Modeling the combined parameter for incipient motion from the force balance on a single proud grain.

We assess the validity and limitations of the "combined parameter" as a parametric representative of the torque balance for a single "proud" grain for the threshold of motion for non-cohesive sediments under monochromatic wave forcing conditions. Threshold was determined by balancing the sum of the particle drag force, pressure gradient force, and added mass force against the stabilizing force of gravity adjusted by the lift force. As expected, the magnitude of the particle drag force was relatively large in the balance equation at threshold for all simulated conditions. The pressure gradient force strongly influenced the timing (phase) of threshold for all simulated conditions. The inclusion of the added mass force was found to have a negligible effect for all simulated conditions. Results were sensitive to the magnitude of the lift force through the specification of the lift coefficient. We conclude that the combined parameter, made up of the Shields parameter and Sleath number, should be modified to include a representation of the lift force. Finally, the results suggest a new interpretation of the bed depth variable in the combined parameter that bridges the regimes of motion from the incipient (i.e. single grain) up to sheet flow and plug flow. [ABSTRACT FROM AUTHOR]