Publication
Unified analytical solution for group-induced infragravity waves based on Green's function
Publisher:
Cambridge University Press (CUP)
Date:
24-07-2023
DOI:
10.1017/JFM.2023.475
Abstract: 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 litude is proportional to the travel distance of wave groups. Combined with the conventional moving-breakpoint forcing model, the predicted litude of the subharmonic in the surf zone by the present solution is in good agreement with laboratory observations.