Abstract
AbstractIn the surf zone, non‐hydrostatic processes are either neglected or estimated using linear wave theory. The recent development of technologies capable of directly measuring the free surface elevation, such as 2‐D lidar scanners, allow for a thorough assessment of the validity of such hypotheses. In this study, we use subsurface pressure and lidar data to study the non‐linear and non‐hydrostatic character of surf zone waves. Non‐hydrostatic effects are found important everywhere in the surf zone (from the outer to the inner surf zones). Surface elevation variance, skewness, and asymmetry estimated from the hydrostatic reconstruction are found to significantly underestimate the values obtained from the lidar data. At the wave‐by‐wave scale, this is explained by the underestimation of the wave crest maximal elevations, even in the inner surf zone, where the wave profile around the broken wave face is smoothed. The classic transfer function based on linear wave theory brings only marginal improvements in this regard, compared to the hydrostatic reconstruction. A recently developed non‐linear weakly dispersive reconstruction is found to consistently outperform the hydrostatic or classic transfer function reconstructions over the entire surf zone, with relative errors on the surface elevation variance and skewness around 5% on average. In both the outer and inner surf zones, this method correctly reproduces the steep front of breaking and broken waves and their individual wave height to within 10%. The performance of this irrotational method supports the hypothesis that the flow under broken waves is dominated by irrotational motions.
Highlights
In the surf zone, waves undergo rapid changes in shape, passing from steep and skewed waves right before breaking to sawtooth-shaped asymmetric bores in what is referred to as the inner surf zone (e.g., Basco, 1985; Battjes, 1988)
We show that nonhydrostatic effects remain strong over the entire surf zone, i.e. fluid accelerations are important and the hypothesis of a hydrostatic pressure field leads to large deviations of the real surface elevation
We use sub-surface pressure and surface elevation lidar data collected at the macrotidal, dissipative site of Saltburn-by-the-Sea, UK, to study the non-hydrostatic and non-linear character of surf zone waves
Summary
Waves undergo rapid changes in shape, passing from steep and skewed waves right before breaking to sawtooth-shaped asymmetric bores in what is referred to as the inner surf zone (e.g., Basco, 1985; Battjes, 1988). The supposedly negligible non-hydrostatic effects in the inner surf zone encouraged researchers to use the non-linear shallow water equations (NSWE) to simulate wave propagation in the inner surf zone (Kobayashi et al, 1989; Raubenheimer et al., 1996; Bonneton, 2007) This modelling approach, where the wave front is treated as a shock, reproduces quite well the non-linear distortion associated with saw-tooth waves in the surf zone, their celerity and the energy dissipation related to breaking processes (Bonneton, 2007). The recent development of techniques capable of directly measuring the free surface based on acoustic (Bonneton et al, 2018; Mouragues et al, 2019) or lidar technology (Martins et al., 2017a) highlighted the limits of linear wave theory, which strongly underestimates the non-hydrostatic character of shoaling and breaking waves This has implications in the estimates of surface elevation second (variance) and third-order (skewness and asymmetry) parameters as well as elevation extrema and distributions. In situ methods for characterizing non-hydrostatic wave processes in the surf zone
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