Transportational Cyclic Steps Created by Submarine Long-Runout Turbidity Currents

Abstract

In recent years, it has become a common understanding among researchers that one of the significant agents for forming a variety of submarine geomorphologies is turbidity currents that travel long distances, so-called long-runout turbidity currents. In this study, we present a mathematical model of the formation of cyclic steps due to long-runout turbidity currents based on the assumption that the highly concentrated layer near the bottom of the turbidity currents achieves an equilibrium state. The model uses the four governing equations: the momentum equation, the continuity equation, the diffusion/dispersion equation of suspended sediment, and the continuity equation of sediment on the bed (the Exner equation). We simplify the governing equations by ignoring the entrainment from ambient water since there is a distinct density interface above the highly concentrated lower layer of long-runout turbidity currents. We determine the dimensions of cyclic steps based on the solution. Agreement between the predictions and field observations turns out to be reasonable.