Dry deposition of particles to wave surfaces: I. Mathematical modeling

Previous estimates of dry deposition to water surfaces were generally based on deposition to flat, solid surfaces. This paper examines the effects of waves on dry deposition rates by numerically simulating particle trajectories over wave surfaces. Airflows over two-dimensional sine waves with height-to-length ratios 2a/λ=0.1, 0.07, and 0.03 were calculated with a commercial computational fluid dynamics model. Results from the airflow simulations (velocity, kinetic energy, energy dissipation rate, and shear stress) provided inputs for a stochastic particle trajectory model. Particles were released from a height of 300 non-dimensional wall units at different locations along the wave. For those between 1 and 20 μm, deposition was found to be greatest for particles released to the upslope portion of the wave, followed by the trough, crest and downslope. Overall deposition rates were enhanced due to the presence of waves. Increases ranged from 5% (dp=80 μm) to 100% (dp=1 μm) for waves with 2a/λ=0.07 and 0.1 and were approximately 50% greater (dp=1−80 μm) for 2a/λ=0.03. Deposition rates were enhanced due to increases in impaction and turbulent transport, both of which increase with increasing wave slope. However, an increased slope also produced regions of low or reversed flow in the trough and downslope, which decreased deposition rates. Due to these competing effects with respect to wave slope, deposition rates did not increase monotonically with wave slope.