The Relationship between Sea-Swell Bound Wave Height and Wave Shape

Abstract

The nonlinear wave shape, expressed by skewness and asymmetry, can be calculated from surface elevation or pressure time series using bispectral analysis. Here, it is shown that the same analysis technique can be used to calculate the bound superharmonic wave height. Using measured near-bed pressures from three different field experiments, it is demonstrated that there is a clear relationship between this bound wave height and the nonlinear wave shape, independent of the measurement time and location. This implies that knowledge on the spatially varying bound wave height can be used to improve wave shape-induced sediment transport predictions. Given the frequency-directional sea-swell wave spectrum, the bound wave height can be predicted using second order wave theory. This paper shows that in relatively deep water, where conditions are not too nonlinear, this theory can accurately predict the bispectrally estimated bound superharmonic wave height. However, in relatively shallow water, the mismatch between observed and predicted bound wave height increases significantly due to wave breaking, strong currents, and increased wave nonlinearity. These processes are often included in phase-averaged wind-wave models that predict the evolution of the frequency-directional spectrum over variable bathymetry through source terms in a wave action balance, including the transfer of energy to bound super harmonics. The possibility to calculate and compare with the observed bound super harmonic wave height opens the door to improved model predictions of the bound wave height, nonlinear wave shape and associated sediment transport in large-scale morphodynamic models at low additional computational cost.

Dispersive characteristics of non-linear waves propagating and breaking over a mildly sloping laboratory beach

“…where H{•} is the Hilbert transform. S k and A s are measures of wave asymmetry along the horizontal and vertical axes respectively and also inform on the energy content at high harmonics (Elgar, 1987;Martins et al, 2020b;de Wit et al, 2020). For the same imposed wave height, A1 and A3 differed in the shoaling region, with a more intense shoaling process noted during A3 (Fig.…”

Experimental study on the effect of an oyster reef on the nonlinear characteristics of irregular waves

“…Even if the height, period and water depth of the waves are completely the same, because of the difference in topographic conditions and the rapid change of hydrodynamic conditions, the incident wave and the conversion to locked wave may be different, resulting in different nonlinear parameters (Ma et al, 2015). Since the locked wave and the free wave follow different dispersion relationship, triad interaction analysis is a relatively simple method for distinguishing the locked wave and the free wave energy (De Wit et al, 2020). Analyzing the complete three-dimensional spectrum requires high-resolution spatial information, which is difficult to obtain.…”