Friction effects on quasi-steady dam-break wave propagation on horizontal beds

The propagation of dam-break waves on different rough beds was observed to be quasi-steady in the range $11.3 < x/h_{dam} 18.8$ , where $x$ is measured from dam position. These speeds converge with steady ideal fluids model Stoker ( Water Waves 1957, Interscience) when tailwater depth $h_2$ becomes greater than ${\sim }0.5k_s$ $0.001< k_s/h_{dam}< 0.2$ $k_s$ roughness and $h_{dam}$ behind dam. Hence, this convergence encourages use Stoker's steady, fluid solution develop more general models, including friction effects due bed and/or viscosity. new experimental data support a MacLaurin series for celerity $c$ analogy terms $\sqrt [4]{{h_2}/{h_{dam}}}$ derived model, being depth. Compared retarding effect tailwater, 1 mm found equivalent $\sim$ 13 $\mathrm {\mu }$ m viscous length ${\nu }/{\sqrt {gh_{dam}}}$ ${\nu}$ kinematic viscosity g acceleration gravity) 1700 tailwater. While quantifies similar small depths acting separately, illustrate first time complex interplay between ‘wet beds’ many details yet investigated. In particular, it shown that amount acts as lubricant, so $c(h_2, h_{dam}, k_s)$ an increasing function $h_2 0.5k_s$ .