Simple Power Law for Transport Ratio with Bimodal Distribution of Coarse Sediment

Using a discrete particle model, we have simulated sheet flow transport of coarse bimodal sediment distributions in the bottom boundary layer over a range of oscillatory waves and steady currents. The ratio of large grain to small grain diameter was varied as 5:4, 3:2, and 2:1. For each bimodal distribution, the mass ratio $M_{L}/M_{S}$ ($M_{L}$ and $M_{S}$ are the masses of large and small grains respectively -- the total mass was fixed for all runs) was varied from 1/9 up to 9/1. We find that, independent of wave and current forcing for the range of conditions considered, the ratio of large to small grain time-average transport rate obeys the power law $Q_{L}/Q_{S}=C(M_{L}/M_{S})^{k}$, where $Q_{L}$ and $Q_{S}$ are the time-average transport rates of the large grains and small grains respectively and $C$ and $k$ are regression constants. A linear regression in log space (including 81 different simulations per diameter ratio) suggests that \textit{k$\approx $D}$_{L}/D_{S}$ with R$^{2}>$0.9. The robust nature of the results suggests that the new power law may have a broad range of applications for shear flows of bimodal granular mixtures.