Abstract
AbstractThe inability of the linear wave dispersion relation to characterize the dispersive properties of non-linear shoaling and breaking waves in the nearshore has long been recognised. Yet, it remains widely used with linear wave theory to convert between sub-surface pressure, wave orbital velocities and the free surface elevation associated with non-linear nearshore waves. Here, we present a non-linear fully dispersive method for reconstructing the free surface elevation from sub-surface hydrodynamic measurements. This reconstruction requires knowledge of the dispersive properties of the wave field through the dominant wavenumbers magnitude κ, representative in an energy-averaged sense of a mixed sea-state composed of both free and forced components. The present approach is effective starting from intermediate water depths - where non-linear interactions between triads intensify - up to the surf zone, where most wave components are forced and travel approximately at the speed of non-dispersive shallow-water waves. In laboratory conditions, where measurements of κ are available, the non-linear fully dispersive method successfully reconstructs sea-surface energy levels at high frequencies in diverse non-linear and dispersive conditions. In the field, we investigate the potential of a reconstruction that uses a Boussinesq approximation of κ, since such measurements are generally lacking. Overall, the proposed approach offers great potential for collecting more accurate measurements under storm conditions, both in terms of sea-surface energy levels at high frequencies and wave-by-wave statistics (e.g. wave extrema). Through its control on the efficiency of non-linear energy transfers between triads, the spectral bandwidth is shown to greatly influence non-linear effects in the transfer functions between sub-surface hydrodynamics and the sea-surface elevation.
Highlights
In recent years, remote sensing approaches based on lidar technology (Brodie et al 2015; Martins et al 2017b, 2020b) or stereo-video imagery have seen tremendous developments and allow the collection of accurate and direct measurements of the sea surface elevation in nearshore areas
If the pressure field at the sea bottom p is known in both time and space, linear wave theory allows an estimation of the free surface elevation z as Denotes content that is immediately available upon publication as open access
The laboratory dataset was collected during GLOBEX, which was performed in a 110-m-long, 1-m-wide, and 1.2-mhigh wave flume located in the Scheldegoot in Delft, the Netherlands (Ruessink et al 2013)
Summary
Remote sensing approaches based on lidar technology (Brodie et al 2015; Martins et al 2017b, 2020b) or stereo-video imagery (de Vries et al 2011; Guimarães et al 2020) have seen tremendous developments and allow the collection of accurate and direct measurements of the sea surface elevation in nearshore areas. Near the breaking point or in the surf zone, most components of the sea surface spectrum associated with a typical incident swell propagate approximately at the speed of nondispersive shallow-water waves (Thornton and Guza 1982; Elgar and Guza 1985b; Herbers et al 2002; Martins et al 2021) For such shallow water depths, Bonneton et al (2018) proposed a nonlinear weakly dispersive reconstruction method, which works in the temporal domain and has the advantage of not requiring prior knowledge of k(v). The nonlinear fully dispersive reconstruction is first assessed (section 4) with a laboratory dataset collected at high spatial and temporal resolution [Gently Sloping Beach Experiment (GLOBEX); Ruessink et al 2013] This dataset represents an ideal situation, where unidirectional waves are considered and k spectra can be accurately determined from the highly resolved surface elevation measurements.
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