Taylor Dispersion of Contaminants by Dual-peak Spectral Random Waves

Recent extensive and important studies have provided detailed information and compelling evidence on how the presence of waves influences the vertical diffusivity/dispersivity in the coastal environment, which can affect various water quality considerations such as the distribution of suspended sediments in the water column as well as the potential of eutrophication. Comparatively, how the presence of waves influences the horizontal diffusivity/dispersivity has received only scant attention in the literature. Our previous works investigated the role played by the Taylor mechanism due to the wave-induced drift profile which leads to the longitudinal dispersion of contaminants in the horizontal direction, under regular sinusoidal waves and random waves with single-peak spectra. Natural waves in the coastal environment, however, often possess dual-peak spectra, comprising both higher frequency wind waves and lower frequency swells. In this study, the Taylor dispersion of contaminants under random waves with dual-peak spectra is examined through analytical derivation and numerical calculations. The effects of various dual-peak spectral parameters on the horizontal dispersion, including the proportion of lower frequency energy, peak frequency ratio and spectral shape parameter, are investigated. The results show that the relative energy distribution between the dual peaks has the most significant effect. Compared with single-peak spectra with equivalent energy, the Taylor dispersion with dual-peak spectra is stronger when the lower frequency is close to the peak frequency of the single-peak spectrum, and weaker with the higher frequency instead. Thus, it can be concluded that with a dual-peak wave spectrum, wind-dominated seas with higher frequency lead to stronger dispersion in the horizontal direction than swell-dominated seas with lower frequency.