Formulation of Friction Laws for Long Waves on a Smooth Dry Bed

Hydraulic experiments were conducted using a mobile-bottom inclined channel which yielded stationary frontal waves on a smooth dry bed. A Laser-Doppler velocimeter was used to measure mean velocities and Reynolds stresses, whose vertical distributions were well approximated by similarity laws. A bottom boundary layer developed on the slope from behind the tip of the long waves, where its turbulence structure was found to be similar to non-free surface flow over a flat plate. Numerical simulation using a presented friction law successfully reproduced both the surface profile and the runup height of a surge front.