condition was generated using the JONSWAP spectrum with a significant wave height approximately equal to the freeboard. A total of 179 green water events were collected in the random wave condition. By examining the green water events in random waves, three different flow types are categorized: collapse of overtopping wave, fall of bulk water, and breaking wave crest. The aerated flow velocity was measured using bubble image velocimetry, while the void fraction was measured using fiber optic reflectometry. For the plane focusing wave condition, measurements of impact pressure were synchronized with the flow velocity and void fraction measurements. The relationship between the peak pressures and the pressure rise times is examined. For the high-intensity impact in the deck impingement events, the peak pressures are observed to be proportional to the aeration levels. The maximum horizontal velocities in the green water events in random waves are well represented by the lognormal distribution. Ritter’s solution is shown to quantitatively describe the green water velocity distributions under both the focusing wave condition and the random wave condition. A prediction equation for green water velocity distribution under random waves is proposed.

Characterizing the Longshore Sediment Transport Pattern on Beaches in the Gulf of Arauco, Chile, to Assess Morphological Shoreline Evolution

Gomez, M.; Villagran, M.; Martinez, C., and Belmonte, A., 2018. Characterizing the Longshore Sediment Transport Pattern on Beaches in the Gulf of Arauco, Chile, to Assess Morphological Shoreline Evolution. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 656–660. Coconut Creek (Florida), ISSN 0749-0208.Coastal evolution is an important research topic worldwide and has become increasingly relevant due to growing anthropogenic pressure on the coast and a climate change scenario (Masselink et al., 2016). The Gulf of Arauco covers an area of roughly 40,000 km2 and has a sandy-rocky coastline located in a very seismic environment. The area has suffered several major earthquakes during the last century (Valdivia 1960, Maule 2010) and seismic displacement has widely affected the coastline (Bejar-Pizarro et al., 2010). Despite these findings, the morphological evolution of sandy coastlines is mainly caused by wave-driven littoral processes. In this paper, using numerical modeling (Delft3D), we aim to characterize the longshore sediment transport (LST) direction at several spots (7 beaches) spread along the coastline of the Gulf of Arauco. Wave patterns were identified at each study site, revealing the importance of Santa Maria Island, located at the entrance to the gulf, despite the approach direction of deep water waves. The island acts as a moderator of wave patterns, softening the highly energetic swell that comes from the Antarctic Ocean and sorting the wave propagation inside the gulf. Moreover, LST patterns were characterized at each site for dominant wave conditions (SW swell and NW winter storms) and it was possible to explain how each condition has a different response at each spot, even under similar co-seismic displacements. Adaptation capabilities differ from site to site, suggesting a dynamic equilibrium of beaches in the area.

Energy Dissipation in the Inner Surf Zone: New Insights From LiDAR‐Based Roller Geometry Measurements

AbstractThe spatial and temporal variation of energy dissipation rates in breaking waves controls the mean circulation of the surf zone. As this circulation plays an important role in the morphodynamics of beaches, it is vital to develop better understanding of the energy dissipation processes in breaking and broken waves. In this paper, we present the first direct field measurements of roller geometry extracted from a LiDAR data set of broken waves to obtain new insights into wave energy dissipation in the inner surf zone. We use a roller model to show that most existing roller area formulations in the literature lead to considerable overestimation of the wave energy dissipation, which is found to be close to, but smaller than, the energy dissipation in a hydraulic jump of the same height. The role of the roller density is also investigated, and we propose that it should be incorporated into modified roller area formulations until better knowledge of the roller area and its link with the mean roller density is acquired. Finally, using previously published results from deepwater wave breaking studies, we propose a scaling law for energy dissipation in the inner surf zone, which achieves satisfactory results at both the time‐averaged and wave‐by‐wave scales.

Estimation of Depth of Closure Near Gangneung Port in Korea

Kang, H., Chun, I., and Oh, B., 2018. Estimation of the Depth of Closure Near Gangneung Port in Korea. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1361–1365. Coconut Creek (Florida), ISSN 0749-0208.Various methods to cope with coastal erosion have been tried in the East Coast of Korea, among which the regional sediment management (RSM) is now being perceived as a very efficient way for managing limited sand resources in a macroscopic scale in both time and space. To apply RSM, it is necessary to set up the littoral cell, a control volume concept whose offshore boundary is given by the depth of closure (DOC). In this study, an independent littoral cell near Gangneung Port was set up, and a method to determine its DOC was proposed and applied utilizing the existing data of deep-water wave climate. Within the method, several formulas were tested, and the results showed that that the average DOC of the study area varied from 10 m to 52 m depending on sediment size, wave condition, and the formula used. Finally, the Hallermeier's formula of outer DOC was postulated to give a reasonable DOC of the Gangneung littoral cell.

Extreme wave formation in unidirectional sea due to stochastic wave phase dynamics

The authors consider a stochastic model based on the interaction and phase coupling amongst wave components that are modified envelope soliton solutions to the nonlinear Schrödinger equation. A probabilistic study is carried out and the resulting findings are compared with ocean wave field observations and laboratory experimental results. The wave height probability distribution obtained from the model is found to match well with prior data in the large wave height region. From the eigenvalue spectrum obtained through the Inverse Scattering Transform, it is revealed that the deep-water wave groups move at a speed different from the linear group speed, which justifies the inclusion of phase correction to the envelope solitary wave components. It is determined that phase synchronization amongst elementary solitary wave components can be critical for the formation of extreme waves in unidirectional sea states.