Introduction
Pollutants, once discharged and beyond the initial active entrainment phase, will be passively advected and dispersed in
the water body. The dispersal mechanisms are mainly through turbulent diffusion and longitudinal dispersion with tidal
and wind-induced shear currents. This study addresses the longitudinal dispersive effect due to mass transport induced
by progressive surface waves.
Ever since the classic work of Taylor (1953), there has been extensive research on the longitudinal dispersion generated
by turbulent and laminar shear flows and the resulting variation in velocity profile, in various chemical and hydraulic
engineering applications. Thus far, nearly all investigations on Taylor dispersion involve cross-sectional velocity
variations induced by turbulent or laminar shear stresses. It is therefore not surprising that this dispersion mode is often
referred to as “shear dispersion”, as evidenced in the classic text of Fischer et al. (1979). The term implicitly suggests
that the presence of shear is necessary for the mechanism to take place. In reality, other than the background diffusion,
the only requirement is a cross-sectional variation of the flow profile in steady currents. Such variation can also exist in
water motion that is primarily irrotational. A clear example is surface gravity waves that are commonly considered to be
irrotational in the leading order except near boundaries. For surface waves, it is well known that Lagrangian drift exists
with a varying profile along the water depth. The cross-sectional variations of the steady drift velocity should provide
the necessary agents for Taylor dispersion to take place. Therefore the presence of progressive surface waves should
increase the longitudinal mixing of a contaminant cloud.
The following section quantifies the dispersive effect for the cases of a Stoke drift profile, a drift profile with viscous
effect and also a profile under the cover of a contaminated inextensible surface cover. Discussion on the implication of
the results is provided in the last section.

Authors:
Adrian W K Law (cwklaw@ntu.edu.sg)

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