Transport and diffusion caused by coastal waves have different characteristics from those induced by flows. Through solving the vertical diffusion equation by an analytic method, this paper infers a theoretical formula of dispersion coefficient under the combined action of current and waves. It divides the general dispersion coefficient into six parts, including coefficients due to tidal current, Stokes drift, wave oscillation and interaction among them. It draws a conclusion that the contribution of dispersive effect induced by coastal waves is mainly produced by Stokes drift, while the contributions to time-averaged dispersion coefficient due to wave orbital motion and interaction between current and waves are very small. The results without tidal current are in agreement with the numerical and experimental results, which proves the correctness of the theoretical derivation. This paper introduces the variation characteristics of both the time-averaged and oscillating dispersion coefficients versus relative water depth, and demonstrates the physical implications of the oscillating mixing coefficient due to waves. We also apply the results to the costal vertical circulation and give its characteristics compared to Stokes drift.
