Infragravity Wave Energy Research Articles

風波の波浪諸元に応じた長周期波の標準スペクトル推定法に関する検討

It is well known that a correlation between infragravity wave heights and the properties of wind waves observed in offshore harbor. Hirasihi et al (1997) have proposed a function of infragravity wave spectrum related to a function of wind wave spectrum by a boundary frequency estimated with parameter: αl. The αl can be estimated with the square root of ratio of infragravity wave energy to total wave energy: RL. In this study, a related function between αl and RL for JONSWAP spectrum is proposed and it is confirmed that an averaged value of αl estimated with spectra observed in storm conditions at each observation station may overestimate the infragravity wave heights in calm conditions. Moreover, the related function between Ursell number and αl proposed Hirayama et al (2014) can estimate them with good accuracy.

Discussion of Ford, M.R.; Becker, J.M., and Merrifield, M.A. 2013. Reef Flat Wave Processes and Excavation Pits: Observations and Implications for Majuro Atoll, Marshall Islands.Journal of Coastal Research,29(3), 545–554.

Payo, A. and Muñoz-Perez, J.J., 2013. Discussion of Ford, M.R.; Becker, J.M., and Merrifield, M.A., 2013. Reef flat wave processes and excavation pits: Observations and implications for Majuro Atoll, Marshall Islands.Ford, Becker, and Merrifield observed reef flat wave conditions during two deployments over a 41 day period to investigate the impact of reef flat excavation pits on wave processes at Majuro Atoll. They noticed that the shoreline with the excavation pit received wave heights slightly less (∼8%) than those recorded at the nearby unmodified cross section. They suggested that this net decrease was the net product of a slight increase in sea and swell (SS) wave energy due to a bottom roughness reduction and a decrease in infragravity (IG) wave energy due to the disruption of the cross-shore quasi-standing modes caused by the excavation pit. We argue that, for this particular experiment, the coupling between the SS and IG energy waves may provide an alternative explanation of the observations, and we suggest that further investigations are needed. Although the coupling between SS and IG waves may be important for assessing the impact of excavation pits on IG-dominated shorelines, we show that these excavation pits in SS-dominated surf zones can lead to events such as the observed destruction of the Cadiz (SW Spain) seawall in 1792.

Reef Flat Wave Processes and Excavation Pits: Observations and Implications for Majuro Atoll, Marshall Islands

Ford, M.R.; Becker, J.M., and Merrifield, M.A., 2013. Reef Flat wave processes and excavation pits: observations and implications for Majuro Atoll, Marshall Islands. An experimental deployment of pressure sensors was undertaken to assess the impact of reef flat excavation pits on wave processes at Majuro Atoll, Marshall Islands. Experiments were undertaken on two sections of an 80-m-wide fringing reef flat, one modified by the excavation of a 17-m wide, 4- to 5-m deep pit and the other an unmodified reef flat of comparable width, topography, and incident wave energy. A wave-driven inundation event during the experiment led to minor amounts of debris overwashing the road surface. The event was associated with southerly swell that was normally incident to the study site at high tide, resulting in enhanced shoreline energy in both the sea and swell and the infragravity frequency bands. The shoreline with the excavation pit received slightly smaller wave heights (∼8%) for all wave conditions, including the overwash event, compared to the unmodified shoreline. The statistically significant difference is largely a result of a decrease in infragravity wave energy over and shoreward of the pit that compensates for a weak increase in sea and swell energy. The influence on infragravity energy levels is likely to depend on the pit geometry and position, as well as the wave forcing; hence, not all pits are likely to lead to net wave energy dissipation. Implications of the findings are discussed with respect to the impacts of reef flat excavation on a highly developed, urbanised atoll.

Wave-induced extreme water levels in the Puerto Morelos fringing reef lagoon

Abstract. Wave-induced extreme water levels in the Puerto Morelos fringing reef lagoon are investigated by means of a phase-resolving non-hydrostatic wave model (SWASH). This model solves the nonlinear shallow water equations including non-hydrostatic pressure. The one-dimensional version of the model is implemented in order to investigate wave transformation in fringing reefs. Firstly, the numerical model is validated with (i) laboratory experiments conducted on a physical model (Demirbilek et al., 2007)and (ii) field observations (Coronado et al., 2007). Numerical results show good agreement with both experimental and field data. The comparison against the physical model results, for energetic wave conditions, indicates that high- and low-frequency wave transformation is well reproduced. Moreover, extreme water-level conditions measured during the passage of Hurricane Ivan in Puerto Morelos are also estimated by the numerical tool. Subsequently, the model is implemented at different along-reef locations in Puerto Morelos. Extreme water levels, wave-induced setup, and infragravity wave energy are estimated inside the reef lagoon for different storm wave conditions (Hs >2 m). The numerical results revealed a strong correlation between the offshore sea-swell wave energy and the setup. In contrast, infragravity waves are shown to be the result of a more complex pattern which heavily relies on the reef geometry. Indeed, the southern end of the reef lagoon provides evidence of resonance excitation, suggesting that the reef barrier may act as either a natural flood protection morphological feature, or as an inundation hazard enhancer depending on the incident wave conditions.

Observation of wave transformation on a sloping type B shore platform under wind-wave and swell conditions

An instrumented field study of the across-shore evolution of wave characteristics was conducted under wind-wave and swell-wave conditions on a sloping type B shore platform along the mesotidal, fetch-limited coast of Auckland, New Zealand, based on spectral analysis of hydrodynamic data recorded in pressure-sensor time series during a 24-h deployment on 24–25 November 2008. The results highlight the ability of the shore platform in dissipating wave energy reaching the cliff toe under wind-wave and swell-wave conditions, and the spectral redistribution of wave energy. As waves propagated onto the platform surface and towards the cliff toe, infragravity-wave energy became progressively more dominant, while gravity waves were dissipated. Wave height and period in the central sector of the platform and at the cliff toe were not markedly affected by differences in incident-wave conditions observed during the survey. The findings confirm the importance of platform morphology in modulating wave-energy delivery to the cliff toe. In contrast to previous studies, infragravity-wave height at the cliff toe did not appear to be correlated to incident-wave conditions.

Field Measurements of Wave Characteristics on a Near‐Horizontal Shore Platform, Mahia Peninsula, North Island, New Zealand

AbstractWaves are an important process responsible for the initiation and subsequent development of intertidal shore platforms. However, few field studies to date have described wave processes on shore platforms. A field experiment was conducted using an across‐shore array of wave gauges, including a directional sensor, on a near‐horizontal platform at Mahia Peninsula, North Island, New Zealand. Results show that the platform is very efficient in filtering wave energy at gravity wave frequencies (>0.05 Hz), with 40–80% reduction in wave height measured across the 140 m wide platform. By contrast, infragravity waves are present on the platform and increase in magnitude towards the cliff toe. Directional wave analysis indicates that wave reflection is mainly restricted to infragravity wave frequencies, demonstrating the differences in gravity and infragravity wave behaviour on the platform studied. Results indicate that, under fair weather conditions, the role of waves as an agent of cliff toe erosion is likely to be limited at present, although they are probably important for removing sediments accumulated at the cliff toe. The observed increase in infragravity wave energy towards the cliff toe implies that these long‐period waves may be important geomorphic agents on shore platforms.

Evidence for infragravity wave-tide resonance in deep oceans

Ocean tides are the oscillatory motions of seawater forced by the gravitational attraction of the Moon and Sun with periods of a half to a day and wavelengths of the semi-Pacific to Pacific scale. Ocean infragravity (IG) waves are sea-surface gravity waves with periods of several minutes and wavelengths of several dozen kilometres. Here we report the first evidence of the resonance between these two ubiquitous phenomena, mutually very different in period and wavelength, in deep oceans. The evidence comes from long-term, large-scale observations with arrays of broadband ocean-bottom seismometers located at depths of more than 4,000 m in the Pacific Ocean. This observational evidence is substantiated by a theoretical argument that IG waves and the tide can resonantly couple and that such coupling occurs over unexpectedly wide areas of the Pacific Ocean. Through this resonant coupling, some of ocean tidal energy is transferred in deep oceans to IG wave energy.

Infragravity Wave Motions and Runup over Shallow Fringing Reefs

This paper presents the results of a combined laboratory and numerical investigation into the role of infragravity motions in the wave runup process over fringing coral reefs. Laboratory experiments were performed with a reef profile typical of fringing reef systems along the southeast coast of Guam. Spectral analysis of the measured time histories of surface elevation over the reef face and flats show significant changes to the wave energy spectrum shoreward of the break point. Most of the wave energy in the incident wave frequency band is dissipated within a few wavelengths of the reef face with the wave motions over the reef flat and shoreline dominated by oscillations at infragravity periods [O(100s) prototype]. The infragravity wave energy is minimum at the reef crest and increases as waves propagate shoreward over the reef flat and also with increasing water level on the reef. The dominant infragravity mode is the first reef oscillation mode with a wavelength approximately equal to four times the wi...

Refraction and reflection of infragravity waves near submarine canyons

The propagation of infragravity waves (ocean surface waves with periods from 20 to 200 s) over complex inner shelf (water depths from about 3 to 50 m) bathymetry is investigated with field observations from the southern California coast. A wave‐ray‐path‐based model is used to describe radiation from adjacent beaches, refraction over slopes (smooth changes in bathymetry), and partial reflection from submarine canyons (sharp changes in bathymetry). In both the field observations and the model simulations the importance of the canyons depends on the directional spectrum of the infragravity wave field radiating from the shoreline and on the distance from the canyons. Averaged over the wide range of conditions observed, a refraction‐only model has reduced skill near the abrupt bathymetry, whereas a combined refraction and reflection model accurately describes the distribution of infragravity wave energy on the inner shelf, including the localized effects of steep‐walled submarine canyons.

Turbulence intensity in the wave boundary layer and bottom friction under (mainly) flat bed conditions

Variations with wave energy of near‐bed turbulence and the wave friction factor are investigated in the near‐shore zone for bed states spanning low‐steepness sand ripples and flat bed, and for wave energies extending well into the sheet flow regime. The measurements were made using a 1.7‐MHz pulse‐coherent Doppler profiler in ca. 3‐m mean water depth. Near‐bed turbulence intensities, phase‐averaged over the highest‐1/3 waves, peak at phases between 10° and 55° after the wave crest, this phase decreasing with increasing wave Reynolds number. Wave friction factors computed from near‐bed vertical turbulence intensity fall within the range predicted by existing semi‐empirical formulae, and exhibit broadly similar trends. At the higher end of the observed wave energy range (i.e., in the sheet flow regime), however, the measured friction factors increase with sea‐and‐swell energy faster than the predictions. This anomalous increase is correlated with infragravity wave energy and with mean cross‐shore current speed, but not with other forcing parameters including mean long‐shore current speed, wave skewness, wave asymmetry and wave breaking frequency. It is argued that the anomaly is partly due to additional near‐bed turbulence associated with infragravity waves, and therefore that these data are not inconsistent with Wilson's (1989) parameterization for bottom roughness in oscillatory sheet flow. Peak near‐bed turbulence intensities are independent of wave Reynolds number for Re ≲ 1.2 × 106, but proportional to Re for Re ≳ 1.2 × 106, this abrupt change possibly indicating a critical dependence on Re of turbulence production in the WBL over flat or nearly flat mobile beds.

Nonlinear generation and loss of infragravity wave energy

Nonlinear energy transfers with sea and swell (frequencies 0.05–0.40 Hz) were responsible for much of the generation and loss of infragravity wave energy (frequencies 0.005–0.050 Hz) observed under moderate‐ and low‐energy conditions on a natural beach. Cases with energetic shear waves were excluded, and mean currents, a likely shear wave energy source, were neglected. Within 150 m of the shore, estimated nonlinear energy transfers to (or from) the infragravity band roughly balanced the divergence (or convergence) of the infragravity energy flux, consistent with a conservative energy equation. Addition of significant dissipation (requiring a bottom drag coefficient exceeding about 10−2) degraded the energy balance.

A study of the relation between ocean storms and the Earth's hum

We previously showed that the Earth's “hum” is generated primarily in the northern oceans during the northern hemisphere winter and in the southern oceans during the summer. To gain further insight into the process that converts ocean storm energy into elastic energy through coupling of ocean waves with the seafloor, we here investigate a 4‐day‐long time window in the year 2000 that is free of large earthquakes but contains two large “hum” events. From a comparison of the time functions of two events and their relative arrival times at the two arrays in California and Japan, we infer that the generation of the “hum” events occurs close to shore and comprises three elements: (1) short‐period ocean waves interact nonlinearly to produce infragravity waves as the storm reaches the coast of North America; (2) infragravity waves interact with the seafloor locally to generate long‐period Rayleigh waves; and (3) some free infragravity wave energy radiates out into the open ocean, propagates across the north Pacific basin, and couples to the seafloor when it reaches distant coasts northeast of Japan. We also compare the yearly fluctuations in the amplitudes observed on the two arrays in the low‐frequency “hum” band (specifically at 240 s) and in the microseismic band (2–25 s). During the winter, strong correlation between the amplitude fluctuations in the “hum” and microseismic bands at BDSN is consistent with a common generation mechanism of both types of seismic noise from nonlinear interaction of ocean waves near the west coast of North America.

Numerical experiments of swash oscillations on steep and gentle beaches

A weakly non-linear Boussinesq model with a slot-type shoreline boundary is used to simulate swash oscillations on beaches. Numerical simulations of swash were compared with laboratory measurements and in general good agreement found (less than 15% root-mean-square error of surface elevation except in regular waves). A series of numerical experiments on shoreline movement were then performed for a range of beach slopes and incident wave conditions. The resulting swash characteristics are then discussed in terms of their physical nature and spectral properties. On steep slopes, both individual bores and infragravity waves are equally significant in driving the swash while infragravity waves alone drive them on mild slopes. Swash excursions on any given slope are found to be highest when individual bores from a partially saturated surf zone ride on top of low-frequency waves. This is confirmed by the relationship found between swash excursion and wave groupiness in the surf zone. Swash excursions increase with increasing incident wave energy, even in fully saturated surf zones. However, a poor correlation is found between swash excursion and the surf similarity parameter due to the involvement of infragravity wave energy in the swash.

A new estimator for directional properties of nearshore waves

The infragravity wave (periods between roughly 20 and 200 s) energy balance in shallow, nearshore waters is believed to be effected by generation by groups of sea and swell, dissipation, shoreline reflection, and refractive trapping. Observations obtained with alongshore oriented arrays of current meters or pressure gauges have been previously used to identify concentrations of energy at the frequency‐alongshore wavenumbers of refractively trapped edge waves, but seaward and shoreward propagating waves were not differentiated. Surfzone dissipation theoretically limits edge wave growth, and a different analysis (using the approximation of shore‐normal propagation) shows that the energy flux of shoreward propagating infragravity waves decreases owing to surfzone dissipation. Here an estimator is developed that yields the alongshore wavenumber‐frequency spectra of seaward and shoreward propagating waves, using the WKB approximation and observations from an alongshore‐oriented array of pressure and velocity sensors. Example spectra, estimated using data from the spatially sparse and relatively short SandyDuck arrays, suggests that strong dissipation of shoreward propagating infragravity waves occurs over a wide range of alongshore wavenumbers, effectively suppressing the excitation of edge wave modes.

Numerical modeling of infragravity wave response during DELILAH

The nearshore circulation model SHORECIRC is applied to simulate the infragravity wave conditions at two intervals during the 1990 DELILAH campaign at Duck, N. C. The model has been extended to solve the energy equation for random short waves (on the timescale of the wave groups) which acts as a wave driver for the long‐wave model. To simulate the wave conditions an algorithm has been derived which synthesizes a directional offshore wavefield from measured data including the bound, directional low‐frequency components. The model‐data comparison shows that the mean short wave transformation and mean longshore current are predicted well. The structure of the infragravity spectrum as measured in the nearshore array is correctly represented, albeit that the energy levels are underpredicted in most locations. The 2‐D frequency longshore‐wavenumber spectra show that the infragravity wave energy consists mostly of edge waves, and that the computations qualitatively resemble the measurements. It is shown that for 1 day, bar‐trapped edge waves are present. The model is also used to show that the influence of the longshore variability is small for this particular beach and that the directional spreading in the offshore wave field is critical in predicting the nearshore infragravity wave conditions correctly. Edge waves which propagate against the current are generated by the directionally broad short‐wave forcing and to a lesser extent by back‐scattering. The nonlinear terms are relatively unimportant for the prediction of the infragravity wave climate. The cross‐shore gradient of the onshore‐directed radiation stress is the most important of the forcing terms.

Physical processes in an Indian Ocean atoll

Detailed measurements of water levels, and tide and wave-induced currents were undertaken to examine physical processes and their relationship with morphology in the Cocos (Keeling) Islands, a medium sized atoll in the Indian Ocean. Results indicate that the atoll structure controls both lagoon circulation and the spatial pattern of energy distribution. Lagoon circulation is tide dominated (currents 16–31 cms-1) with flushing (2–5 days) of the lagoon occurring through the deep leeward passages. Wave- and tide-driven unidirectional flows through shallow passages (26–65 cms-1) are important mechanisms of ocean to lagoon water exchange and contribute up to 24% of the lagoon neap tide prism. Reef flats are dominated by wave energy (maximum velocity 140 cms-1, east) with measurements of the attenuation of wave energy between reef flats and shallow lagoon (80–90%) conforming to measurements from fringing and barrier reefs. Spectral analysis shows that the characteristics of wave energy vary on different sectors of the atoll, with gravity wave energy dominating the east, and infragravity wave energy dominating the southern reef flat and passages. Wave setup at the reef crest is considered to be responsible for an identified 0.1 m higher water level in the southern as opposed to eastern and northern atoll, which promotes higher reef flat growth. Transmission of gravity waves across reef flats requires threshold water depths of 0.65 (east) and 0.70 m (south). The higher southern reef is an effective filter of gravity wave energy for most tidal elevations. Differences in the type and magnitude of physical processes within the atoll are discussed with relation to geomorphic development on Cocos.

Morphodynamics of meso- and macrotidal beaches: examples from central Queensland, Australia

Detailed measurements of the morphology, waves, and longshore and cross-shore currents were conducted on two beaches on the low- to medium-energy, macrotidal coastline of central Queensland (Australia). Nine Mile Beach is characterised by a relatively steep upper profile, a low-gradient intertidal zone with one or two swash bars, transverse bar/rip morphology at low-tide level and a very low-gradient, dissipative subtidal zone. The beach is composed of fine to medium sand and experiences a modal wave height of 0.75 m and a mean spring-tide range of 3.6 m. Lambert's Beach possesses a steep, coarse-grained, reflective upper profile, and a low-gradient dissipative low tide terrace composed of fine to medium sand. Subdued rip channels intersect the low tide terrace and the beach is subject to a modal wave height of 0.6 m and a mean spring-tide range of 4.6 m. The two beaches are classified as Low Tide Bar/Rip and Low Tide Terrace beaches, respectively, following the model of Masselink and Short (1993). During the present investigation, the Low Tide Bar/Rip beach (Nine Mile Beach) exhibited a larger temporal variability than the Low Tide Terrace beach (Lambert's Beach), despite similar hydrodynamic conditions over the survey period. This difference is principally attributed to the differences in the beach morphologies and the types of morphological changes that occurred. On Nine Mile Beach, morphologic changes were primarily associated with secondary features (swash bars and low tide bar/rip system), whereas on Lambert's Beach the changes in morphology were largely the result of adjustments of the overall beach profile. A number of surf zone processes were investigated, including incident-wave attenuation, infragravity-wave energy, bed return flow and longshore currents. The influence of the tide on surf zone dynamics was found to be insignificant, except in the case of longshore currents. On Nine Mile Beach, the longshore current associated with the nearshore cell circulation was stronger during low tide. On Lambert's Beach, the shore-parallel current on the low tide terrace was largely driven by the tide. A beach profile zonation was defined for Nine Mile Beach and Lambert's Beach based on an examination of the varying influence of swash, surf zone and shoaling wave processes. The four-part tidal zonation consists of: (1) an upper intertidal zone across which swash and aeolian processes are the major influence; (2) a mid-intertidal zone dominated by swash and surf zone processes; (3) a lower intertidal zone controlled by surf zone and shoaling wave processes; and (4) a subtidal zone largely influenced by shoaling wave processes.

Infragravity-Frequency (0.005–0.05 Hz) Motions on the Shelf. Part I: Forced Waves

Abstract In Part I, the energy levels of ocean surface waves at infragravity frequencies (nominally 0.005–0.05 Hz) locally forced by swell in 13-m water depth were shown to be predicted accurately by second-order nonlinear wave theory. However, forced infragravity waves were consistently much less energetic than free infragravity waves. Here, in Part II, observations in depths between 8 and 204 m, on Atlantic and Pacific shelves, are used to investigate the sources and variability of free infragravity wave energy. Both free and forced infragravity energy levels generally increase with increasing swell energy and decreasing water depth, but their dependencies are markedly different. Although free waves usually dominate the infragravity frequency band, forced waves contribute a significant fraction of the total infragravity energy with high energy swell and/or in very shallow water. The observed h−1 variation of free infragravity energy with increasing water depth h is stronger than the h−1/2 dependence pre...

Infragravity waves induced by short-wave groups

A theoretical model for infragravity waves generated by incident short-wave groups is developed. Both normal and oblique short-wave incidence is considered. The depth-integrated conservation equations for mass and momentum averaged over a short-wave period are equivalent to the nonlinear shallow-water equations with a forcing term. In linearized form these equations combine to a second-order long-wave equation including forcing, and this is the equation we solve. The forcing term is expressed in terms of the short-wave radiation stress, and the modelling of these short waves in regard to their breaking and dynamic surf zone behaviour is essential. The model takes into account the time-varying position of the initial break point as well as a (partial) transmission of grouping into the surf zone. The former produces a dynamic set-up, while the latter is equivalent to the short-wave forcing that takes place outside the surf zone. These two effects have a mutual dependence which is modelled by a parameter K, and their relative strength is estimated. Before the waves break, the standard assumption of energy conservation leads to a variation of the radiation stress, which causes a bound, long wave, and the shoaling bottom results in a modification of the solution known for constant depth. The respective effects of this incident bound, long wave and of oscillations of the break-point position are shown to be of the same order of magnitude, and they oppose each other to some extent. The transfer of energy from the short waves to waves at infragravity frequencies is analysed using the depth-integrated conservation equation of energy. For the case of normally incident groups a semi-analytical steady-state solution for the infragravity wave motion is given for a plane beach and small primary-wave modulations. Examples of the resulting surface elevation as well as the corresponding particle velocity and mean infragravity-wave energy flux are presented. Also the sensitivity to the variation of input parameters is analysed. The model results are compared with laboratory experiments from the literature. The qualitative agreement is good, but quantitatively the model overestimates the infragravity wave activity. This can, in part, be attributed to the neglect of frictional effects.

Bound infragravity waves

Model predictions of bound (i.e., nonlinearly forced by and coupled to wave groups) infragravity wave energy are compared with about 2 years of observations in 8‐ to 13‐m depths at Imperial Beach, California, and Barbers Point, Hawaii. Frequency‐directional spectra of free waves at sea and swell frequencies, estimated with a small array of four pressure sensors, are used to predict the bound wave spectra below 0.04 Hz. The predicted total bound wave energy is always less than the observed infragravity energy, and the underprediction increases with increasing water depth and especially with decreasing swell energy. At most half, and usually much less, of the observed infragravity energy is bound. Bound wave spectra are also predicted with data from a single wave gage in 183‐m depth at Point Conception, California, and the assumption of unidirectional sea and swell. Even with energetic swell, less than 10% of the total observed infragravity energy in 183‐m depth is bound. Free waves, either leaky or edge waves, are more energetic than bound waves at both the shallow and deep sites. The low level of infragravity energy observed in 183‐m depth compared with 8‐ to 13‐m depths, with similarly moderate sea and swell energy, suggests that leaky (and very high‐mode edge) waves contribute less than 10% of the infragravity energy in 8–13 m. Most of the free infragravity energy in shallow water is refractively trapped and does not reach deep water.