The Influence of Free Long Wave Generation on the Shoaling of Forced Infragravity Waves

Abstract

Different conceptual models for forced infragravity (long) waves exist in the literature, which suggest different models for the behavior of shoaling forced waves and the possible radiation of free long waves in that process. These are discussed in terms of existing literature. A simple numerical model is built to evaluate the wave shape in space and time during shoaling of forced waves with concurrent radiation of free long waves to ensure mass continuity. The same qualitative results were found when performing simulations with the COULWAVE model using the radiation stress term in the momentum equation to force the generation and propagation of bound waves. Both model results indicate a strong frequency dependence in the shoaling rate and on the lag of the total long wave with respect to the forcing, consistent with observations in the literature and more complex evolution models. In this approach, a lag of the long wave is only observed in the time domain, not in the space domain. In addition the COULWAVE is used to investigate dissipation rates of incident free and forced long waves inside the surf zone. The results also show a strong frequency dependence, as previously suggested in the literature, which can contribute to the total rate of decay of the incident forced wave after short wave breaking.

Free and Forced Components of Shoaling Long Waves in the Absence of Short-Wave Breaking

“…However, in their example, the origin of the FLW is not specified and is added (at the toe of the slope) to the shoaling BLW (TLW), while in this present study we consider the addition of a FLW generated from depth variation to the (locked) BLW. Moura and Baldock (2017) also noted that adding FLWs to the BLW shoaling process could alter the phase relationship between long waves and wave groups.…”

“…In contrast, there are two established mechanisms for the case where wave groups break in shallow water, which have been used to describe the generation of free long waves: bound-wave release (Inch et al 2017;Masselink 1995) and breakpoint forcing (Symonds et al 1982;Contardo et al 2018;Contardo andSymonds 2013, 2016;Moura and Baldock 2017;Pomeroy et al 2012). While these additional mechanisms relating specifically to breaking are very important to long-wave generation in the nearshore, in this study we focus on an alternative generation mechanism of free long waves by nonbreaking wave groups interacting with depth variations outside of the breaking region.…”

Unified analytical solution for group-induced infragravity waves based on Green's function

“…The key indicator of the occurrence of energy transfer is the non-equilibrium phase coupling between infragravity waves and wave groups due to the presence of additional infragravity waves that lag the equilibrium bound subharmonic by π/2. In intermediate water, the additional wave manifests itself as a bound subharmonic induced by the perturbation of the bottom slope (Bowers 1992;Van Leeuwen 1992;Janssen et al 2003;Zou 2011); in shallow water, it is interpreted as a free subharmonic (Mei & Benmoussa 1984;Nielsen & Baldock 2010;Moura & Baldock 2019;Contardo et al 2021). Free infragravity waves can also be generated in the surf zone as dynamic wave-induced set-up through the moving-breakpoint forcing mechanism (Symonds, Huntley & Bowen 1982;Contardo, Symonds & Dufois 2018).…”

“…In intermediate water, the additional wave manifests itself as a bound subharmonic induced by the perturbation of the bottom slope (Bowers 1992; Van Leeuwen 1992; Janssen et al. 2003; Zou 2011); in shallow water, it is interpreted as a free subharmonic (Mei & Benmoussa 1984; Nielsen & Baldock 2010; Moura & Baldock 2019; Contardo et al. 2021).…”