Bed Shear Stress in Experimental Flash Flood Bores over Dry Beds and over Flowing Water: A Comparison of Methods

Abstract

Hydraulic parameters, including bed shear stress, are challenging to calculate for flash floods. Applying theoretical equations to strongly unsteady flows requires comprehensive and accurate flow data that are difficult to collect for natural events. To empirically evaluate the extent to which simpler calculations can reasonably predict shear stresses in rapidly changing hydrographs, and to determine how bed shear stresses differ for hydraulic bores propagating over dry beds compared to shallow water, we conducted laboratory flume experiments on idealized short-duration flash floods with bores. We compared the Saint-Venant shallow water equation, which theoretically captures the depth-averaged momentum balance of gradually varying unsteady flow to eight simpler methods, with assumptions that are not met in these flows. The Saint-Venant method predicts higher shear stresses immediately after bore arrival, but all of the simpler methods are nonlinearly correlated with the Saint-Venant method even when flow is rapidly changing. While none of the methods we evaluated should strictly apply to rapid changes in depth and velocity of bores, the correlations we found between methods just after bore arrival suggest that, for applications where shear stresses must be calculated but data are insufficient to apply the full Saint-Venant equations, simpler methods may provide meaningful shear stress constraints. Compared to flood bores propagating over a dry bed, bores propagating over shallow flowing water had steeper water surfaces but resulted in significantly lower bed shear stresses immediately after bore arrival. The common characteristic of tsunamis and waves moving onshore, and of dam breaks and flash floods occurring in rivers, is the presence of a sudden large increase in water depth and velocity termed flood bores. These result in an abrupt and large increase in shear stress (the force of the water on the bed), causing fatalities and extensive damage to infrastructures. We generated flood bores in a flume, with instrumentation that automatically monitored water depth, velocity, turbulence and water surface slope of bores arriving on a dry flume bed, with additional experiments of bores arriving on an existing shallow flow. We then calculated and compared the temporal change in shear stress by different methods, and found that, with the exception of the immediate arrival of a bore, shear stress calculated using simple assumptions is similar to the most demanding method. Another conclusion is that the shear stress is very large upon arrival of a bore on a dry bed—larger even than over a body of water. Hence, flood bores unexpectedly arriving on a dry bed are particularly dangerous to people, and their potential damage quantified by shear stress can be calculated using simplified formulas.