Measurements of bed shear stresses near the tip of dam-break waves on a rough bed

Abstract

Shear plates have previously been used to measure bed shear stresses under swash and dam-break waves. The present study has been focused on the large bed shear stresses near the tip and even at distances less than one plate length from the tip. In order to resolve this rapid stress variation, the shear plate was calibrated with respect to its step response as well as statically. Step response calibration enables the effects of the time lag and the natural frequency of the shear plate system to be removed. Thus, the initial variation of the bed shear stress during and just after the rise of the water level is resolved and opens the opportunity to investigate the boundary layer development close to the tip where other measurements have not previously succeeded. The bed shear stress $\tau_{{{\text{bed}}}} \left( t \right)$ initially increases almost linearly with time to a maximum, which occurs about 0.2 s after the passage of the contact point, while it takes about 2.0 s for the water surface level h(t) to rise to a quasi-steady level under the present experimental conditions. Thus, with h(t) and $\tau_{{{\text{bed}}}} \left( t \right)$ varying with different timescales, the simple assumption of $\tau_{{{\text{bed}}}} = \tau_{{{\text{bed}}}} \left( {\frac{{{\text{roughness}}}}{{{\text{depth}}}}} \right)$ is not supported. For a given dam-break, the peak bed shear stress depends on the tailwater level. In our tests with initial dam depth 400 mm and bed roughness 84 mm, $\tau_{{{\text{bed}}}}$ peaks at 210 Pa ± 20 Pa on dry beds decreases to peak values of the order 40 Pa with 98 mm tailwater depths. Quasi-steady $\tau_{{{\text{bed}}}}$-values reached while the water surface is still quasi-steady, which are of the order 5–10 Pa. For dry beds, $\tau_{{{\text{bed}}}}$ shows a single peak followed by a smooth monotonical decay, while tailwater depths above 40 mm may lead to two almost equal, successive $\tau_{{{\text{bed}}}}$-peaks and an oscillating decay.

Graphic abstract