Shoaling and shoreline dissipation of low‐frequency waves

Abstract

[1] The growth rate, shoreline reflection, and dissipation of low-frequency waves are investigated using data obtained from physical experiments in the Delft University of Technology research flume and by parameter variation using the numerical model Delft3D-SurfBeat. The growth rate of the shoaling incoming long wave varies with depth with an exponent between 0.25 and 2.5. The exponent depends on a dimensionless normalized bed slope parameter b, which distinguishes between a mild-slope regime and a steep-slope regime. This dependency on b alone is valid if the forcing short waves are not in shallow water; that is, the forcing is off-resonant. The b parameter also controls the reflection coefficient at the shoreline because for small values of b, long waves are shown to break. In this mild-slope regime the dissipation due to breaking of the long waves in the vicinity of the shoreline is much higher than the dissipation due to bottom friction, confirming the findings of Thomson et al. (2006) and Henderson et al. (2006). The energy transfer from low frequencies to higher frequencies is partly due to triad interactions between low-and high-frequency waves but with decreasing depth is increasingly dominated by long-wave self-self interactions, which cause the long-wave front to steepen up and eventually break. The role of the breaking process in the near-shore evolution of the long waves is experimentally confirmed by observations of monochromatic free long waves propagating on a plane sloping beach, which shows strikingly similar characteristics, including the steepening and breaking.

Fully Nonlinear Boussinesq-Type Modelling of Infragravity Wave Transformation Over a Low-Sloping Beach

“…Its amplitude then starts to decrease (j to k), while its shape evolves toward a sawtooth profile. These transformations, resembling the behavior of typical inner surf-zone waves, has been identified by van Dongeren et al (2007) as infragravity-wave breaking. The nonlinear transformations of the IG wave are characterized further in Figure 4, which shows the cross-shore evolution of the wave skewness (Sk) and the asymmetry (As) in the surf zone.…”

“…In this paper, we focus on the experiment A-1 analyzed in van Dongeren et al 2007, where a very low reflection coefficient (R~0.1) of the infragravity waves was observed at the shoreline. Bichromatic waves of primary frequency f 1 =0.6714 Hz and f 2 =0.4761 Hz, and amplitudes a 1 =0.06 m a 2 =0.012 m were generated on the horizontal part of the beach and were then propagating and breaking over a 1:35 sloping beach.…”

“…The infragravity part of the signal, defined as the component of frequency Δf=f 1 -f 2 and its higher harmonics (see van Dongeren et al, 2007) is more specifically studied in Figure 3. The main discrepancies between model and data are observed at the most offshore locations, but the agreement increases significantly in the surf zone.…”

“…More precisely, we investigate the ability of our numerical model to predict wave dynamics for a case involving a strong infragravity-wave dissipation. This validation study is based on van Noorloos (2003) bichromatic wave experiments, analyzed in Van Dongeren et al (2007). Our numerical model is first introduced.…”

Spectral Description of Energy Dissipation in Breaking Wave Groups

“…While there has been significant work on the characteristics of the generated infragravity wave environment (e.g. van Dongeren et al 2007), investigation of the dissipation of the wave groups themselves has been lacking. Svendsen and Veeramony (2001) showed that some aspect of the wave group structure does survive the breaking process and is indeed seen in the surf zone; however, while they investigated the occurrence of breaking, they did not look into quantifying the level of dissipation in these wave groups.…”