“…Liu et al. (2023) showed that fully nonlinear analysis of the infragravity wave energy budget is required for reef topography where the depth sharply reduces when offshore waves propagate over the foreslope into the reef flat. Figure 1.Definition sketch of variables for wave groups propagating over variable bottom.…”
Section: Governing Equationsmentioning
confidence: 99%
“…As wave groups propagate over variable depth, however, the equilibrium solution is no longer valid. For instance, with diminishing depth on a sloping beach towards the shore, the incident bound infragravity waves increasingly lag behind wave groups and gain more energy through nonlinear interaction with wave groups outside the surf zone, as observed in laboratory experiments (Van Leeuwen 1992;Guérin, de Bakker & Bertin 2019), numerical modelling (List 1992;Melito et al 2022;Liu et al 2023) and field experiments (Elgar & Guza 1985;Masselink 1995;Contardo & Symonds 2013;Inch et al 2017). This process of energy transfer from primary waves to infragravity waves is subject to offshore wave conditions and tidal modulation of local depth (Thomson et al 2006;Bertin et al 2020) even in a microtidal environment (Melito et al 2022).…”
Section: Introductionmentioning
confidence: 98%
“…2022; Liu et al. 2023) and field experiments (Elgar & Guza 1985; Masselink 1995; Contardo & Symonds 2013; Inch et al. 2017).…”
Section: Introductionmentioning
confidence: 99%
“…Green's function has been applied in a wide range of problems related to water waves, including harbour resonance (Miles 1974), internal waves (Voisin 1991), waves over continental shelf (Miles 1972), wave-structure interactions (Telste & Noblesse 1986;Wang, Ning & Zou 2020) and numerous studies based on the boundary element method (e.g. Longuet-Higgins & Cokelet 1976;Liu et al 2011;Ning et al 2015;Zheng et al 2020). Using the present generalised solution proposed, existing solutions (Longuet-Higgins & Stewart 1962;Van Leeuwen 1992;Schäffer 1993;Janssen et al 2003;Zou 2011;Contardo et al 2021;Liao et al 2021) for non-breaking waves are unified.…”
Short-wave group forcing is a major driving mechanism of infragravity waves. The subharmonic response to wave group forcing approaches resonance in shallow water where the group velocity is equal to the shallow-water wave-propagating speed. Currently, there is a lack of understanding of the connection between the free and bound components of group-induced infragravity waves and the consistency among existing solutions for off- and near-resonance conditions in intermediate and shallow water. Here, a unified solution of group-induced subharmonics is derived based on Green's function for the first time. The new solution is valid for any resonance intensity and is able to describe group-induced subharmonic behaviour at all water depths consistently from a new angle. The proposed solution reduces to existing solutions for intermediate depth (Longuet-Higgins & Stewart, J. Fluid Mech., vol. 13, 1962, pp. 481–504; Zou, Phys. Oceanogr., vol. 41, 2011, pp. 1842–1859), shallow water and/or over a plane sloping beach (Van Leeuwen, PhD thesis, TU Delft, 1992; Schäffer, J. Fluid Mech., vol. 247, 1993, pp. 551–588; Janssen et al., J. Geophys. Res., vol. 108, 2003, p. 3252; Contardo et al., J. Phys. Oceanogr., vol. 51, 2021, pp. 1465–1487; Liao et al., J. Phys. Oceanogr., vol. 51, 2021, pp. 2749–2765). Unlike previous solutions, the Green's function-based solution describes all subharmonics as free subharmonics continuously radiated away from each point source in the group-induced forcing field determined by wave radiation stress gradients. The superposition of all these free subharmonics yields so-called bound subharmonics by previous studies due to group-modulated emission of each free subharmonic through the source field bound to the wave group. Therefore, this solution provides theoretical evidence that the group-induced subharmonic at any observation point is dependent on the surrounding radiation stress field and topography. Under full-resonance conditions in shallow water, downwave-propagating subharmonics excited at all source locations interfere with each other constructively; therefore, their superposed amplitude is proportional to the travel distance of wave groups. Combined with the conventional moving-breakpoint forcing model, the predicted amplitude of the subharmonic in the surf zone by the present solution is in good agreement with laboratory observations.
“…Liu et al. (2023) showed that fully nonlinear analysis of the infragravity wave energy budget is required for reef topography where the depth sharply reduces when offshore waves propagate over the foreslope into the reef flat. Figure 1.Definition sketch of variables for wave groups propagating over variable bottom.…”
Section: Governing Equationsmentioning
confidence: 99%
“…As wave groups propagate over variable depth, however, the equilibrium solution is no longer valid. For instance, with diminishing depth on a sloping beach towards the shore, the incident bound infragravity waves increasingly lag behind wave groups and gain more energy through nonlinear interaction with wave groups outside the surf zone, as observed in laboratory experiments (Van Leeuwen 1992;Guérin, de Bakker & Bertin 2019), numerical modelling (List 1992;Melito et al 2022;Liu et al 2023) and field experiments (Elgar & Guza 1985;Masselink 1995;Contardo & Symonds 2013;Inch et al 2017). This process of energy transfer from primary waves to infragravity waves is subject to offshore wave conditions and tidal modulation of local depth (Thomson et al 2006;Bertin et al 2020) even in a microtidal environment (Melito et al 2022).…”
Section: Introductionmentioning
confidence: 98%
“…2022; Liu et al. 2023) and field experiments (Elgar & Guza 1985; Masselink 1995; Contardo & Symonds 2013; Inch et al. 2017).…”
Section: Introductionmentioning
confidence: 99%
“…Green's function has been applied in a wide range of problems related to water waves, including harbour resonance (Miles 1974), internal waves (Voisin 1991), waves over continental shelf (Miles 1972), wave-structure interactions (Telste & Noblesse 1986;Wang, Ning & Zou 2020) and numerous studies based on the boundary element method (e.g. Longuet-Higgins & Cokelet 1976;Liu et al 2011;Ning et al 2015;Zheng et al 2020). Using the present generalised solution proposed, existing solutions (Longuet-Higgins & Stewart 1962;Van Leeuwen 1992;Schäffer 1993;Janssen et al 2003;Zou 2011;Contardo et al 2021;Liao et al 2021) for non-breaking waves are unified.…”
Short-wave group forcing is a major driving mechanism of infragravity waves. The subharmonic response to wave group forcing approaches resonance in shallow water where the group velocity is equal to the shallow-water wave-propagating speed. Currently, there is a lack of understanding of the connection between the free and bound components of group-induced infragravity waves and the consistency among existing solutions for off- and near-resonance conditions in intermediate and shallow water. Here, a unified solution of group-induced subharmonics is derived based on Green's function for the first time. The new solution is valid for any resonance intensity and is able to describe group-induced subharmonic behaviour at all water depths consistently from a new angle. The proposed solution reduces to existing solutions for intermediate depth (Longuet-Higgins & Stewart, J. Fluid Mech., vol. 13, 1962, pp. 481–504; Zou, Phys. Oceanogr., vol. 41, 2011, pp. 1842–1859), shallow water and/or over a plane sloping beach (Van Leeuwen, PhD thesis, TU Delft, 1992; Schäffer, J. Fluid Mech., vol. 247, 1993, pp. 551–588; Janssen et al., J. Geophys. Res., vol. 108, 2003, p. 3252; Contardo et al., J. Phys. Oceanogr., vol. 51, 2021, pp. 1465–1487; Liao et al., J. Phys. Oceanogr., vol. 51, 2021, pp. 2749–2765). Unlike previous solutions, the Green's function-based solution describes all subharmonics as free subharmonics continuously radiated away from each point source in the group-induced forcing field determined by wave radiation stress gradients. The superposition of all these free subharmonics yields so-called bound subharmonics by previous studies due to group-modulated emission of each free subharmonic through the source field bound to the wave group. Therefore, this solution provides theoretical evidence that the group-induced subharmonic at any observation point is dependent on the surrounding radiation stress field and topography. Under full-resonance conditions in shallow water, downwave-propagating subharmonics excited at all source locations interfere with each other constructively; therefore, their superposed amplitude is proportional to the travel distance of wave groups. Combined with the conventional moving-breakpoint forcing model, the predicted amplitude of the subharmonic in the surf zone by the present solution is in good agreement with laboratory observations.
“…They are generated by two widely acknowledged mechanisms: bound wave and moving breakpoint [10]. Actually, they are the mutual transformation or joint action of multiple mechanisms in many cases [11] instead of a single mechanism. Moreover, Bertin et al [12] presented another generation mechanism: bore merging.…”
The sandbar-lagoon system presents a rich variety of values. At the same time, the degradation of ecosystems and coastal erosion caused by human activities and climate change are even more severe. A series of ecological conservation and restoration projects focused on vegetation rehabilitation have been implemented. However, there is insufficient scientific evidence to guide coastal engineering in the presence of vegetation. In this paper, ten tests were presented to experimentally investigate nonlinear wave propagation in a vegetated sandbar-lagoon system. The following conclusions can be obtained. In the absence of vegetation, the low-frequency wave energy proportion gradually increases with the rise of incident wave height. Double-peaked and even multi-peaked spectra are notable throughout the propagation in tests with larger incident wave heights. Wave height decay and wave energy dissipation due to vegetation effects increase as the incident wave height increases. The dependence of the wave energy dissipation induced by vegetation on the incident wave energy (the square of wave height) presents a linear relationship. Vegetation plays an important and complex role in both sea-swell wave and infragravity wave attenuation.
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