Statistical model on the surface elevation of waves with breaking

In the surface wind drift layer with constant momentum flux, two sets of the consistent surface eleva- tion expressions with breaking and occurrence conditions for breaking are deduced from the first in- tegrals of the energy and vortex variations and the kinetic and mathematic breaking criterions, then the expression of the surface elevation with wave breaking is established by using the Heaviside function. On the basis of the form of the sea surface elevation with wave breaking and the understanding of small slope sea waves, a triple composite function of real sea waves is presented including the func- tions for the breaking, weak-nonlinear and basic waves. The expression of the triple composite func- tion and the normal distribution of basic waves are the expected theoretical model for surface elevation statistics.     

Evaluating crude oil chemical dispersion efficacy in a flow-through wave tank under regular non-breaking wave and breaking wave conditions

Testing dispersant effectiveness under conditions similar to that of the open environment is required for improvements in operational procedures and the formulation of regulatory guidelines. To this end, a novel wave tank facility was fabricated to study the dispersion of crude oil under regular non-breaking and irregular breaking wave conditions. This wave tank facility was designed for operation in a flow-through mode to simulate both wave- and current-driven hydrodynamic conditions. We report here an evaluation of the effectiveness of chemical dispersants (Corexit^® EC9500A and SPC 1000^™) on two crude oils (Medium South American [MESA] and Alaska North Slope [ANS]) under two different wave conditions (regular non-breaking and plunging breaking waves) in this wave tank. The dispersant effectiveness was assessed by measuring the water column oil concentration and dispersed oil droplet size distribution. In the absence of dispersants, nearly 8-19% of the test crude oils were dispersed and diluted under regular wave and breaking wave conditions. In the presence of dispersants, about 21-36% of the crude oils were dispersed and diluted under regular waves, and 42-62% under breaking waves. Consistently, physical dispersion under regular waves produced large oil droplets (volumetric mean diameter or VMD ? 300 μm), whereas chemical dispersion under breaking waves created small droplets (VMD ? 50 μm). The data can provide useful information for developing better operational guidelines for dispersant use and improved predictive models on dispersant effectiveness in the field.     

Frequency-Dependent Energy Dissipation of Irregular Breaking Waves

Results of field experiments and simulation are used to study the hypothesis that energy dissipation from irregular breaking waves can have a nonuniform distribution over the frequency. It was found that the wave energy dissipation in the outer surf zone is practically independent of the frequency and can be approximated by a constant. A quadratic or a selective (at the frequency band of second–third harmonics) dependence of energy dissipation on frequency was found to form in the inner part of the surf zone, where it is controlled by wave asymmetry and bed slope. The dissipation of the energy of breaking waves was shown to proceed in such a way as to compensate for the effect of processes of linear or nonlinear deformation of waves.     

An experimental comparison of the velocities and energies of focused spilling waves in deep water

Ocean Dynamics - It is important to achieve a better understanding of the wave energy variations occurring as a steep wave evolves towards breaking. Laboratory experiments of focused waves are...     

Statistics of breaking waves and its applications to estimation of air-sea fluxes (Ⅰ)——Theoretical models

Wave breaking statistics, such as the whitecap coverage and average volume of broken seawater, are evaluated in terms of wave parameters by use of wave breaking model (Yuan et al., 1988) taking the fifth order Stokes's wave as the analog of the original wave field. Based on the observed fact that breaking waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean, the influence of wave breaking on air-sea fluxes of heat and moisture is investigated. Theoretical expressions of bubble-volume flux and sea spray spectrum at the sea surface and models for bubble-induced and spray droplet-induced heat and moisture fluxes are established. This work can be taken as the basis for further understanding the mechanism of air-sea coupling and parameterization models.     

Statistics of breaking waves and its applications to estimation of air-sea fluxes (I)--Theoretical models

Wave breaking statistics, such as the whitecap coverage and average volume of broken seawater, are evaluated in terms of wave parameters by use of wave breaking model (Yuan et al., 1988) taking the fifth order Stokes's wave as the analog of the original wave field. Based on the observed fact that breaking waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean, the influence of wave breaking on air-sea fluxes of heat and moisture is investigated. Theoretical expressions of bubble-volume flux and sea spray spectrum at the sea surface and models for bubble-induced and spray droplet-induced heat and moisture fluxes are established. This work can be taken as the basis for further understanding the mechanism of air-sea coupling and parameterization models.     

Steep wave,turbulence, and sediment concentration statistics beneath a breaking wave field and their implications for sediment transport

A new methodology based on wavelet analysis is used to estimate steep wave statistics under depth-limited conditions and the corresponding high concentration sediment statistics. Steep waves here are defined as wave crests within the wavelet transform exceeding a root mean square derived acceleration threshold. The method is applied to laboratory data obtained in a large-scale wave-flume experiment conducted in 2005 at Oregon State University's O. H. Hinsdale Wave Research Laboratory from an acoustic Doppler velocimeter and a fiber optic backscatter sensor array above a mobile sand bed. The steep wave and high concentration statistical results for the erosive condition suggest that sand suspensions are intermittent when a wave-breaking timescale (the ratio of breaking wave height and rms wave velocity) is used to detect the concurrence among steep wave, high velocity turbulent fluctuations, and sand concentration events near the bed. More importantly, at 1 cm above the bed, though the accretive case has more steep wave events, the erosive case has more steep waves and concurrent high concentration events, suggesting a more intense breaking wave process near the sensors. The use of a longer time window, based on the dominant wave period in the detection process of steep wave and high concentration events at 1 cm above the bed, does not change the resulting statistics for the erosive condition. However, increased percentages of high concentration events correlated with steep wave and high velocity turbulence events for the accretive condition are obtained. These increased percentages are conjectured to be due to advection of non-local turbulent events and sediment concentration peaks from upstream.     

Why ripples become sweiis,and swells in shallow water decay rapidly

Abstract

In an ocean with a horizontal bottom where no wind is blowing it is shown that the spin (angular momentum) of the ocean is conserved. Thus, when energy is dissipated, at least one of three things will happen: i) Wave spectra may move towards lower frequencies. ii) The directional distribution may be changed towards long-crested waves. iii) Shear currents may be generated. By neglecting ii) and iii), the frequency shift of a spectrum is calculated due to molecular dissipation. When all energy transforming phenomena as e.g. wave breaking and turbulence generation are taken into account, the conservation of spin seems to be able to explain the frequency shift of wave spectra. In shallow water it is shown that there is energy transfer from the waves to shear currents.     

Longshore variations in nearshore wave processes at magilligan point,northern ireland

Magilligan Point is a recurved cuspate foreland at the mouth of Lough Foyle. Two wave regimes intersect in the estuary mouth and the manner of their interplay controls shoreline changes. Ocean swell waves from the N and NE are refracted around the recurve, losing both height and energy longshore. Width of the surf zone decreases and waves tend to steepen, although both these changes and wave refraction owe something to nearshore geometry. Angle of wave approach becomes more acute and a westerly flowing longshore current moves sand S and SW along the beach. Estuary waves from the S and SW are wind-driven with high-frequencies and steepnesses. They generate a northeasterly current which returns material N, but dies out as the waves become obliterated by nearshore attenuation and breaking of swell. It is possible to identify a time-averaged null-point where shoreline wave power is balanced, although this tends to shift over short periods causing rapid morphological changes. The existence of two independent, but counteractive cells ensures the long-term maintenance of the foreland, without requiring major or continuous supplies of fresh sediment.     

Statistics of breaking waves and its applications to estimation of air-sea fluxes (I)

Wave breaking statistics, such as the whitecap coverage and average volume of broken seawater, are evaluated in terms of wave parameters by use of wave breaking model (Yuan et al., 1988) taking the fifth order Stokes’s wave as the analog of the original wave field. Based on the observed fact that breaking waves play an important role in the exchange of mass, momentum and energy between the atmosphere and the ocean, the influence of wave breaking on air-sea fluxes of heat and moisture is investigated. Theoretical expressions of bubble-volume flux and sea spray spectrum at the sea surface and models for bubble-induced and spray droplet-induced heat and moisture fluxes are established. This work can be taken as the basis for further understanding the mechanism of air-sea coupling and parameterization models.     

Observations of coastal cliff base waves,sand levels,and cliff top shaking

Concurrent observations of waves at the base of a southern California coastal cliff and seismic cliff motion were used to explore wave–cliff interaction and test proxies for wave forcing on coastal cliffs. Time series of waves and sand levels at the cliff base were extracted from pressure sensor observations programmatically and used to compute various wave impact metrics (e.g. significant cliff base wave height). Wave–cliff interaction was controlled by tide, incident waves, and beach sand levels, and varied from low tides with no wave–cliff impacts, to high tides with continuous wave–cliff interaction. Observed cliff base wave heights differed from standard Normal and Rayleigh distributions. Cliff base wave spectra levels were elevated at sea swell and infragravity frequencies. Coastal cliff top response to wave impacts was characterized using microseismic shaking in a frequency band (20–45 Hz) sensitive to wave breaking and cliff impacts. Response in the 20–45 Hz band was well correlated with wave–cliff impact metrics including cliff base significant wave height and hourly maximum water depth at the cliff base (r² = 0.75). With site‐specific calibration relating wave impacts and shaking, and acceptable anthropogenic (traffic) noise levels, cliff top seismic observations are a viable proxy for cliff base wave conditions. The methods presented here are applicable to other coastal settings and can provide coastal managers with real time coastal conditions. Copyright © 2016 John Wiley & Sons, Ltd.     

Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf, submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.     

Links between wave forcing,offshore islands and a macro‐tidal headland‐bound bay beach

Profiles were analysed in conjunction with wave climate to assess offshore island influences on an embayed beach at Tenby, Wales. Time series analyses showed medium and short‐term beach oscillation, with volume exchanges between zones lagging by up to six months. Dominant southerly and southwesterly waves caused sub and low tidal longshore drift from south towards north, while less frequent southeasterly waves generated counter drift. Modelled inshore breaking waves had less energy than offshore ones and the former behaved differently between the low and high tidal zones (spring tidal range of 7 · 5 m). Variations in wave direction from directly behind the islands resulted in reduced wave heights and statistical analyses agreed with wave model results. These were correlated to morphological change and it was concluded that offshore islands change wave dynamics and modify the morphology of embayed beaches in their lee. Consequently, this work provides significant new insights into offshore island influences, shoreline behaviour and especially tidal setting Copyright © 2013 John Wiley & Sons, Ltd.     

Erosion and accretion processes in a muddy dissipative coast,the Chao Phraya River delta,Thailand

Seasonal variation in seabed elevation in the muddy intertidal zone of the Chao Phraya River delta, an area of serious coastal erosion for 40 years, was assessed using information on waves and tides predicted by numerical simulations. The study area is under the influence of the Southeast Asian monsoon climate and lies in the innermost part of a sheltered gulf, across which a low‐gradient slope has developed. Observations, aimed at evaluating the effectiveness of a prototype breakwater on mitigating coastal erosion, indicated that the seasonal variation in the seabed elevation, typically about 30 cm, was caused primarily by seasonal changes in wave direction and height. The breakwater seems to have contributed to a net rise in the seabed level at sites behind the structure. Seabed erosion was most apparent during the northeast monsoon, when waves are weak. Erosion under this low wave energy state was attributed to the combined effect of wave breaking and the low tidal level. A difference in the observed seabed accretion rate between the transitional intermonsoon period and the succeeding southwest monsoon period was attributed to the direction of the wave energy flux; offshore sediments seem to have been supplied efficiently to the study area by waves during the transitional period. Another potential cause of seabed erosion and accretion during the wet southwest monsoon season was the discharge of water and sediments from local canals associated with intense tropical rainfall; this discharge seems to be linked to land use in the coastal area. The results of this study show the importance of monitoring across‐shore sediment transport for better understanding of coastal erosion processes. Copyright © 2010 John Wiley & Sons, Ltd.     

Wave transformation across a macrotidal shore platform under low to moderate energy conditions

We investigate how waves are transformed across a shore platform as this is a central question in rock coast geomorphology. We present results from deployment of three pressure transducers over four days, across a sloping, wide (~200 m) cliff‐backed shore platform in a macrotidal setting, in South Wales, United Kingdom. Cross‐shore variations in wave heights were evident under the predominantly low to moderate (significant wave height < 1.4 m) energy conditions measured. At the outer transducer 50 m from the seaward edge of the platform (163 m from the cliff) high tide water depths were 8+ m meaning that waves crossed the shore platform without breaking. At the mid‐platform position water depth was 5 m. Water depth at the inner transducer (6 m from the cliff platform junction) at high tide was 1.4 m. This shallow water depth forced wave breaking, thereby limiting wave heights on the inner platform. Maximum wave height at the middle and inner transducers were 2.41 and 2.39 m, respectively, and significant wave height 1.35 m and 1.34 m, respectively. Inner platform high tide wave heights were generally larger where energy was up to 335% greater than near the seaward edge where waves were smaller. Infragravity energy was less than 13% of the total energy spectra with energy in the swell, wind and capillary frequencies accounting for 87% of the total energy. Wave transformation is thus spatially variable and is strongly modulated by platform elevation and the tidal range. While shore platforms in microtidal environments have been shown to be highly dissipative, in this macro‐tidal setting up to 90% of the offshore wave energy reached the landward cliff at high tide, so that the shore platform cliff is much more reflective. Copyright © 2017 John Wiley & Sons, Ltd.     

ST radar observations of atmospheric waves over mountainous areas: a review

Lee and mountain waves are dominant dynamic processes in the atmosphere above mountain areas. ST VHF radars had been intensively used to investigate these wave processes. These studies are summarized in this work. After discussing features of long-period quasi-stationary lee waves, attention is drawn to the frequent occurrence of freely propagating waves of shorter periods, which seem to be more common and characteristic for wave processes generated over mountainous areas. Characteristics of these waves such as their relation to the topography and background winds, the possibility of trapping by and breaking in the tropopause region and their propagation into the stratosphere is investigated. These orographically produced waves transport energy and momentum into the troposphere and stratosphere, which is considered an important contribution to the kinetic energy of the lower atmosphere. The occurrence of inertia-gravity waves in the stratosphere had been confused with lee waves, which is discussed in conclusion. Finally further questions on mountain and lee waves are drawn up, which remain to be solved and where investigations with ST radars could play a fundamental role.     

Experimental study of near-bed concentration and sediment vertical mixing parameter for vertical concentration distribution in the surf zone

Two formulae for the near-bed concentration(C_a) and the sediment vertical mixing parameter(m) are established based on a large scale wave flume experiment.The advantage of the new formulae is that the turbulent kinetic energy induced by wave breaking can be taken into account;the formula for C_a is in terms of the near-bed,time-averaged turbulent kinetic energy,and the formula for m is in terms of depth-and time-averaged turbulent kinetic energy.A new expression for suspended sediment load also is established by depth integration of the vertical distribution of the suspended sediment concentration obtained on basis of the new formulae.Equation validation is done by comparing the predicted C_a and m to measurements for different types of waves(regular wave,wave group,and irregular wave),and good agreement is found.The advantages of the proposed formulae over previous formulae also are discussed.     

Foredune vegetation patterns and alongshore environmental gradients: Moçambique Beach,Santa Catarina Island,Brazil

This paper examines patterns of foredune vegetation along an embayment in southern Brazil and the relationships between variations in percent cover and diversity, and environmental factors such as beach/surfzone type and exposure to wind and wave energy. The study was conducted on Moçambique Beach, Brazil, which displays significant alongshore variations in exposure to the prevailing winds and waves, beach/surfzone morphodynamic type, type and dimensions of the dune systems and foredune vegetation cover and diversity. Two vegetation surveys were carried out in contiguous 1 m² quadrats across the foredune. The presence/absence, percent cover of the species, diversity and similarity between the vegetation of the profiles surveyed and their relation with environmental conditions are examined. The results show that the vegetation cover decreases from south to north, possibly reflecting the increasing exposure to wind and wave energy. Distinct patterns of species distributions occur along Moçambique beach, such that different plant species are dominant on the southern, middle and northern ends of the beach. A cluster analysis demonstrated two associations: the first one is represented by the profiles located in the lower energy zone of the beach, and the second association is represented by the profiles more exposed to wind and wave energy, sediment deposition and salt spray. The diversity of species decreases northwards, possibly influenced by the surfzone type, number of breaking waves and degree of aeolian transport. The presence/absence of the species and the vegetation cover on the foredune reflect the varying levels of exposure of the beach and foredune to the winds and waves and also reflect the volume of sediment deposition on the foredune and the beach mobility determined by the morphodynamic beach/surfzone type. Copyright © 2008 John Wiley & Sons, Ltd.     

Improvements to the statistical theoretical model for wave breaking based on the ratio of breaking wave kinetic and potential energy

An improvement was proposed for the statistical theory of breaking entrainment depth and surface whitecap coverage of real sea waves in this study. The ratio of the kinetic and potential energy was estimated on a theoretical level, and optimal constants were determined to improve the statistical theory model for wave breaking. We also performed a sensitivity test to the model constants. A comparison between the model and in situ observations indicated that the level of agreement was better than has been achieved in previous studies.     

Assessment of chemical dispersant effectiveness in a wave tank under regular non-breaking and breaking wave conditions

Current chemical dispersant effectiveness tests for product selection are commonly performed with bench-scale testing apparatus. However, for the assessment of oil dispersant effectiveness under real sea state conditions, test protocols are required to have hydrodynamic conditions closer to the natural environment, including transport and dilution effects. To achieve this goal, Fisheries and Oceans Canada and the US Environmental Protection Agency (EPA) designed and constructed a wave tank system to study chemical dispersant effectiveness under controlled mixing energy conditions (regular non-breaking, spilling breaking, and plunging breaking waves). Quantification of oil dispersant effectiveness was based on observed changes in dispersed oil concentrations and oil-droplet size distribution. The study results quantitatively demonstrated that total dispersed oil concentration and breakup kinetics of oil droplets in the water column were strongly dependent on the presence of chemical dispersants and the influence of breaking waves. These data on the effectiveness of dispersants as a function of sea state will have significant implications in the drafting of future operational guidelines for dispersant use at sea.