Infragravity wave generation on shore platforms: Bound long wave versus breakpoint forcing
Introduction
Shore platforms exist within a continuum of forms and are typically observed as (quasi-) horizontal or low gradient (tanβ < 0.05) rocky surfaces that occur within or close to the intertidal zone of rocky coasts and are commonly backed by cliffs (Trenhaile, 1987; Sunamura, 1992). The surface of shore platforms ranges from very smooth (like a sandy beach) to very rough and depends on geological factors such as the lithology and stratigraphic characteristics of the bed. Shore platforms are of particular interest to coastal scientists as they directly control the transformation of waves propagating across its surface (e.g., Farrell et al., 2009; Ogawa et al., 2011; Poate et al., 2018), and thus the amount of wave energy reaching the base of coastal cliffs. In turn, this is important in driving coastal cliff recession rates, but rock platforms also provide key evidence for the age, inheritance and mode of development of rocky coasts. Although existing across a spectrum of forms, two end-member types of shore platform have been commonly described in previous studies (e.g., Sunamura, 1992): Type A platforms are gently sloping ( ≈ 0.01–0.05) and usually extend into the sub-tidal zone and Type B platforms are sub-horizontal with a low tide cliff or reef-type feature, the upper part of which can sometimes be seen at low tide (Kennedy, 2016). Shore platform type appears predominantly controlled by tidal range (Trenhaile, 1987) with sloping platforms typical of large tidal environments (mean spring tidal range > 2 m) and sub-horizontal platforms more common in regions with a small tidal range (mean spring tidal range < 2 m). However, the balance of rock resistance versus wave force is also highly significant (Sunamura, 1992) and sea level history and morphological inheritance also provide important controls on shore platform geometry (e.g., Stephenson et al., 2017).
Infragravity waves are low frequency (0.005–0.04 Hz; 20–200 s) waves that can dominate the spectrum of water motions and sediment transport processes within the inner surf zone (Bertin et al., 2018). There are two widely accepted mechanisms for the generation of infragravity waves, both related to the variation in sea-swell energy induced by wave groups. The first theory for infragravity wave generation was proposed by Biesel (1952), and later by Longuet-Higgins and Stewart (1962) and Hasselmann (1962), who demonstrated theoretically that the modulation of short wave height by wave groups induces a variation in water level causing it to become depressed under groups of large waves, and enhanced where the sea-swell waves are smaller. This variation in water level creates a second-order wave that is ‘bound’ to the wave groups. The bound infragravity wave propagates at the group velocity and has the same wavelength and period as the wave groups, but is 180° out of phase (i.e., the trough of the bound infragravity wave is coincident with the largest waves in the wave group). It is commonly assumed that the bound long wave is released by short-wave breaking and continues to propagate to the shore as a free wave (e.g., Masselink, 1995; Inch et al., 2017). The second generation mechanism, proposed by Symonds et al. (1982), is the time-varying breakpoint in which freely propagating infragravity waves are generated as dynamic set-up/down oscillations as a result of the spatially fluctuating breakpoint of different sized wave groups. According to this mechanism two infragravity waves are generated, both originating at the sea-swell wave breakpoint and with the same frequency as the wave groups: a set-up wave propagating to the shore (in phase with wave groups) and a set-down wave travelling out to sea (in anti-phase with wave groups).
Laboratory studies have demonstrated that the relative importance of the two generation mechanisms is largely controlled by the beach slope, with bound infragravity waves dominating on mild sloping beaches, and steeper beaches being more conducive to breakpoint generated infragravity waves (e.g., Battjes et al., 2004; Van Dongeren et al., 2007). In addition to bed slope, sea-swell wave steepness has also been shown to have an influence on the generation of infragravity waves (Baldock and Huntley, 2002; Baldock, 2012).
Energetic infragravity wave motions have been suggested as a mechanism to perform geomorphic work, for example by directly impacting the cliff face, and for removing cliff-toe debris (Dickson et al., 2013). Additionally, infragravity waves may increase the level of sea-swell energy at the base of cliffs backing shore platforms by reducing short-wave dissipation through the increase in the local water depth under the infragravity wave crests (i.e., relatively large sea-swell waves ‘ride’ the infragravity wave crests). However, to date, detailed infragravity wave studies have focused primarily on sandy beaches.
Some of the data presented here have previously been used to quantify incident wave dissipation and platform roughness effects (Poate et al., 2016, 2018) and to model incident and infragravity wave signals (McCall et al., 2017), however, prior to these, few published studies have focused on infragravity wave transformation over rocky shore platforms. Beetham and Kench (2011) undertook two field experiments on sub-horizontal shore platforms in New Zealand, however, the study was relatively modest in its analysis and experimental set-up as data were only collected by five pressure sensors deployed for up to 36 h, and wave conditions were low-moderate with maximum offshore wave heights not exceeding 1.5 m. The results of this study were mostly consistent with those from sandy beaches, with infragravity wave height linearly dependent on the offshore sea-swell wave height and increasing shoreward with a maximum infragravity wave height of 0.20 m close to shore. Infragravity wave shoaling, quantified as the change in wave height from the platform edge to the cliff toe, was strongest on the wider of the two platforms. A shoreward increase in infragravity wave height and the increasing significance of infragravity energy relative to sea-swell energy on the inner platform, analogous to dissipative sandy beaches, has also been observed on other sub-horizontal shore platforms in New Zealand and in Australia by Marshall and Stephenson (2011) and Ogawa et al. (2011, 2015).
Coral reefs have a morphology that is analogous to sub-horizontal shore platforms, with a relatively horizontal reef flat and a low tide reef step, and have been the subject of several infragravity wave studies (e.g., Lugo-Fernandez et al., 1998; Brander et al., 2004; Pomeroy et al., 2012; Pequignet et al., 2014; Cheriton et al., 2016; Masselink et al., 2019). Coral reefs exist primarily in microtidal regions and have a large bed roughness, and thus friction coefficient, compared to sandy beaches. On a fringing reef in Western Australia, Pomeroy et al. (2012) found that the water motion shoreward of the reef crest was dominated by infragravity waves and that the dominant generation mechanism of the infragravity waves was the time-varying breakpoint at the steep reef crest. This was supported by numerical simulations and is consistent with the theory that breakpoint-generated infragravity waves are more prevalent in steep sloping regimes. The efficiency of the time-varying breakpoint for infragravity wave generation was also observed on coral reefs by Pequignet et al. (2009, 2014) and Becker et al. (2016), and in numerical modelling by Van Dongeren et al. (2013) and Masselink et al. (2019).
Whilst a number of studies have investigated infragravity waves on sub-horizontal shore platforms and similar coral reefs, there are few studies from sloping shore platforms. In a study of wave transformation at five sloping shore platforms around the UK, Poate et al. (2018) observed the total infragravity energy to either remain constant or decrease in the shoreward direction through bed roughness. This characteristic of infragravity waves on rocky platforms, generated by bound wave theory, was supported by Jager (2016), based on the analysis of the field data collected on one of these sloping platforms and supported by XBeach numerical modelling. Recently, an approximate 10 % increase in total infragravity energy was observed across a sloping platform in a macro-tidal setting by Stephenson et al. (2018); however, low-energy wave conditions, measurements at only three cross-shore locations and a largely qualitative analysis limit the ability of their study to elucidate more fully the geomorphic significance of infragravity waves on such platforms.
This paper investigates and compares the generation and transformation of infragravity waves on contrasting sub-horizontal and sloping shore platforms. Field data from a sub-horizontal platform at Leigh, New Zealand, and a sloping platform at Lilstock, UK, are analysed and complimented by numerical modelling using the XBeach model (phase-resolving). The specific objectives of this study are to: (1) assess the relative importance of the bound wave and the time-varying breakpoint theories of infragravity wave generation on the two platforms; (2) investigate and quantify the transformation of infragravity energy across the platforms; and (3) discuss the geomorphic implications of the findings.
Section snippets
Site description
Data presented in this paper originate from two field sites: Lilstock (LST) in Somerset, UK, and Tatapouri (TAT) on the east coast of the North Island in New Zealand (Fig. 1). Both sites are part of a larger project looking at wave transformation across rocky platforms, with data from LST presented in Poate et al. (2016, 2018) and McCall et al. (2017). LST experiences macrotidal conditions, with a mean spring range of 10.7 m, and is characterised by a wide (300 m), rather smooth and uniformly
Event summary
Wave conditions at the seaward-most sensors during the LST and TAT field experiments are presented in Fig. 3. At LST, the largest values of were during the middle and latter half of the study period, during which exceeded 1 m at high tide at the seaward-most sensor, with a maximum value of 1.91 m during tide 6. Peak wave periods ranged between 4 and 13 s, with a mean of 6.7 s. At TAT, measured at the ADCP ranged between 0.59 and 1.57 m, peaking during tide 1 before decreasing for the
Bound long wave versus breakpoint forcing
The numerical modelling results agree very well with the field data and indicate that the infragravity waves on the sloping platform (LST) have characteristics akin to those observed on dissipative beaches (e.g., Ruessink, 1998; Janssen et al., 2003; Inch et al., 2017), whilst infragravity wave observations on the sub-horizontal platform (TAT) agree well with those from steep beaches and coral reefs (e.g., Baldock, 2006; Lara et al., 2011; Pomeroy et al., 2012; Masselink et al., 2019).
Conclusion
This paper set out to investigate and compare the generation and transformation of infragravity waves on contrasting sloping and sub-horizontal shore platforms. Using field data from a sloping platform at Lilstock, UK, and a sub-horizontal platform at Leigh, New Zealand, complimented by numerical modelling (XBeach model), we have assessed the relative importance of the bound wave and the time-varying breakpoint theories of infragravity wave generation. Field measurements of wave transformation
Acknowledgements
This research was funded by EPSRC grantEP/L02523X/1, Waves Across Shore Platforms, awarded to GM and MJA. We would like to thank our field and technical team: Peter Ganderton, Tim Scott, Olivier Burvingt, Pedro Almeida and Kate Adams. The data on which this paper is based are available from TP or via the online repository found at http://hdl.handle.net/10026.1/9105.
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