Reassessment of hydrodynamic equations: Minimum flow velocity to initiate boulder transport by high energy events (storms, tsunamis)

Coastal boulders are good evidence of high-energy events, but the distinction between storm and tsunami boulders remains difficult to identify and mathematical models are still in their preliminary stages. In a pioneering contribution, Nott (1997, 2003) developed hydrodynamic equations to assess the minimum wave height required to initiate transport of a coastal boulder by tsunamis or storm surges. These equations are widely cited and used, but they can be improved. In this study, Nott's equations have been revised: (1) the equation for the submerged boulder scenario has been revised by rearranging the lift area of the lift force, (2) the subaerial boulder scenario has been reconsidered by rearranging lift area and omitting inappropriate use of inertia force, and (3) the joint bounded scenario was revised by balancing force components in the lifting direction, and the effect of slope at the pre-transport location is tested. Calculations are performed for four case studies: boulders in Western and Eastern Australia (data after Nott, 1997, 2003), boulders in southeastern Italy (data after Scicchitano et al., 2007), storm boulders in Iceland (data after Etienne and Paris, 2010), and 2004 tsunami boulders in Sumatra (data after Paris et al., 2009). The minimum flow velocity required to initiate the transport of submerged boulders in the revised equation is less than that in Nott's equation (e.g., reductions up to 56% for submerged boulders and 65% for joint bounded blocks). The minimum flow velocity required to initiate the transport of subaerial boulders from the revised equation also differed in comparison with Nott's equation (e.g., 4-22% for boulders detached from a seawall by the 2004 tsunami in Sumatra), while Nott's equation was not applicable to some boulders (e.g., beach rock boulders transported from the nearshore by the 2004 tsunami). If we consider a joint bounded scenario for storm boulders in Iceland, the minimum flow velocity differs -43 to +41% from the results from Nott's equation. A boulder transport histogram is then introduced to represent the range of flow velocity that satisfies the requirements for initial transport of a boulder in different modes: sliding, rolling, and saltation. The boulder transport histogram can be used to predict the possible initial transport mode of a boulder from the flow velocity. These theoretical results are compared to field data, thus suggesting the initial transport mode of boulders and their pre-transport locations. The boulder transport histogram would be a valuable tool to reconstruct the magnitude of prehistoric high energy events such as tsunamis or storm surges in terms of flow velocity.