Abstract
More than three decades ago, it was noted that the ocean infragravity bound wave increasingly lags behind the forcing short-wave groups when propagating towards the shore. To date, the most recent theoretical prediction of this so-called phase lag remained a first-order approximation in terms of depth variations. Here, a new semi-analytical solution is proposed which does not rely on this approximation. Strong agreement is obtained when the new solution is compared with high-resolution laboratory data involving both bichromatic and random wave conditions. This newly proposed theoretical phase lag is then extensively compared with the former one, highlighting an increasing discrepancy between the two solutions as the relative bottom slope increases. The four influencing parameters, namely the bottom slope, the water depth, the incident short-wave peak period and the incident group period, are shown to impact, each in a specific way, the bound wave phase lag. While the latter is seen to increase with lower water depths and/or with higher short-wave peak periods, both the bottom slope and the group period can affect the phase lag in a different manner. Indeed, steeper bed slopes induce lower phase lags in shallow water but higher ones in deep water, while higher group periods induce higher phase lags for gentle slopes but lower ones for steep slopes.
Highlights
Infragravity (IG) waves are ocean surface waves with frequencies typically ranging from 0.004 to0.04 Hz
The present work provides a new investigation of the bound wave phase lag based on the pioneer and reference work of Schäffer [12] for modeling group-forced long waves reaching the shore
Despite an occasional slight overestimation of the phase lag in the shoaling zone, these comparisons extend the applicability of the J03 near-resonant solution to the Gently sLOping Beach EXperiments (GLOBEX) dataset
Summary
Infragravity (IG) waves are ocean surface waves with frequencies typically ranging from 0.004 to. 0.04 Hz. Munk [1] and Tucker [2] initially named them “surf beats” when they reported low-frequency oscillations of the sea surface associated with the presence of short-wave groups. Since the observation that these long waves can be quite energetic when reaching the shoreline (e.g., [3,4]), their study became increasingly popular among the coastal community. The substantial role of IG waves in nearshore hydrodynamics, sediment transport, or even dune and barrier breaching is well confirmed by field and laboratory experiments, as well as numerical modeling studies (see Bertin et al [8] for a recent review). The first theoretical demonstration of the existence of IG waves was the one of Biésel [9], which shows that a modulation of the short-wave amplitude within a wave group causes the mean water level to be lower (respectively, higher) where the short waves are higher (respectively, lower)
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