Shoaling and shoreline dissipation of low-frequency waves

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 β, which distinguishes between a mild‐slope regime and a steep‐slope regime. This dependency on β alone is valid if the forcing short waves are not in shallow water; that is, the forcing is off‐resonant. The β parameter also controls the reflection coefficient at the shoreline because for small values of β, 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.