Numerical modeling of the beach process of marine plastics: 2. A diagnostic approach with onshore-offshore advection-diffusion equations for buoyant plastics.

A model is proposed for the beach process of buoyant marine plastics, specifically its beaching and backwashing, by introducing beaching and backwashing diffusion coefficients and the onshore-offshore advection-diffusion equations of plastics for the upper layers in the beach and adjacent coastal sea. The backwashing diffusion coefficient was estimated from the average residence time of the beached plastics and the beach width, and then the beaching diffusion coefficient was estimated from the flux-balance assumption between the beaching and backwashing fluxes. Finite difference calculations in the staggered-grid system demonstrated that the amount of beached plastics responds as predicted by the linear system analysis when the beach had an exponential decay type of unit impulse response regardless of the ratio between the residence time and the period of beaching flux fluctuation from the nearshore. The condition in which the flux balance assumption holds was also discussed.